In a realistic environment, where the target may be missed and false-alarms may be detected, it is prudent to capture such phenomena in the tracking algorithm. Two methods are considered: the maximum likelihood probabilistic data association (ML-PDA) algorithm and the maximum likelihood probabilistic multi-hypothesis tracker (ML-PMHT). In this paper we compare the ML-PDA and ML-PMHT based on their Cramer-Rao lower bounds (CRLBs), the key difference being the form of the scalar information reduction factor (IRF). The IRF is presented for ML-PMHT in a new form that makes it more computationally tractable and also easier to directly compare with that of the ML-PDA.

With the rapid proliferation of Machine-Learning (ML) and Deep Learning (DL) based decision systems, properly characterizing their often unpredictable performance is a key challenge. In this work we introduce the notion of a Sequential Data-Driven Decision Function (S-D3F), as a data-driven analogue to the Sequential Probability Ratio Test (SPRT). Key performance metrics for sequential analysis are shown suitable for use in analyzing the S-D3F’s performance both in terms of error probabilities and average stopping times. The notion of rate function from large deviations theory is extended to this S-D3F test, and it is shown that with a sequential approach the S-D3F can outperform its Fixed Sample-Size (FSS) counterpart in the D3F as the average number of samples needed to make a decision diverges.

This paper presents a mechanism for evaluating the Root Mean Square Error (RMSE) of a Minimum Variance Unbiased Estimator (MVUE) of a target state in 3D space using acoustic measurements. The target state is represented by $(\theta, \phi, r)$ and it is estimated using Time Difference of Arrival measurements at the sensors and we assume that the sound-speed c is unknown. We then examine the interaction between azimuth angle $\theta$ on range RMSE, and the impacts of measurement noise variance on RMSE of $(\theta, \phi, r, c)$ estimates. These results and analytical formulations can be used as a baseline to evaluate proper 3D array geometry design, as well as inform the potential RMSE improvements when using a biased minimum mean square error (MMSE) estimator over an unbiased (MVUE) one for the same set of measurements.

Maritime situational awareness (MSA) refers to the effective understanding of activities related to maritime environment. Central to MSA, particularly concerning non-military vessels, is the automatic identification system (AIS), which provides real-time data on vessel movements. However, anomalies such as intentional AIS transponder disablement pose significant challenges to MSA, potentially indicating illicit activities. This paper introduces the Dark-VADER (dark vessel AIS delay event recognition) algorithm, designed to detect AIS switchoffs by comparing the frequency of message reception from a vessel under examination with that of neighboring vessels. Leveraging a statistical hypothesis testing procedure based on a Bernoulli process, the algorithm distinguishes between normal and anomalous behavior. Validation using real-world AIS data confirms the fitness of the selected distribution model for times between message arrivals, essential for the algorithm’s operation. Overall, this preliminary work provides a foundational framework for improving maritime AIS anomaly detection, with avenues for future development towards more robust and dynamic approaches.

This paper explores filtering methods to protect range-based localization systems from spoofing attacks on vehicles with directional receivers. It focuses on scenarios where multiple spoofers, potentially from unmanned vehicles, disrupt vehicle localization by strategically positioning themselves between the target and the transmitter. The paper introduces an Adaptive Resilience Navigation Filter (ARNF) that detects ongoing attacks, identifies compromised signals, and mitigates their effects using statistical hypothesis testing. Simulations demonstrate the ARNF’s effectiveness under realistic Global Navigation Satellite System conditions, comparing it with the 2-Stage Extended Kalman Fitter and an ideal Clairvoyant Extended Kalman Filter.

This paper applies Maximum Likelihood Estimation (MLE) to the identification of a stochastic error model of a gyroscope. The error model used for illustration features an Ornstein-Uhlenbeck process with an unknown time constant driven by a process noise with unknown variance, and a white measurement noise also with unknown variance. As the setup of MLE, the likelihood function ($L F)$ is derived in the steady-state Kalman filter framework and is defined in reference to the parameters of the Kalman filter gain and innovation variance. The resulting log-likelihood function (LLF) is a quadratic function of the measurements, facilitating the evaluation of the Cramér-Rao Lower Bound (CRLB) and makes it possible to confirm the statistical efficiency, i.e., optimality, of the ML estimator presented in this paper.

Seabed-to-space situational awareness (S3A) aims to organize, fuse, and synthesize the massive volume of information collected from heterogeneous sensors, i.e., underwater, terrestrial, and space-based sensors, and therefrom extract knowledge thence available to defence operators, enabling informed decision-making. Heterogeneous sensors provide observations of targets in different domains (e.g., air, water surface, undersea), and with different modalities, perspectives, latencies, and update rates. They complement each other, and an effective approach is needed to combine the data they generate. This paper introduces a comprehensive framework for multi-target tracking based on the sum-product algorithm (SPA) that models the different characteristics of the sensors and handles the appearance of targets in a complex multi-domain environment both through spontaneous births and through spawning from existing targets. The efficacy of this approach is demonstrated through a simulated maritime scenario informed by real-world observation streams.

Maneuvering target tracking, where the system undergoes abrupt changes in the underlying motion model, can be challenging. We propose a model-based deep learning approach for prediction of maneuvering targets to exploit partial knowledge of the system physics-based models during training, without requiring an explicit characterization or fine tuning of model parameters. We formulate a supervised training scheme to learn the dynamics of state-space models and capture the jump processes governing model transitions by minimizing the prediction loss of an encoder-decoder network from model-based generated data. The effectiveness of the proposed method is demonstrated in two maneuvering target tracking scenarios using synthetic and real-world test data. The results show that the model-based encoder-decoder network achieves notably improved performance in terms of target prediction compared to conventional multiple-model solutions, especially when facing model inaccuracies, jumps, and dominant nonlinearities during target maneuvers.

This paper develops computationally efficient algorithms for the analysis of acoustic data to localize a target through improved angle of arrival estimation. The passive target localization problem has a wide range of applications in wireless communication, navigation, acoustic sensor networks, indoor localization, to name a few. We have focused on novel formulations and solution methods for target localization using Time Differences of Arrival (TDOA) among distinct pairs of passive sensor nodes in an acoustic sensor network with known sensor positions.

Quickest detection problems are fairly common in surveillance applications, as framing surveillance alerts as a change in an observation sequence’s statistics is often apt. In this work, we consider the scenario where an appropriate statistical description of our observations is not available, neither before nor after the transient we are trying to detect. In this vein, we explore the use of the database Lempel-Ziv, or LZ77, procedure, to detect this transient in the observation data. This algorithm is known to have phrase lengths that are asymptotically distributed as Gaussian random variables, which allows us to form a quickest detection problem around statistics of the coded output. This work specifies procedures to perform source-agnostic transient detection using Locally Optimal (LO) statistic to augment a Page CUSUM test. The work also shows an application to acoustic data.

All practical sensing operations must work with quantized data. Along with measurements, each sensor is assumed to have some "label" value that is relevant to its stochastic measurement parameterization and must be communicated to the decision center. We are interested in cases that require very low communication cost, and thus require very "coarse" quantization of the measurements as well as the labels (2-bit values, for instance). Censoring is used to control the expected communication cost—each sensor decides locally whether or not to send its data to the decision center based on the value of its label as well as the value of its measurement. In this work we formalize the test statistic based on censored and quantized data.

Today, the maritime domain is at the cusp of a new era, driven by technological advances in automation, robotics, multisensor perception, and artificial intelligence (AI), together with digitalization and connectivity. Smart ship infrastructure and technology, remotely controlled and autonomous ship operation to improve safety, security, cost efficiency, and sustainability are the future of maritime transportation[1], representing now the engine of 90% of global trade[2]. Ships will soon benefit from recent developments in sensors, telecommunications, and computing technologies to turn the smart shipping revolution into reality[3]and[4], as it has already happened for autonomous vehicles such as driverless cars, aerial drones, unmanned (or remotely piloted) aircraft, and underwater vehicles.

In this paper we present how automatic maritime anomaly detection tools can be successfully applied in real-world situations such as the major event of the container vesselEver Given, which grounded in the Suez Canal on March 23rd 2021. The anomaly detector is designed to process the available sequence of Automatic Identification System (AIS) reports, information from ground-based or satellite radar systems if available, and contextual information defining the expected nominal behavior of navigation. A statistical hypothesis testing procedure is sequentially run to decide whether or not a deviation from the nominal behavior happened within a specific time period, for instance two consecutive data points. We show, based on the recorded AIS data from theEver Given, that the proposed detector could have been triggered and alerted to anomalous behavior fully 19 minutes before the grounding.

Consider a test at a particular point in space for the existence of a point target using intensity measurements from passive sensors distributed uniformly around the test location. The distance from the test location of a particular sensor is relevant to the decision making, and is considered "labeling" on the sensor’s intensity data. This work considers the case where both the intensity data and the label (distance) values are coarsely quantized to decrease communication cost. It will be shown that, for a given per-measurement communication budget, there exists an ideal quantization rule. The results provide a method for choosing between possible apportionments of the communication budget between data (intensity) and labeling (distance).

This paper develops an easily-implementable version of Page's CUSUM quickest-detection test, designed to work in certain composite hypothesis scenarios with time-varying data statistics. The decision statistic can be cast in a recursive form and is particularly suited for on-line analysis. By back-testing our approach on publicly-available COVID-19 data we find reliable early warning of infection flare-ups, in fact sufficiently early that the tool may be of use to decision-makers on the timing of restrictive measures that may in the future need to be taken.

Many threats (terrorist attacks, military actions, etc.) can be modeled by someone with relevant expert knowledge. A “threat” here implies a sequence of actions that evolve over time and are intended to culminate in a goal that from the article's perspective is unfavorable. This work presents a method to model probabilistically these types of processes using hidden Markov models (HMMs). We thence present a detection scheme based on random finite set (RFS) filters-specifically a multi-Bernoulli approach-that allows for detection of multiple threat processes using a single observed data stream. Key here is that associated with threats are a list of entities that are a priori unknown and must be inferred, but once (probabilistically) identified, aid greatly in the data association step, and inference on the perceived threat.

In this paper, we address the problem of predicting vessel trajectories based on Automatic Identification System (AIS) data. The goal is to learn the predictive distribution of maritime traffic patterns using historical data during the training phase, in order to be able to forecast future target trajectory samples online on the basis of both the extracted knowledge and the available observation sequence. We explore neural sequence-to-sequence models based on the Long Short-Term Memory (LSTM) encoder-decoder architecture to effectively capture long-term temporal dependencies of sequential AIS data and increase the overall predictive power. The experimental evaluation on a real-world AIS dataset demonstrates the effectiveness of sequence-to-sequence recurrent neural networks (RNNs) for vessel trajectory prediction and shows their potential benefits compared to model-based methods.

This letter is focused on the problem of estimating the two parameters of a uniform distribution - its support boundaries - and the application of the Cramér-Rao-Leibniz Lower Bound, a replacement for the Cramér-Rao Lower Bound when the latter does not hold.

In this article, we present a fully analytical model for the evaluation of the electromagnetic (EM) field scattered from a composite target in a generic bistatic configuration. The scenario comprises a rectangular parallelepiped target with smooth dielectric faces lying over a rough background surface, modeled as a stochastic process. The single- and multiple-bounce scattering contributions arising from the target, the rough background, and their interactions have been derived under the Kirchhoff approximation (KA)-geometrical optics (GO) solution. This framework enables the evaluation of the bistatic radar cross section (RCS) of the considered composite target via closed-form expressions. The proposed model exhibits good agreement with the literature results based on accurate and well-established numerical methods. Our analytical model is therefore proposed as a valid alternative to numerical techniques, being able to provide reliable results at a negligible computational burden. Finally, the role of the main scene parameters, i.e., target orientation, surface roughness, and polarization in the bistatic RCS of the target, have been analyzed and discussed.

Piecewise mean-reverting stochastic processes have been recently proposed and validated as an effective model for long-term object prediction. In this paper, we exploit the Ornstein-Uhlenbeck (OU) dynamic model to represent an anomaly as any deviation of the long-run mean velocity from the nominal condition. This amounts to modeling the anomaly as an unknown switching control input that can affect the dynamics of the object. Under this model, the problem of joint anomaly detection and tracking can be addressed within the Bayesian random set framework by means of a hybrid Bernoulli filter (HBF) that sequentially estimates a Bernoulli random set (empty under nominal behavior) for the unknown long-run mean velocity, and a random vector for the kinematic state of the object. An additional challenge is represented by the fact that two extra parameters, i.e. the reversion rate and the noise covariance of the underlying OU process, need to be specified for Bayes-optimal prediction. We propose a multiple-model adaptive filter (MMA-HBF) for anomaly detection, tracking and simultaneous estimation of the OU unknown parameters. The effectiveness of these tools is demonstrated on a simulated maritime scenario.

Unlabeled detection is an emerging paradigm for modern decentralized decision systems faced with big-data applications, and for all those applications in which data must be fused without exploiting their identity, due to the lack of provenance labels, or to uncontrolled data shuffling. Our focus here is on binary alphabets, and we ask: If our data have been shuffled in an unknown way, can a reliable decision about the underlying state of nature be made? Should the decision be made after an attempt to estimate the lost labels? And do there exist easily implementable decision rules? In answering these questions, we gain much insight: We show that two greedy algorithms previously introduced in the literature are equivalent to the GLRT, whose performance can be quite poor, and the detector known as ULR is equivalent to a simple counting rule. A new detector based on the central limit theorem is simply implementable and offers close-to-optimal performance in many scenarios of practical interest.

Inspired by the fair regularity of the motion of ships, we present a method to derive a representation of the commercial maritime traffic in the form of a graph, whose nodes represent way-point areas, or regions of likely direction changes, and whose edges represent navigational legs with constant cruise velocity. The proposed method is based on the representation of a ship's velocity with an Ornstein-Uhlenbeck process and on the detection of changes of its long-run mean to identify navigational way-points. In order to assess the graph representativeness of the traffic, two performance metrics are introduced, leading to distinct graph construction criteria. Finally, the proposed method is validated against real-world Automatic Identification System data collected in a large area.

One of the main attributes of the Quanta Tracking (QT) algorithm is its ability to track dim targets. As this algorithm has been presented, the question usually arises, what is the lowest Signal-to-Noise-Ratio (SNR) that can be tracked by this algorithm? This is not the simple straightforward question to answer that it appears. Before it can be determined how small might be an SNR that can be tracked, a few definitions have to be established. First, the very definition of SNR needs to be decided. Then the definition of what it means to successfully track has to be decided. After these two definitions are determined then the experiment can be performed to answer the main question. In this paper, we define SNR for this application and the threshold for a target being “tracked”. Finally, we obtain results that measure how low can the SNR be for this algorithm to track.

In this paper, methods are developed and evaluated for the correlation of Gaussian mixture tracks from two sensors. The hypothesis likelihoods for the case of a single target are given using the minimum mean square error and the maximum likelihood estimates of common origin between two Gaussian mixtures. A correlation test is developed as a likelihood ratio of the single target hypothesis to the hypothesis of two separate targets. The negative log likelihood cost is formulated and used in an optimal assignment method to perform track-to-track correlation for multiple targets between two sensors. Simulations were performed to compare the minimum mean square error and maximum likelihood approaches with Gaussian mixture tracks to a baseline method using unbiased converted measurements for sensors with a given probability of detection and bias significance. Results are shown to compare the performance of the correlation methods with respect to probability of correct correlation and root mean squared error versus track density for several different aspect angles between two sensors.

It has been shown in previous works that the trajectory of a thrusting/ballistic object in three-dimensional space is observable with two-dimensional measurements from a stationary passive sensor. The measurements can either start from the launch point or start in flight, i.e., with delayed acquisition. The observability of the target trajectory was investigated by testing the invertibility of the Fisher Information Matrix (FIM) numerically. This work discusses the observability of the trajectory via the uniqueness of the target state vector for a certain sequence of 2-d angle-only measurements (azimuth and elevation angles) from a single fixed passive sensor. The discussion starts with polynomial motion from which the results are extended to nonlinear thrusting/ballistic motion. Two cases: (i) known thrust and drag coefficient, (ii) unknown thrust and drag coefficient are considered. The gravity acceleration is shown to be the crucial part that guarantees the observability in all the cases.

A novel anomaly detection procedure is presented, based on the Ornstein-Uhlenbeck (OU) mean-reverting stochastic process. The considered anomaly is a vessel that deviates from a planned route, changing its nominal velocity. In order to hide this behavior, the vessel switches off its Automatic Identification System (AIS) device for a certain time, and then tries to revert to the previous nominal velocity. The decision that has to be taken is either declaring that a deviation happened or not, relying only upon two consecutive AIS contacts. A proper statistical hypothesis testing procedure that builds on the changes in the OU process long-term velocity parameter of the vessel is the core of the proposed approach and enables for the solution of the anomaly detection problem.

Suppose that the energy made available to a sensor network at the beginning of a time slot is proportional to the success of the network inferential task during the previous slot. And further, assume that such energy is to be apportioned to charge the individual sensors, such that the more energy one sensor receives, the better it does its job. Then, the information gathered by the network in the long run consequently obeys a multiplicative rule, which enables us to adapt some results from portfolio theory to design the optimal apportionment. Two regimes emerge, one in which the expected value of the long-run information is key and all the energy is assigned to the “best” sensor, and another - more tricky - where the expected logarithm of the long-run information matters, and the solution is given by Cover's log-optimal apportionment.

Consider a binary hypothesis where data are independent and identically distributed under the null hypothesis, and known only to be independent under the alternative. The statistician observes an n- vector Xn(n ≫ 1) and makes a decision using the optimal likelihood ratio test. This seems a widely-known detection problem, but: What if only the set of samples of Xnare made available to the statistician, while the positions of the individual samples inside the vector are not? Does there exist an optimal test in that case? What is the fundamental performance limit? Are there nicely-performing practical detectors with affordable computational complexity? Answers to these questions are in large part unknown, despite the fact that the problem - which is becoming known under the name of unlabeled detection - is very relevant in modern sensor network applications where the sample positions can be lost due to their means of delivery from the remote units, or because of network attacks.

Many threats in the form of human actions (terrorist attacks, military actions, etc.) can be modeled by someone with relevant expert knowledge. A model would be a hypothesis or guess as to how a threat would develop and what kind of observable evidence it would produce along the way. We present a method of stochastically modeling these types of processes using Hidden Markov Models (HMMs). We then present a detection scheme using a Bernoulli Filter - an increasingly popular application of random finite set statistics

Global Navigation Satellite System-Reflectometry (GNSS-R), is succesfully employed for ocean altimetric and scatterometric applications. Recently, it has been suggested that GNSS-R can also be used for ship detection applications. To this purpose, an accurate electromagnetic modeling of the bistatic radar cross section of a ship lying over the sea surface would be very helpful. However, existing models are typically limited to monostatic configurations, thus restricting their applicability in multistatic scenarios, such as GNSS-R systems. In this work, we show a procedure to determine the bistatic radar cross section of a ship target, under the geometrical optics approximation. Numerical results show the impact of the geometry of acquisition and polarization on the bistatic radar cross section.

In this paper, a comparative study of spaceborne Global Navigation Satellite System (GNSS)-Reflectometry for ship detection applications is provided. The analysis is conducted by evaluating the impact of 1) the acquisition geometry and 2) the received signal polarization on ship detectability in GNSS-R data. In particular, the backscattering acquisition geometry is demonstrated to be more suitable for ship detection applications, thus allowing for the detection of 20 m-length ships. Even very large ships are hardly detectable in the conventional forward-scattering geometry. Moreover, receiving right-hand circular polarization is demonstrated to provide significant improvements of the signal-to-noise-plus-clutter with respect to the conventional left-hand circular polarization channel, conventionally exploited in GNSS-R remote sensing. The study is based on a numerical tool for the bistatic radar cross section of the ship, which is presented in a companion paper.

Direction-of-arrival (DOA) estimation and tracking of signals using passive sensor arrays is a classic problem that becomes challenging when the number of sources varies over time and the signal-to-noise ratio is low. In this paper, we pose this problem as minimum mean OSPA (MMOSPA) estimation, which minimizes the the optimal sub-pattern assignment (OSPA) metric of the posterior random finite set (RFS). A particle filter implementation of the MMOSPA estimator is developed for simultaneous source enumeration and DOA tracking. The performance of the new method is demonstrated by means of an experiment with a large sonar array in Florida.

We consider the problem of point target detection on images and focal plane arrays (FPA). Imaging sensors are becoming ubiquitous tools in several applications, such as biomedical systems, autonomous surveillance systems, target tracking systems, and robotics. In these applications, matched filter and template matching are commonly used detection strategies, however, these approaches are unable to provide sub-pixel accuracy and avenues for adaptive pixel-width selection for computationally efficient image processing. In this paper, we derive the maximum likelihood estimator (MLE) of target location on images. The proposed MLE is optimal under the assumption that the FPA contains a point target that has its signal intensity spread in multiple image pixels in the form of a Gaussian point spread function (PSF) with known standard deviation. Further, we derive the Cramér-Rao lower bound (CRLB) of the estimate and present the hypothesis test for target acceptance, resulting in a novel maximum likelihood detector (MLD) for images. Simulation results are provided to validate the performance of the proposed MLE and MLD; it is shown that the MLE is efficient in very low SNR values, starting at -15 dB, and the MLD achieves probability of detection of near unity with zero false alarms starting at 0 dB.

We develop an Expectation-Maximization (EM) algorithm for the simultaneous tracking and shape estimation of a star-convex object based on multiple spatially distributed measurements. In order to formulate the problem within the EM framework, the unknown measurement sources on the object are modeled as hidden variables. As the measurement sources are continuous quantities, we develop a suitable discretization method that allows for a closed-form EM iteration. The performance of the EM approach is demonstrated in comparison with a recursive Gaussian filter based on the Random Hypersurface Model (RHM).

One regularity condition for the classical Cramér-Rao lower bound (CRLB) of an unbiased estimator to hold is that the support of the likelihood function (LF) should be independent of the parameter to be estimated. This has been shown to be too stringent and the CRLB has been shown to be valid for the case of parameter-dependent support as long as the LF is continuous at the boundary of its support. For the case where the LF is not continuous at the boundary of its support, a new modified CRLB - designated as the Cramér-Rao-Leibniz lower bound (CRLLB) as it relies on the Leibniz integral rule - has been presented for the scalar parameter and measurement case in [3]. The CRLLB for multidimensional parameter and measurements has been developed in [8]. The present work applies the multidimensional CRLLB to n-dimensional measurement noise with the raised fractional cosine and the truncated Laplace distributions inside an (n - 1)-sphere.

In previous works, it has been shown that the estimation problem of a thrusting/ballistic object in the three-dimensional space can be solved with two-dimensional measurements (azimuth and elevation angles starting from the launch time) assuming the launch point is perfectly known. In this paper, the problem is extended to estimate the target's trajectory with measurements starting after the launch time, i.e., delayed acquisition. Compared to the situation of acquisition at launch time, one has an additional unknown speed (magnitude of the velocity vector) and the unknown acquisition location. The 2D angle measurements are all obtained from a single fixed passive sensor. The parameter vector, in this case, has dimension 8 (velocity vector azimuth angle and elevation angle, drag coefficient, specific thrust, target speed and 3D acquisition position). The invertibility of the Fisher Information Matrix (FIM) of the parameter vector is investigated to test the observability (estimability) of the system. The simulation results prove the statistical efficiency and unbiasedness of the Maximum Likelihood estimator, that is, the Cramer-Rao lower bound (the inverse of the FIM if it is invertible) can be used as the actual covariance.

In modern heterogeneous sensor networks huge volumes of information rapidly flow across the system, and it is often too difficult or costly to associate data to the sensors that produced them. Then, the set of observations appears to be unlabeled: What comes from whom? We study the classical problem of detecting a known signal embedded in Gaussian noise, but under the peculiar assumption that the signal samples have been scrambled (e.g., in time or space) in an unknown way. Our study sheds light on questions like: How much detection performance is contained in the samples' values and how much in their ordering? Are there nicely-performing detectors with affordable computational complexity?

We tackle distributed detection of a noncooperative target with a wireless sensor network. When the target is present, sensors observe an (unknown) deterministic signal with attenuation depending on the distance between the sensor and the (unknown) target positions, embedded in symmetric and unimodal noise. The fusion center receives quantized sensor observations through error-prone binary symmetric channels and is in charge of performing a more-accurate global decision. The resulting problem is a two-sided parameter testing with nuisance parameters (i.e., the target position) present only under the alternative hypothesis. After introducing the generalized likelihood ratio test for the problem, we develop a novel fusion rule corresponding to a generalized Rao test, based on Davies' framework, to reduce the computational complexity. Also, a rationale for threshold-optimization is proposed and confirmed by simulations. Finally, the aforementioned rules are compared in terms of performance and computational complexity.

Ship traffic monitoring is a foundation for many maritime security domains, and monitoring system specifications underscore the necessity to track vessels beyond territorial waters. However, vessels in open seas are seldom continuously observed. Thus, the problem of long-term vessel prediction becomes crucial. This paper focuses attention on the performance assessment of the Ornstein-Uhlenbeck (OU) model for long-term vessel prediction, compared with usual and well-established nearly constant velocity (NCV) model. Heterogeneous data, such as automatic identification system (AIS) data, high-frequency surface wave radar data, and synthetic aperture radar data, are exploited to this aim. Two different association procedures are also presented to cue dwells in case of gaps in the transmission of AIS messages. Suitable metrics have been introduced for the assessment. Considerable advantages of the OU model are pointed out with respect to the NCV model.

There is good reason to model an asymmetric threat (a structured action such as a terrorist attack) as an hmm whose observations are cluttered. Recently a Bernoulli filter was presented that can process cluttered observations ("transactions") and is capable of detecting if there is an HMM present, and if so, estimate the state of the HMM. An important question in this context is: when is the HMM-in-clutter problem feasible? In other words, what system properties allow for a solvable problem? In this paper we show that, given a Gaussian approximation of the pdf of the log-likelihood, approximate detection error bounds can be derived. These error bounds allow a prediction of the detection performance, i.e. a prediction of the probability of detection given an "operating point" of transaction-level false alarm rate and miss probability. Simulations show that our analysis accurately predicts detectability of such threats. Our purpose here is to make statements about what sort of threats can be detected, and what quality of observations are necessary that this be accomplished.

Parametric estimation for the generative social sensing model proposed in [19,20] is addressed. First, we provide a detailed analysis of the estimation performance bounds, in terms of the Fisher information matrix, with emphasis on the fundamental scaling laws as the number of network agents and/or the number of monitored agents' activities is large. Then, we examine two viable estimation procedures that can be useful even in such large dataset applications: the Expectation-Maximization and the Fisher scoring algorithms, which both achieve the aforementioned performance bounds.

In this letter, we study the problem of estimating the long-run mean of the Ornstein-Uhlenbeck (OU) stochastic process and its effect on the long-term prediction of future vessel states, which is a crucial problem for Maritime Situational Awareness (MSA). We employ a sample mean estimator (SME) to estimate the key OU parameter from the observations, computing the closedform SME covariance error in both the random and constant sampling time regimes, providing a fundamental building block of the overall long-term state prediction covariance. We show also that the SME is: √n-consistent when the sampling time is random; asymptotically efficient when the sampling time is constant; and very close to the Cramer-Rao lower bound in the cases of practical interest for MSA.

Detecting node failures in mobile wireless networks is very challenging because the network topology can be highly dynamic, the network may not be always connected, and the resources are limited. In this paper, we take a probabilistic approach and propose two node failure detection schemes that systematically combine localized monitoring, location estimation and node collaboration. Extensive simulation results in both connected and disconnected networks demonstrate that our schemes achieve high failure detection rates (close to an upper bound) and low false positive rates, and incur low communication overhead. Compared to approaches that use centralized monitoring, our approach has up to 80 percent lower communication overhead, and only slightly lower detection rates and slightly higher false positive rates. In addition, our approach has the advantage that it is applicable to both connected and disconnected networks while centralized monitoring is only applicable to connected networks. Compared to other approaches that use localized monitoring, our approach has similar failure detection rates, up to 57 percent lower communication overhead and much lower false positive rates (e.g., 0.01 versus 0.27 in some settings).

Hidden Markov Models (HMMs) are powerful statistical techniques with many applications, and in this paper they are used for modeling asymmetric threats. The observations generated by such HMMs are generally cluttered with observations that are not related to the HMM. In this paper a Bernoulli filter is proposed, which processes cluttered observations and is capable of detecting if there is an HMM present, and if so, estimate the state of the HMM. Results show that the proposed filter is capable of detecting and estimating an HMM except in circumstances where the probability of observing the HMM is lower than the probability of receiving a clutter observation.

In practical target tracking problems, the target detection performance of the sensors may be unknown and may change rapidly with time. In this work we develop a target tracking procedure able to adapt and react to time-varying changes of the detection capability for a network of sensors. The proposed tracking strategy is based on a Bayesian framework, in which the dynamic target state is augmented to include the sensor detection probabilities. The method is validated using computer simulations and real-world experiments conducted by the NATO Science and Technology Organization (STO) - Centre for Maritime Research and Experimentation (CMRE).

The two title concepts have been evolving rather rapidly, but independent of each other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image processing as it can describe a measure of similarity between images. Its minimization might, for example, suggest the best match in image alignment. On the other hand, MMOSPA estimation has been applied largely to multi-target tracking. The Optimal Sub-Pattern Assignment (OSPA) measures the distance between two sets and the Mean OSPA (MOSPA) can be minimized to give the Minimum MOPSA (MMOSPA), which improves MMSE estimation of the target locations when the labeling of the targets in the set is not important. Approximate and exact algorithms have evolved for both Wasserstein barycenters and MMOSPA estimation. Here, we draw connections between the two perspectives and elaborate how they can benefit from each other.

A key challenge in multi-target tracking is that the number of possible measurement-to-target associations grows exponentially with the number of targets. The popular PMHT approach bypasses this problem by using an arguably wrong assignment model that, however, allows evaluating the likelihood function with complexity linear both in numbers of targets and of measurements. Unfortunately, the resulting tracking quality may suffer due the wrong assignment model. In this paper, we propose a hybrid data association model that combines both the PMHT and original models. In this vein, the likelihood function can be evaluated efficiently in polynomial time while still providing tracking results close to the exact (but, in large scale cases, intractable) solution resulting from the original “correct” model. The feasibility of the new hybrid assignment model is demonstrated by means of maximum likelihood estimation of closely-spaced targets. Extension to marginalized probability calculation - that is, the joint probabilistic data association filter (JPDAF) [1] is in [2].

This paper presents a Bayesian multi-sensor tracking strategy for a network of autonomous underwater vehicles (AUVs) for the purpose of anti-submarine warfare (ASW). A bistatic configuration and the corresponding acoustic model for the bistatic signal-to-noise ratio (SNR) is used. The Bayesian posterior distribution of the target state based on all available information from sensors and on the acoustic model is reconstructed via particle filtering methods, taking into account the port-starboard ambiguity typical of horizontal line arrays. The posterior distribution is the optimal estimation procedure, the only approximation derives from the particle representation. The effectiveness of the proposed algorithm is demonstrated on a real data set collected by the NATO Centre for Maritime Research and Experimentation (CMRE) during the NATO Proud Manta 2012 exercise (ExPOMA12).

Information fusion is the keystone of many surveillance systems, in which the security of the information is a crucial aspect. This paper proposes a method to fuse information exchanging only encrypted data, through a secure extension of the popular consensus gossip algorithm using secure multi-party computation methodology. Sensor entities exchange only encrypted information and never have direct access to the data while iteratively reaching consensus. The agents do not have access to the final value and can just retrieve partial information, for instance a binary decision. An innovative implementation of the consensus algorithm in the encrypted domain is proposed and analyzed.

In one of his landmark papers, Cover established the fundamental scaling laws of learning with nearest-neighbor rules (T.M. Cover, 1968). With the recent advances on distributed nearest-neighbor learning in sensor networks novel trade-offs arise, involving the faithfulness of message representation (quantization bits) and the number of delivered messages (transmitting sensors). This is the main theme of this paper.

ABSTRACT Multi‐input multi‐output orthogonal frequency‐division multiplexing (MIMO‐OFDM) has been actively studied for high data rate communications over the bandwidth‐limited underwater acoustic (UWA) channels. Unlike existing receivers that treat the intercarrier interference (ICI) as additive noise, in this paper, the proposed receiver considers ICI explicitly together with the co‐channel interference (CCI) due to parallel transmissions in MIMO‐OFDM. Using a recently developed progressive receiver framework, the proposed receiver starts with low‐complexity ICI‐ignorant processing and then progresses to ICI‐aware processing with increasing ICI levels. The key components of the proposed receiver include the following: (1) compressed sensing‐based sparse channel estimation, (2) soft‐input soft‐output minimum mean square error/Markov chain Monte Carlo detector for interference mitigation, and (3) soft nonbinary low‐density parity check decoding. In addition to simulation, we use real data from the Surface Processes and Acoustic Communications Experiment 2008 (SPACE08) and the Mobile Acoustic Communications Experiment 2010 (MACE10) to verify the system performance, where the transmitter in SPACE08 was stationary and that in MACE10 was slowly moving. Simulation and experimental results show that explicitly addressing ICI and CCI significantly improves the performance of MIMO‐OFDM in UWA systems. Copyright © 2012 John Wiley & Sons, Ltd.

Recently it has been shown that the Multi-Sensor Probability Hypothesis Density (MS-PHD) has some optimality properties in the regime of large number of sensors [1, 2], achieving the same performance of the Bayes multi-sensor/multi-target posterior in the Random Finite Set (RFS) framework [3]. However, when the number of sensors N is relatively large, the traditional PHD filter loses its computational efficiency, the complexity being exponential in N. On the other hand, the complexity of the full Bayes posterior is only linear in N, and this paper suggests an idea for its computation using Sequential Monte Carlo (SMC) methods. The MS-PHD is then evaluated, and numerical examples show that it is possible to deal with a scenario where the number of sensors is very large while targets, appearing and disappearing, evolve in time.

In this work, we introduce the particle PHD forward filter - backward simulator (PHD-FFBSi) capable of dealing with uncertainties in the labeling of tracks that appear when tracking two targets in close proximity with measurements that do not discriminate between them. The Forward Filter Backward Simulator is a smoothing technique based on rejection sampling for the calculation of the probabilities of association between targets and tracks. The forward filter is a particle implementation of the Probability Hypothesis Density (PHD) filter that presents advantages over an SIR filter. Difficulties that arise due to the presence of target birth and death processes are addressed through modifications to the fast FFBSi. Simulations show the new particle filter of asymptotically linear complexity in the number of particles calculates correct target label probabilities at varying levels of measurement noise.

A wireless sensor network is engaged in a statistical learning task, to be accomplished in a decentralized fashion. The focus here is in distributed Nearest-Neighbor (NN) regression, in the presence of communication constraints. We first introduce a general channel access policy which allows the fusion center to recover training-set labels ordered according to the NN criterion, in the absence of any data exchange among sensors. Then, two different paradigms are considered, where the communication cost is measured as: i) the channel accesses; ii) the quantization bits. In the former scenario, we propose a distributed NN strategy reaching an asymptotic performance of twice the minimum achievable mean-square error, with only one sensor transmitting information. In the latter case, we achieve universally consistent distributed NN regression even with one-bit quantized labels.

This paper investigates moving target localization by the biased time-of-arrivals (TOAs), where an extracted TOA is biased by the unknown Doppler of the target. The phenomenon applies to radar and sonar systems that employ Doppler tolerant waveforms. While in principle those would allow the estimation of both position and velocity using position-only measurements, we unfortunately find that the Fisher information matrix is ill-conditioned. However, a Quasi-maximum likelihood estimator based on the misspecified model is suggested, and its performance is analyzed.

In this letter, we propose the Rao test as a simpler alternative to the generalized likelihood ratio test (GLRT) for multisensor fusion. We consider sensors observing an unknown deterministic parameter with symmetric and unimodal noise. A decision fusion center (DFC) receives quantized sensor observations through error-prone binary symmetric channels and makes a global decision. We analyze the optimal quantizer thresholds and we study the performance of the Rao test in comparison to the GLRT. Also, a theoretical comparison is made and asymptotic performance is derived in a scenario with homogeneous sensors. All the results are confirmed through simulations.

Recently significant progress has been made on point-to-point underwater acoustic communications, and the interest has grown on the application of those techniques in multiuser communication settings, where the asynchronous nature of multiuser communication poses a grand challenge. This paper develops a time-asynchronous multiuser reception approach for orthogonal frequency-division multiplexing (OFDM) transmissions in underwater acoustic channels. The received data burst is segmented and apportioned to multiple processing units in an overlapped fashion, where the length of the processing unit depends on the maximum asynchronism among users on the OFDM block level. Interference cancellation is adopted to reduce the interblock interference between overlapped processing units. Within each processing unit, the residual inter-block interference from multiple users is aggregated as one external interference which can be parameterized. Multiuser channel estimation, data detection, and interference mitigation are then carried out in an iterative fashion. Simulation and emulated experimental results demonstrate the robustness of the proposed receiver with signal asynchronism among multiple users in both time-invariant and time-varying environments. It is observed that the receiver decoding performance degrades as the channel time variation and the maximum relative delay among users increase.

A multiple-input multiple-output (MIMO) radar can improve system performance with waveform and spatial diversities. Mathematically, the multiple independent waveforms increase the dimension of signal space, so optimal transmission power allocation deserves investigation. The majority of the literature prefers to omit the effect of propagation attenuation, and considers the receiving gain vectors to be independently and identically distributed (i.i.d.) in power allocation. In this paper, we integrate the propagation losses into MIMO radar signal model, and investigate the power allocation problems under three popular criteria: maximizing the mutual information, minimizing the minimum mean square errors, and maximizing the echo energy. As their objective functions are either convex or concave, the optimal strategies are theoretically guaranteed.

The interaction between a smart target and a smart MIMO radar is investigated from a game theory perspective. Since the target and the radar form an adversarial system, their interaction is modeled as a two-person zero-sum game. The mutual information criterion is used to formulate the utility functions. The unilateral, hierarchical, and symmetric games are studied, and the equilibria solutions are derived.

In this paper, we propose a practical scheme, Non-Binary Joint Network-Channel Coding (NB-JNCC), for reliable multi-path multi-hop communication in arbitrary large-scale wireless networks. NB-JNCC seamlessly couples channel coding and network coding to effectively combat the detrimental effect of fading of wireless channels. Specifically, NB-JNCC combines non-binary irregular low-density parity-check (LDPC) channel coding and random linear network coding through iterative joint decoding, which helps to fully exploit the spatial diversity and redundancy residing in both channel codes and network codes. In addition, since it operates over a high order Galois field, NB-JNCC can be directly combined with high order modulation without the need of any bit-to-symbol conversion nor its inverse. Through both analysis and simulation, we demonstrate the significant performance improvement of NB-JNCC over other schemes.

Minimum mean squared error estimates generally are not optimal in terms of a common track error statistic used in tracking benchmarks, namely a form of the Mean Optimal Sub-pattern Assignment (MOSPA) metric. We derive an explicit solution for the MOSPA-optimal estimates for two scalar targets. We also generalize previous work on permutation variant and invariant PDF decompositions by Blom and Bloem (avoiding the use of measure theory), demonstrating how the means of these PDFs may be used to approximate minimum MOSPA estimates. These methods based upon PDF manipulation may be used with general PDFs for an arbitrary number of targets having states of arbitrary dimensionality. The results are also applicable within the context of channel estimation.

Optimizing over a variant of the Mean Optimal Subpattern Assignment (MOSPA) metric is equivalent to optimizing over the track accuracy statistic often used in target tracking benchmarks. Past work has shown how obtaining a Minimum MOSPA (MMOSPA) estimate for target locations from a Probability Density Function (PDF) outperforms more traditional methods (e.g. maximum likelihood (ML) or Minimum Mean Squared Error (MMSE) estimates) with regard to track accuracy metrics. In this paper, we derive an approximation to the MMOSPA estimator in the two-target case, which is generally very complicated, based on minimizing a Bhattacharyya-like bound. It has a particularly nice form for Gaussian mixtures. We thence compare the new estimator to that obtained from using the MMSE and the optimal MMOSPA estimators.

Bearings-only localization with light-of-sight (LOS) propagation is well understood. This paper concentrates on bearing-only localization with non-line-of-sight (NLOS) measurements, where the target radiation arrives at the sensor after a specular reflection. The wrinkle is that the reflecting surface is circular (inner side of a circle), and is assumed known. Since the target-sensor geometry has multiple configurations, the maximum likelihood (ML) solution may not exist. However, if a concentric opaque circle (such as the earth) exists within the reflecting one, the propagation path is unique; a grid search based ML is available for such a circumstance. Since ML is computationally consuming, two suboptimal algorithms based on small angle approximation are developed. Their performances are numerically compared.

A random parameter is estimated by a distributed network of sensors that communicate over a common MAC. The channel implies an enforced additive fusion rule, and the goal here is to design a power-constrained forwarding strategy and the post-processing by the fusion center. To get an explicit solution we appeal to asymptotics, meaning that we design the locally optimal scheme for the limiting case that the received power goes to zero.

As is clear from the ambiguity function (AF) uncertainty principle and the underlying matched filtering operation, pulse compression (PC) radars cannot accurately and simultaneously measure both the time delay and Doppler shift of moving targets. On the other hand, compressed sensing (CS) radar would seem to be emerging as a means to do just that, jointly to estimate the delay and Doppler shift, through convex optimization instead of matched filtering, such that PC resolution limits no longer apply. However, it turns out that the AF is closely related to the CS “dictionary coherence coefficient,” which affects the optimization recoverability. In this paper we formalize this relationship.

The information filter is a form of the Kalman filter that, in many of its realizations, allows optimal, unbiased, recursive state estimation without an initial state estimate. We review a number of forms of the information filter. We then derive the coefficients for the sliding-window Kalman finite impulse response (FIR) smoother (also known as a receding or moving horizon Kalman FIR smoother) starting from the equations for the information filter. The resulting FIR smoother has a simple, recursive form for calculating the coefficients, allowing them to be calculated with$O(N)$complexity versus the$O(N^{2})$to$O(N^{3})$complexity of previous approaches, where$N$is the length of the batch. It also allows for a control input, something not present in previous algorithms. This method is only limited in the assumption that the state transition matrix is invertible, which, however, is satisfied in most practical problems.

In this paper, we study nonbinary regular LDPC cycle codes whose parity check matrix H has fixed column weight j = 2 and fixed row weight d. Through graph analysis, we show that the parity check matrix H of a regular cycle code can be put into an equivalent structure in the form of concatenation of row-permuted block-diagonal matrices if d is even, or, if d is odd and the code's associated graph contains at least one spanning subgraph that consists of disjoint edges. This equivalent structure of H enables: i) parallel processing in lineartime encoding; ii) considerable resource reduction on the code storage for encoding and decoding; and iii) parallel processing in sequential belief-propagation decoding, which increases the throughput without compromising performance or complexity. On the code's structure design, we propose a novel design methodology based on the equivalent structure of H. Finally, we present various numerical results on the code performance and the decoding complexity.

In this paper, we present a novel method to construct nonbinary irregular LDPC codes whose parity check matrix has only column weights of 2 and t, where t ¿ 3. The constructed codes can be encoded in linear time and in a parallel fashion. Also, they can achieve near-Shannon-limit performance over both AWGN and Rayleigh fading channels with a moderate field size. Analysis based on nonbinary EXIT charts is presented. Codes constructed by the proposed method with block lengths ranging from 1, 000 bits to 10, 000 bits are simulated. Simulation results show that codes of rate 1/2 and length 10, 000 bits can achieve block-error-rate (BLER) of 10-5within 1.1 dB and 1.3 dB away from the Shannon limits of the AWGN and Rayleigh channels, respectively. In an AWGN channel, codes of rate r = 8/9 and length around 4,000 bits can achieve BLER of 10-5within 1.1 dB from the Shannon limit, while codes of rate r = 15/16 and length around 9,000 bits can achieve BLER of 10-5within 1.0 dB from the Shannon limit. We conjecture that to further lower the error floor (e.g., to a BLER of 10-10), a column weight no less than 3 is preferred and may be necessary, especially for codes with high rate and over Galois fields of small to moderate sizes.

In this paper, we propose a practical scheme, called Non-Binary Joint Network-Channel Decoding (NB-JNCD) for reliable communication in wireless networks. It seamlessly couples channel coding and network coding, and can effectively combat the detrimental effect of fading of wireless channels, especially in large networks. On a high order Galois field, NB-JNCD combines non-binary LDPC channel coding and random linear network coding through iterative joint decoding, which helps fully exploit the spatial diversity and redundancy residing in both codes. Furthermore, the scheme can unify non-binary source coding and high order modulation without the need of any bit-to-symbol conversion and its inverse. Through analysis and simulation, we demonstrate the significant performance improvement of NB-JNCD against other schemes.

Using group theory, we analyze cycle GF(2p) codes that use Cayley graphs as their associated graphs. First, we show that through row and column permutations the parity check matrix H can be put in a concatenation form of row-permuted block-diagonal matrices. Encoding utilizing this form can be performed in linear time and in parallel. Second, we derive a rule to determine the nonzero entries of H and present determinate and semi-determinate codes. Our simulations show that the determinate and semi-determinate codes have better performance than codes with randomly generated nonzero entries for GF(16) and GF(64), and have similar performance for GF(256). The constructed determinate and semi-determinate codes over GF(64) and GF(256) can outperform the binary irregular counterparts of the same block lengths. One distinct advantage for determinate and semi-determinate codes is that they greatly reduce the storage cost of H for decoding. The results in this correspondence are appealing for the implementation of efficient encoders and decoders for this class of promising LDPC codes, especially when the block length is large.

In this paper, we consider a model for the dynamic multiple-fault diagnosis (DMFD) problem arising in online monitoring of complex systems and present a solution. This problem involves real-time inference of the most likely set of faults and their time-evolution based on blocks of unreliable test outcomes over time. In the DMFD problem, there is a finite set of mutually independent fault states, and a finite set of sensors (tests) is used to monitor their status. We model the dependence of test outcomes on the fault states via the traditional D-matrix (fault dictionary). The tests are imperfect in the sense that they can have missed detections, false alarms, or may be available asynchronously. Based on the imperfect observations over time, the problem is to identify the most likely evolution of fault states over time. The DMFD problem is an intractable NP-hard combinatorial optimization problem. Consequently, we decompose the DMFD problem into a series of decoupled subproblems, one for each sample epoch. For a single-epoch MFD, we develop a fast and high-quality deterministic simulated annealing method. Based on the sequential inferences, a local search-and-update scheme is applied to further improve the solution. Finally, we discuss how the method can be extended to dependent faults.

The problem of detecting an anomaly (or abnormal event) is such that the distribution of observations is different before and after an unknown onset time, and the objective is to detect the change by statistically matching the observed pattern with that predicted by a model. In the context of asymmetric threats, the detection of an abnormal situation refers to the discovery of suspicious activities of a hostile nation or group out of noisy, scattered, and partial intelligence data. The problem becomes complex in a low signal-to-noise ratio environment, such as asymmetric threats, because the ldquosignalrdquo observations are far fewer than ldquonoiserdquo observations. Furthermore, the signal observations are ldquohiddenrdquo in the noise. In this paper, we illustrate the capabilities of hidden Markov models (HMMs), combined with feature-aided tracking, for the detection of asymmetric threats. A transaction-based probabilistic model is proposed to combine HMMs and feature-aided tracking. A procedure analogous to Page's test is used for the quickest detection of abnormal events. The simulation results show that our method is able to detect the modeled pattern of an asymmetric threat with a high performance as compared to a maximum likelihood-based data mining technique. Performance analysis shows that the detection of HMMs improves with increase in the complexity of HMMs (i.e., the number of states in an HMM).

Recently, significant attention in compressed sensing has been focused on basis pursuit, exchanging the cardinality operator with the l1-norm, which leads to a linear formulation. Here, we want to look beyond using the l1-norm in two ways: investigating non-linear solutions of higher complexity, but closer to the original problem for one, and improving known low complexity solutions based on matching pursuit using rollout concepts. Our simulation results concur with previous findings that once x is "sparse enough", many algorithms find the correct solution, but for averagely sparse problems we find that the l1-norm often does not converge to the correct solution - in fact being outperformed by matching pursuit based algorithms at lower complexity. The non-linear algorithm we suggest has increased complexity, but shows superior performance in this setting.

In this article we introduce a sequential procedure for detecting a target using distributed sensors in a two dimensional region. The detection is carried out in a mobile fusion center (in a way familiar to hockey fans, we envision this as a Zamboni machine) which successively counts the number of binary decisions reported by local sensors lying inside its field of view. The proposed sequential detection procedure is based on a two-dimensional scan statistic - this is an emerging tool from the statistics field that has been applied to a variety of anomaly detection problems such as of epidemics or computer intrusion; but that seem to be unfamiliar within the signal processing community. Analytical and simulation results are presented for system-level detection.

Stochastic resonance (SR) is a phenomenon long investigated by physicists that has recently attracted some interest in the signal processing literature. In this paper, we explore the potential benefits of the SR effect for shift-in-mean detection problems, specifically focusing on sequential decision rules. Amenable formulas for the optimal distribution of the SR noise, as well as an asymptotic comparison with the traditional Neyman-Pearson approach are obtained.

In this paper, we study non-binary regular LDPC cycle codes whose parity check matrix has fixed column weight 2 and fixed row weight d. We prove that the parity check matrix of any regular cycle code can be put into a concatenation form of row-permuted block-diagonal matrices after row and column permutations if d is even, or, if d is odd and the code's associated graph contains at least one spanning subgraph that consists of disjoint edges. Utilizing this structure enables parallel processing in linear-time encoding, and parallel processing in sequential belief-propagation decoding, which increases the throughput without compromising performance or complexity. Numerical results are presented to compare the code performance and the decoding complexity.

Multicarrier modulation in the form of OFDM has been actively pursued for underwater acoustic communication recently. In this paper, we present a desirable property of OFDM that one signal design can be easily scaled to fit into different transmission bandwidths with negligible changes on the receiver. We have tested the proposed design with data collected from experiments at AUV Fest, Panama City, FL, June 2007, and at the Buzzards Bay, MA, Aug. 2007. With QPSK modulation, we have used different bandwidths from 3 kHz to 50 kHz, leading to data rates from 1.5 kbps to 25 kbps after rate 1/2 coding. With 16-QAM modulation, we have used different bandwidths from 12 kHz to 50 kHz, leading to data rates from 12 kbps to 50 kbps. Excellent BER performance has been achieved, which confirms the flexibility of OFDM under different system setups.

Recently, multicarrier modulation in the form of orthogonal frequency division multiplexing (OFDM) has been shown feasible for underwater acoustic communications via effective algorithms to handle the channel time-variability. In this paper, we propose to use nonbinary low density parity check (LDPC) codes to address two other main issues in OFDM: (i) plain (or uncoded) OFDM has poor performance in fading channels, and (ii) OFDM transmission has high peak to average power ratio (PAPR). We develop new methods to construct nonbinary regular and irregular LDPC codes that achieve excellent performance, match well with the underlying modulation, and can be encoded in linear time and in a parallel fashion. Based on the fact that the generator matrix of LDPC codes has high density, we further show how to reduce the PAPR considerably with minimal overhead. Experimental results confirm the excellent performance of the proposed nonbinary LDPC codes in multicarrier underwater acoustic communications.

In this paper, we propose a novel method for detection, synchronization and Doppler scale estimation for underwater acoustic communication using orthogonal frequency division multiplex (OFDM) waveforms. This new method involves transmitting two identical OFDM symbols together with a cyclic prefix, while the receiver uses a bank of parallel self-correlators. Each correlator is matched to a different Doppler scaling factor with respect to the waveform dilation or compression. We characterize the receiver operating characteristic in terms of probability of false alarm and probability of detection. We also analyze the impact of Doppler scale estimation accuracy on the data transmission performance. These analytical results provide guidelines for the selection of the detection threshold and Doppler scale resolution. In addition to computer-based simulations, we have tested the proposed method with real data from an experiment at Buzzards Bay, MA, Dec. 15, 2006. Using only one preamble, the proposed method achieves similar performance on the Doppler scale estimation and the bit error rate as an existing method that uses two linearly-frequencymodulated (LFM) waveforms, one as a preamble and the other as a postamble, around each data burst transmission. Compared with the LFM based method, the proposed method works with a constant detection threshold independent of the noise level and is suited to handle the presence of dense multipath channels. More importantly, the proposed approach does not need to buffer the whole data packet before data demodulation, which facilitates future development of online realtime receivers for multicarrier underwater acoustic communications.

In this paper we develop a fine synchronization algorithm for multiband OFDM transmission in the presence of frequency selective channels. This algorithm is based on maximum a posteriori (MAP) joint timing and channel estimation that incorporates channel statistical information, leading to considerable performance enhancement relative to existing maximum likelihood (ML) approaches. We carry out a thorough performance analysis of the fine timing algorithm, and link the diversity concept widely used in data communications to the timing performance. We show that the probability of the timing offset equal to or larger than Δ taps has a diversity order of NBmin(Δ,L) in Rayleigh fading channels, where NBis the number of subbands and L is the number of channel taps. This result reveals that the timing estimate is very much concentrated around the true timing as the signal to noise ratio (SNR) increases. Our simulations confirm the theoretical analysis, and also demonstrate the robustness of the proposed timing algorithm against model mismatches in a realistic UWB indoor channel.

The impact of delayed sensor alarm data upon a diagnostic inference engine appears not to be well appreciated. In this paper, we illustrate the effect of sensor latency, and we propose an inference approach to obviate it.

This correspondence presents an approach to the detection and isolation of component failures in large-scale systems. In the case of sensors that report at rates of 1 Hz or less, the algorithm can be considered real time. The input is a set of observed test results from multiple sensors, and the algorithm's main task is to deal with sensor errors. The sensors are assumed to be of threshold test (pass/fail) type, but to be vulnerable to noise, in that occasionally true failures are missed, and likewise, there can be false alarms. These errors are further assumed to be independent conditioned on the system's diagnostic state. Their probabilities, of missed detection and of false alarm, are not known a priori and must be estimated (ideally along with the accuracies of these estimates) online, within the inference engine. Further, recognizing a practical concern in most real systems, a sparsely instantiated observation vector must not be a problem. The key ingredients to our solution include the multiple-hypothesis tracking philosophy to complexity management, a Beta prior distribution on the sensor errors, and a quickest detection overlay to detect changes in these error rates when the prior is violated. We provide results illustrating performance in terms of both computational needs and error rate, and show its application both as a filter (i.e., used to "clean" sensor reports) and as a standalone state estimator.

To achieve reliable packet transmission over a wireless link without feedback, we propose a layered coding approach that uses error-correction coding within each packet and erasure-correction coding across the packets. This layered approach is also applicable to an end-to-end data transport over a network where a wireless link is the performance bottleneck. We investigate how to optimally combine the strengths of error- and erasure-correction coding to optimize the system performance with a given resource constraint, or to maximize the resource utilization efficiency subject to a prescribed performance. Our results determine the optimum tradeoff in splitting redundancy between error-correction coding and erasure-correction codes, which depends on the fading statistics and the average signal to noise ratio (SNR) of the wireless channel. For severe fading channels, such as Rayleigh fading channels, the tradeoff leans towards more redundancy on erasure-correction coding across packets, and less so on error-correction coding within each packet. For channels with better fading conditions, more redundancy can be spent on error-correction coding. The analysis has been extended to a limiting case with a large number of packets, and a scenario where only discrete rates are available via a finite number of transmission modes.

Probabilistic multi-hypothesis tracking (PMHT) is an algorithm for tracking multiple targets when measurement-to- target assignments are unknown and must be jointly estimated with the target tracks. Multi-frame assignment PMHT (MF- PMHT) is an algorithm designed to mitigate some performance problems associated with PMHT. In MF-PMHT, the PMHT algorithm is applied to multi-frame sequences in the last L frames of data and considers the set of all possible measurement sequences. While effective in improving tracking performance compared to PMHT, performance of the original MF-PMHT degrades when the target single-frame detection probability is non-unity. This is because missed detections are not considered in the multi-frame sequences. A new MF-PMHT implementation is derived in this paper which explicitly considers missed detections in the multi-frame sequences. Performance of this MF-PMHT is compared to the original MF-PMHT algorithm as well as to a Homothetic PMHT. Simulation results indicate that the new MF- PMHT algorithm performs the same as the original algorithm when there are no missed detections and also performs better than the alternative algorithms considered when there are missed detections.

The cardinalized probability hypothesis density (CPHD) filter is a recursive Bayesian algorithm for estimating multiple target states with varying target number in clutter. In particular, the Gaussian mixture variant (GMCPHD) for linear, Gaussian systems is a candidate for real time multi target tracking. The present work addresses the following three issues: (i) we show the equivalence between the GMCPHD filter and the standard Multi Hypothesis Tracker (MHT) in the case of single targets; (ii) using a Gaussian sum approach, we extend the GMCPHD filter by employing digital road maps for road constraint targets. The utilization of such external information leads to more precise tracks and faster and more reliable target number estimates; (iii) we model the effect of Doppler blindness by a target state dependent detection probability, leading to more stable target number estimation in the case of low Doppler targets.

As part of the track-management process it is necessary to know when new tracks start and when old ones die. Thus some knowledge of the theory of detection of statistical changes is important, and the purpose of this talk is to give the audience some overview of what is available. Specifically, we shall discuss sequential testing, this information necessary as a precursor to an understanding of the procedure and performance of the Page "quickest" detection of statistical changes. We shall also discuss the Shiryaev test, which represents a more Bayesian point of view. We shall present applications to detection of target spawn based on monopulse radar data, and also to the track management of sonar targets whose aspect-dependent SNR is modeled as hidden Markov - the suboptimality of Page procedures for detection of a changes between HMMs is rather surprising.

In active sonar tracking applications, targets frequently undergo fading detection performance in which the target's detection probability can shift suddenly between high and low values. Using a multistatic active sonar problem, we examine the performance of sequential track termination tests where target detections are based on an underlying hidden Markov model (HMM) with high and low detection states. We show that the Page test is not optimal in this problem and that a K/N track termination rule yields better performance. Further we show that a Bayesian sequential test (the Shiryaev test) yields dramatic performance improvements over both the K/N rule and the Page test.

We consider the problem of DOA (direction of arrival) estimation of an acoustic wavefront by a wireless sensor network (WSN) within the SENMA architecture (a mobile agent (MA) repeatedly polls the sensors lying inside its field of view). The sensors, which are random in number and location, are DOA-blind and simply emit a pulse train synchronized to the acoustic event's passage; taken in aggregate, however, the MA can exploit its non-isotropic field of view (FOV) to infer an accurate DOA. In this paper we (i) use a more realistic "soft" FOV; (ii) account for multiple sources; and (iii) suggest a strategy for the MA. We find that the presence of more than one source can improve DOA estimation, and also that an optimal strategy for the MA squints near the expected DOA, as opposed to directly at it.

We introduce a likelihood based multiple access (LBMA) communication/estimation scheme for nonrandom parameter estimation in wireless sensor networks with additive multiple access channels. Constraining the system in terms of energy and allowing the available number of degrees of freedom to scale as nα, 0.5 <; α <; 1, we prove that LBMA is asymptotically efficient. Thus, the new scheme is appropriate for large networks. LBMA is, in addition, simple to implement and relies upon an intuitive approach.

Prognostics, which refers to the inference of an expected time to failure for a system, is made difficult by the need to track and predict the trajectories of real-valued system parameters over essentially unbounded domains and by the need to prescribe a subset of these domains in which an alarm should be raised. In this paper, we propose an idea, one whereby these problems are avoided: Instead of physical system or sensor parameters, a vector corresponding to the failure probabilities of the system's sensors (which of course are bounded within the unit hypercube) is tracked. With the help of a system diagnosis model, the corresponding fault signatures can be identified as terminal states for these probability vectors. To perform tracking, Kalman filters and interacting multiple-model estimators are implemented for each sensor. The work that has been completed thus far shows promising results in both large-scale and small-scale systems, with the impending failures being detected quickly and the prediction of the time until this failure occurs being determined accurately.

Sonar tracking using measurements from multistatic sensors has shown promise: there are benefits in terms of robustness, complementarity (covariance-ellipse intersection) and of course simply due to the increased probability of detection that naturally accrues from a well-designed data fusion system. It is not always clear what the placement of the sources and receivers that gives the best fused measurement covariance for any target-or at least for any target that is of interest-might be. In this paper, we investigate the problem as one of global optimization, in which the objective is to maximize the information provided to the tracker. We assume that the number of sensors is known, so that the optimization is done in a continuous space. We consider "barrier" scenario and numbers of sensors. The strong variability of target strength as a function of aspect is integral to the cost function we optimize. Doppler information is not discarded when constant frequency (Doppler-sensitive) waveforms are available. Numerical results are given, these suggesting that certain sensor geometries should be used

We consider in this paper local sensor quantizer design for large-scale bandwidth and/or energy constrained wireless sensor networks (WSNs) operating in fading channels. In particular, under the Neyman-Pears on framework, we address the design of binary local sensor quantizers for a binary hypothesis problem in the asymptotic regime where the number of sensors is large. Motivated by the sensor censoring idea for reduced communication rate, each sensor either transmits `1' to a fusion center or remains silent. By adopting energy detector as the fusion rule, we develop a procedure to obtain local sensor threshold that maximizes the Kullback-Leibler distance of the distributions of the fusion statistic under the two hypotheses. The proposed quantizer design is well suited for the emerging large scale resource-constrained WSNs applications. Numerical results based on Gaussian and exponential observations are presented to demonstrate the design procedure

In this paper, a previously introduced data mining technique, utilizing the mean field Bayesian data reduction algorithm (BDRA), is extended for use in finding unknown data clusters in a fused multidimensional feature space. In the BDRA the modeling assumption is that the discrete symbol probabilities of each class are a priori uniformly Dirichlet distributed, and where the primary metric for selecting and discretizing all relevant features is an analytic formula for the probability of error conditioned on the training data. In extending the BDRA for this application, notice that its built-in dimensionality reduction aspects are exploited for isolating and automatically sorting out and mining all points contained in each unknown data cluster. To illustrate performance, results are demonstrated using simulated data containing multiple clusters, and where the fused feature space contains relevant classification information

The MLPDA is based on maximizing statistical likelihood according to a precise model in which there is no process noise. The PMHT (probabilistic multi-hypothesis tracker) provides an alternative perspective: each contact may be taken as independent and a-priori equally-equipped to be target-generated. Our results indicate that the MLPMHT is the better tracker in multi-static data. A further advantage of the MLPMHT is that optimal data association with multiple targets is easily incorporated, whereas in the MLPDA it is approximated by excision of measurements that are "taken" by previously-discovered targets. In this paper we apply the MLPMHT and MLPDAF to several data-sets from the MSTWG (multi-static tracking working group) library: two synthetic and two real ones from NURC, plus one from ARL/UT. We also compare the ML trackers to the IMMPDAFAI, a tracker with no "depth" to its assignments: it is found that the IMMPDAFAI is not able to track effectively in such noisy data. Finally, we report on a new genetic implementation of the MLPMHT

In this paper, we introduce an advanced software tool for modeling asymmetric threats, the Adaptive Safety Analysis and Monitoring (ASAM) system. The ASAM system is a hybrid model-based system for assisting intelligence analysts to identify asymmetric threats, to predict possible evolution of the suspicious activities, and to suggest strategies for countering threats. It employs a novel combination of hidden Markov models (HMMs) and Bayesian networks (BNs) to compute the likelihood that a certain threat exists. It provides a distributed processing structure for gathering, sharing, understanding, and using information to assess and predict adversary network states. We illustrate the capabilities of the ASAM system by way of application to a hypothetical model of development of nuclear weapons program by an unknown hostile country. The simulation results show that the ASAM system is able to detect the modeled pattern with a high performance (greater than 95% clutter suppression capability).

For the case of a single resolved target, monopulse-based radar sub-beam angle and sub-bin range measurements carry errors that are approximately Gaussian with known covariances, and hence, a tracker that uses them can be Kalman based. However, the errors accruing from extracting measurements for multiple unresolved targets are not Gaussian. We therefore submit that to track such targets, it is worth the effort to apply a nonlinear (non-Kalman) filter. Specifically, in this letter, we propose a particle filter that operates directly on the monopulse sum/difference data for two unresolved targets. Significant performance improvements are seen versus a scheme in which signal processing (measurement extraction from the monopulse data) and tracking (target state estimation from the extracted measurements) are separated.

We develop optimal probability loading for parallel binary channels, subject to a constraint on the total probability of sending ones. The distinctions from the waterfilling power loading for parallel Gaussian channels, particularly the latter's "dropping" of poor-quality channels, are highlighted. The only binary-input binary-output channel that is never dropped is the Z-channel.

A collaboration scheme for information integration among multiple agencies (and/or various divisions within a single agency) is designed using hierarchical and hybrid Bayesian networks (HHBNs). In this scheme, raw information is represented by transactions (e.g., communication, travel, and financing) and information entities to be integrated are modeled as random variables (e.g., an event occurs, an effect exists, or an action is undertaken). Each random variable has certain states with probabilities assigned to them. Hierarchical is in terms of the model structure and hybrid stems from our usage of both general Bayesian networks (BNs) and hidden Markov models (HMMs, a special form of dynamic BNs). The general BNs are adopted in the top (decision) layer to address global assessment for a specific question (e.g., "Is target A under terrorist threat?" in the context of counterterrorism). HMMs function in the bottom (observation) layer to report processed evidence to the upper layer BN based on the local information available to a particular agency or a division. A software tool, termed the adaptive safety analysis and monitoring (ASAM) system, is developed to implement HHBNs for information integration either in a centralized or in a distributed fashion. As an example, a terrorist attack scenario gleaned from open sources is modeled and analyzed to illustrate the functionality of the proposed framework.

We investigate an adaptive MIMO-OFDM system with a feedback link that can only convey a finite number of bits. We consider three different transmitter configurations: i) beamforming applied per OFDM subcarrier, ii) precoded spatial multiplexing applied per subcarrier, and iii) precoded orthogonal space time block coding applied per subcarrier. Depending on the channel realization, the receiver selects the optimal beamforming vector or precoding matrix from a finite-size codebook on each subcarrier, and informs the transmitter through finite-rate feedback. Exploiting the fact that the channel responses across OFDM subcarriers are correlated, we propose two methods to reduce the amount of feedback. One is recursive feedback encoding that selects the optimal beamforming/precoding choices sequentially across the subcarriers, and adopts a smaller-size time-varying codebook per subcarrier depending on prior decisions. The other is trellis-based feedback encoding that selects the optimal decisions for all subcarriers at once along a trellis structure via the Viterbi algorithm. Our methods are applicable to different transmitter configurations in a unified fashion. Simulation results demonstrate that the trellis-based approach outperforms the recursive method as well as an existing interpolation-based alternative at high signal-to-noise-ratio, as the latter suffers from "diversity loss"

We consider a MIMO-OFDM system with transmit beamforming applied on each OFDM subcarrier, where each beamforming vector is drawn from a codebook with finite size. Depending on the channel realization, the receiver decides the optimal beamforming vector on each subcarrier, and informs the transmitter through a rate-limited feedback link. Exploiting the fact that the channel responses across OFDM subcarriers are correlated, we propose two methods to reduce the amount of needed feedback. One is recursive feedback encoding that selects the optimal beamforming vectors sequentially across the subcarriers, and adopts a smaller-size time-varying codebook per subcarrier depending on prior decisions. The other is trellis-based feedback encoding that selects the optimal beamforming vectors for all subcarriers at once along a trellis structure via the A. The trellis-based feedback encoding outperforms the recursive feedback encoding at the expense of encoding complexity at the receiver. Simulation results demonstrate that our trellis-based approach outperforms an existing interpolation-based alternative, as the latter incurs diversity loss at high SNR.

Quantization for estimation is explored for the case that it must be performed jointly with data association; that is, the case in which measurements are of uncertain origin. Data association requires some sort of gating of distributed observations, and a censoring strategy is proposed. Several quantization philosophies are explored, specifically uniform quantization, uniform quantization with measurement exchangeability incorporated (the "type" method), and uniform quantization of sorted measurements. It is shown, perhaps surprisingly, that the third scheme preserves more information that may be useful for estimation; and a simple procedure for optimal fused estimation based on this third scheme is given. Interestingly, when compared in terms of rate-distortion curves, the schemes two and three perform similarly; their censored versions offer further improvement in performances due to the uncertain-origin property of the measurements.

Following the SENMA concept, we consider a wireless network of very dumb and cheap sensors, polled by a travelling "rover". Sensors are randomly placed and isotropic: individually they have no ability to resolve the direction of arrival (DOA) of an acoustic wave. We assume that the communication load must be as limited as possible, so that these times cannot be communicated to the rover. Notwithstanding the lack of transmission of arrival times and the lack of DOA resolution ability of the individual sensors, DOA estimation is possible, and asymptotic efficiency becomes closely approximated after a reasonable number of rover snapshots. Key features are the directionality of the rover antenna, the area it surveys, and the average number of sensors inside that area, as accorded a Poisson distribution.

The probabilistic association algorithm (PDA) is proposed as a quasi-optimal solution for synchronous overloaded CDMA detection. Overloaded CDMA is useful in applications in which the band is a limited resource and more users are to be conveyed on the same channel. The PDA algorithm, already successfully applied to underloaded CDMA, is extended to the more difficult overloaded CDMA problem. PDA uses dynamic soft updates for the a posteriori probabilities and it is derived under the Gaussian assumption for the superposition of multiuser interference and Gaussian noise. A discussion on the separability of the two-class problem suggests how a dynamic PDA (D-PDA) may solve the problem more effectively in comparison to a fixed-order PDA (F-PDA). Performance results are reported in this paper and show that D-PDA can provide good decoding with limited computational complexity with the bit error rate going to zero as the signal-to-noise ratio increases.

A common model for sonar clutter is of the transmitted signal convolved with a colored Gaussian process relating to the sea-bottom profile. This environment becomes strongly non-Gaussian if there are multiple realizations - the univariate statistics remain Gaussian, but the joint probability density function (PDF) is not. It turns out that the gains versus a Gaussian-assumption can be substantial.

The purpose of this paper is to analytically demonstrate the effect that the overall quantization, M, has on the relative performance of the BDRA (Bayesian Data Reduction Algorithm). In particular, it is of interest to show with a straightforward data model how the dimensionality reduction aspects of the BDRA improves overall classification performance on the training data. In other words, it is analytically shown the conditions under which the probability of error, as computed on the data, is lower after dimensionality reduction. Results are illustrated by plotting the analytical probability of error as a function of the number of data merged in the same discrete cell. An interesting result demonstrates that data merged under different classes in the same discrete cell can improve classification performance.

Following the SENMA concept, we consider a wireless network of very dumb and cheap sensors, polled by a travelling "rover". Sensors are randomly placed and isotropic: Individually, they have no ability to resolve the direction of arrival (DOA) of an acoustic wave. However, they do observe the wavefront at different times. We assume that the communication load must be as limited as possible, so that these times cannot be communicated to the rover. Notwithstanding the lack of transmission of arrival times and the lack of DOA resolution ability of the individual sensors, DOA estimation is possible and simple, and asymptotic efficiency becomes closely approximated after a reasonable number of rover snapshots. Key features are the directionality of the rover antenna, the area it surveys, and the average number of sensors inside that area, as accorded a Poisson distribution.

Distributed detection has been intensively studied in the past. In this correspondence, we consider the design of local decision rules in the presence of nonideal transmission channels between the sensors and the fusion center. Under the conditional independence assumption among multiple sensor observations, we show that the optimal local decisions that minimize the error probability at the fusion center amount to a likelihood-ratio test (LRT) given a particular constraint on the fusion rule. This constraint turns out to be quite general and is easily satisfied for most sensible fusion rules. A design example using a parallel sensor fusion structure with binary-symmetric channels (BSCs) between local sensors and the fusion center is given to illustrate the usefulness of the result in obtaining optimal thresholds for local sensor observations. The study that incorporates the transmission channel in the sensor system design may have potential applications in the emerging field of wireless sensor networks.

Distributed binary quantizer design for sensor nets tasked with a hypothesis testing problem is considered in this paper. Allowing for non-ideal transmission channels, we show that under the conditional independence assumption, the optimum binary quantizer, in the sense of minimizing the error probability, should operate on the likelihood ratio (LR) of the local sensor observations. Necessary conditions for optimality are derived to facilitate finding of optimal LRT thresholds through an iterative algorithm. A design example with binary symmetric channels between local sensors and the fusion center is given to illustrate how the results can be applied in sensor signaling design.

The probabilistic data association (PDA) method for multiuser detection (MUD) over synchronous CDMA channels is extended to the signal detection problem in V-BLAST systems. Computer simulations show that the algorithm has an error probability that is significantly lower than that of the V-BLAST optimal order detector and has a computational complexity that is cubic in the number of transmit antennas.

A complex sphere decoding algorithm is presented for signal detection in V-BLAST systems, which has a computational cost that is significantly lower than that of the original complex sphere decoder (SD) for a wide range of SNRs. Simulation results on a 64-QAM system with 23 transmit and 23 receive antennas at an SNR per bit of 24 dB show that the new sphere decoding algorithm obtains the ML solution with an average cost that is at least 6 times lower than that of the original complex SD. Further, the new algorithm also shows robustness with respect to the initial choice of sphere radius.

A common model for sonar clutter is that of the transmitted signal convolved with a colored Gaussian process relating to the sea-bottom profile. Rather surprisingly, this noise becomes strongly non-Gaussian if there are multiple realizations and if a realistic random phase is introduced - the univariate statistics remain Gaussian, but the joint probability density function is not. In this letter, we explore this behavior and we develop optimal detection statistics for a "two-look" situation. It turns out that the gains over a naive assumption of Gaussianity can be substantial.

In this letter, we compare the complexity and efficiency of several methods used for multiuser detection in a synchronous code-division multiple-access system. Various methods are discussed, including decision-feedback (DF) detection, group decision-feedback (GDF) detection, coordinate descent, quadratic programming with constraints, space-alternating generalized EM (SAGE) detection, Tabu search, a Boltzmann machine detector, semidefinite relaxation, probabilistic data association (PDA), branch and bound (BBD), and the sphere decoding (SD) method. The efficiencies of the algorithms, defined as the probability of group detection error divided by the number of floating point computations, are compared under various situations. Of particular interest is the appearance of an "efficient frontier" of algorithms, primarily composed of DF detector, GDF detector, PDA detector, the BBD optimal algorithm, and the SD method. The efficient frontier is the convex hull of algorithms as plotted on probability of error versus computational demands axes: algorithms not on this efficient frontier can be considered dominated by those that are.

A fast optimal algorithm based on the branch-and-bound (BBD) method is proposed for the joint detection of binary symbols of K users in a synchronous code-division multiple-access channel with Gaussian noise. Relationships between the proposed algorithms (depth-first BBD and fast BBD) and both the decorrelating decision-feedback (DF) detector and sphere-decoding algorithm are clearly drawn. It turns out that decorrelating DF detector corresponds to a "one-pass" depth-first BBD; sphere decoding is, in fact, a type of depth-first BBD, but one that can be improved considerably via tight upper bounds and user ordering, as in the fast BBD. A fast "any-time" suboptimal algorithm is also available by simply picking the "current-best" solution in the BBD method. Theoretical results are given on the computational complexity and the performance of the "current-best" suboptimal solution.

We present an approach for the joint segmentation and classification of a time series. The segmentation is on the basis of a menu of possible statistical models: each of these must be describable in terms of a sufficient statistic, but there is no need for these sufficient statistics to be the same, and these can be as complex (for example, cepstral features or autoregressive coefficients) as fits. All that is needed is the probability density function (PDF) of each sufficient statistic under its own assumed model--presumably this comes from training data, and it is particularly appealing that there is no need at all for a joint statistical characterization of all the statistics. There is similarly no need for an a-priori specification of the number of sections, as the approach uses an appropriate penalization of an over-zealous segmentation. The scheme has two stages. In stage one, rough segmentations are implemented sequentially using a piecewise generalized likelihood ratio (GLR); in the second stage, the results from the first stage (both forward and backward) are refined. The computational burden is remarkably small, approximately linear with the length of the time series, and the method is nicely accurate in terms both of discovered number of segments and of segmentation accuracy. A hybrid of the approach with one based on Gibbs sampling is also presented; this combination is somewhat slower but considerably more accurate.

For detection of a permanent and precisely-modeled change in distribution of iid observations, Page's test is optimal. When employed to detect a transient change between known distributions, Page's test is a generalised likelihood ratio test (GLRT). However, the situation of interest here is of transient of unknown scale parameter: a fixed Page procedure tuned to a "short-and-loud" signal uses heavy biasing and low threshold, a combination ill-suited to a "long-but-quiet" signal. We offer an easy alternative to the standard Page: it uses a constant bias and a time-varying threshold. The idea is that the above short signals are detected quickly before post-termination data has a chance to refute them; and that evidence for a long signal is allowed to build, rather than being summarily discarded too early. Results show that the approach works quite well.

A fast optimal algorithm based on the branch and bound (BBD) method is proposed for the joint detection of binary symbols of K users in a synchronous code-division multiple access (CDMA) channel with Gaussian noise. Relationships between the proposed algorithms (depth-first BBD and fast BBD) and both the decorrelating decision feedback (DF) detector and sphere decoding (SD) algorithm are clearly drawn. It turns out that decorrelating DF detector corresponds to a "one-pass" depth-first BBD; sphere decoding is in fact a type of depth-first BBD, but one that can be improved considerably via tight upper bounds and user ordering as in our fast BBD.

In this paper, classification performance results are demonstrated for various data sets found at the University of California at Irvine's (UCI) Repository of machine learning databases. In this case, emphasis is placed on illustrating the combined effect that both feature level and classifier decision fusion has on improving overall performance for each of the data sets. Several different types of classifiers are trained using the UCI data sets. Results are shown by estimating the probability of error on independent evaluation data using cross-validation. Classifier fusion is based on majority voting and the Mean-Field BDRA. Results demonstrate that for a given data set relative performance of the various classifier types differs greatly, and that the estimated probability of error for the fused classifier, based on the Mean-Field BDRA, is lower than the best performing individual feature based classifier.

The probabilistic data association (PDA) method is extended to multiuser detection over symbol-asynchronous code-division multiple access (CDMA) communication channels. A direct extension as well as a sliding window processing method are introduced. While achieving near-optimal performance with O(K/sup 3/) computational complexity in synchronous CDMA, K being the number of users, it is shown that, in asynchronous CDMA, the probability of group detection error of the proposed PDA method is very close to the performance lower bound provided by an ideal clairvoyant optimal detector, and the computational complexity is only marginally increased to O([h/s]K/sup 3/) per symbol, where h and s are the width and the sliding rate of the processing window, respectively. Due to the outstanding performance of the PDA detector in heavily overloaded asynchronous systems, it is observed that an optimally designed synchronous system can be easily outperformed by an arbitrarily designed asynchronous system. Hence, it is proposed to use asynchronous transmission deliberately, even when synchronous transmission is possible - asynchronous is better than synchronous!.

A strategy of user ordering and time labeling for a decision feedback (DF) detector in asynchronous code-division multiple-access communications is proposed and is proved to be optimal for the ideal DF detector. The proposed algorithm requires O(K/sup 4/) offline operations, where K is the number of users. Although error propagation complicates the analysis of the actual DF detector, computer simulations show that, with the proposed user ordering and time labeling, the performance of an actual DF detector overlays the theoretical bound in most cases.

The group decision feedback (GDF) detector is studied in this letter. Given the maximum group size, a grouping algorithm is proposed. It is shown that the proposed grouping algorithm maximizes the symmetric energy of the multiuser detection system. Furthermore, based on a set of lower bounds on asymptotic group effective energy (AGEE) of the GDF detector, it is shown that the proposed grouping algorithm, in fact, maximizes the AGEE lower bound for every group of users. The theoretical analysis of the grouping algorithm enables the offline estimation of the computational cost and the performance of a GDF detector. The computational complexity of a GDF detector is exponential in the largest size of the groups. Simulation results are presented to verify the theoretical conclusions. The results from this letter can be applied to the decision feedback detector by setting the maximum group size to one.

In this paper, a method of classification referred to as the Bayesian data reduction algorithm (BDRA) is developed. The algorithm is based on the assumption that the discrete symbol probabilities of each class are a priori uniformly Dirichlet distributed, and it employs a "greedy" approach (which is similar to a backward sequential feature search) for reducing irrelevant features from the training data of each class. Notice that reducing irrelevant features is synonymous here with selecting those features that provide best classification performance; the metric for making data-reducing decisions is an analytic for the probability of error conditioned on the training data. To illustrate its performance, the BDRA is applied both to simulated and to real data, and it is also compared to other classification methods. Further, the algorithm is extended to deal with the problem of missing features in the data. Results demonstrate that the BDRA performs well despite its relative simplicity. This is significant because the BDRA differs from many other classifiers; as opposed to adjusting the model to obtain a "best fit" for the data, the data, through its quantization, is itself adjusted.

A strategy for user ordering and time labeling for a decision feedback (DF) detector in asynchronous Code-Division Multiple Access (CDMA) communications is discussed. Ordering and labeling would at first appear to be of a complexity exponential in K, the number of users. Surprisingly, optimal sequencing requires only O(K4) operations, and is needed only once per packet: it is thus a cheap way to obtain an often marked improvement in performance, compared to power-ordering and chronological labeling.

Two new algorithms are presented for the segmentation of a white Gaussian-distributed time series having unknown but piecewise-constant variances, a problem for which only dynamic-programming (DP) approaches have. generally been suitable. The first “Sequential/MDL” includes a rough parsing via the GLR, a penalization of busy segmentations via MDL, and a refinement. The second “Gibbs Sampling” approach uses Monte Carlo ideas. From simulation it appears that both schemes are very accurate in terms of their segmentation; but that the Sequential/MDL approach is orders of magnitude lower in its computational needs both than DP or Gibbs, with Gibbs preferable to DP in this regard. The Gibbs approach can, however, be useful and efficient as a final post-processing step.

The selection of a proper transmitted sonar waveform is critical for target detection and parameter estimation. The focus here is on constant-frequency (CF) and chirp (LFM) waveforms, and it is readily seen that these have characteristics that are complementary, both with respect to their accuracies and in regard to their sensitivity to the blind zero-Doppler ridge. We hence explore the use of fused information from different waveforms: a fused system is not only more robust, but is also in some cases outright preferable.

A probabilistic data association (PDA) method is proposed in this paper for multiuser detection over synchronous code division multiple access (CDMA) communication channels. PDA models the undecided user signals as binary random variables. By approximating the interuser interference (IUI) as Gaussian noise with an appropriately elevated covariance matrix, the probability associated with each user signal is iteratively updated. Computer simulations show that the system usually converges within 3-4 iterations, and the resulting probability of error is very close to that of the optimal maximum likelihood (ML) detector. Further modifications are also presented to significantly reduce the computational cost.

The sequential group detection technique is a generalization of the decision feedback detector: in the latter, users are successively demodulated and cancelled one-by-one, while in the former this basic operation is performed simultaneously on groups of users. The computational complexity of a group decision feedback detector (GDFD) is exponential in the largest size of the groups; thus instead of using the partition of users as design parameters, choosing the "maximum group size" is more reasonable in practice. Given the maximum group size, a grouping algorithm is proposed. It is shown that the proposed grouping algorithm maximizes the asymptotic symmetric energy (ASE) of the multiuser detection system. Furthermore, based on a set of lower bounds on the asymptotic group symmetric energy (AGSE) of the GDFD, it is shown that the proposed grouping algorithm, in fact, maximizes the AGSE lower bound for every group of users. Together with a fast computational method based on branch-and-bound, the theoretical analysis of the grouping algorithm enables the offline estimation of the computational cost and the performance of GDFD. Simulation results are presented to verify the theoretical results.

A power-law statistic operating on DFT data has emerged as a basis for a remarkably robust detector of transient signals having unknown structure, location and strength. In this paper we offer a number of improvements to the original power-law detector. Specifically, the power-law detector requires that its data be pre-normalized and spectrally white; a CFAR and self-whitening version is developed and analyzed. Further, it is noted that transient signals tend to be contiguous both in temporal and frequency senses, and consequently new power-law detectors in the frequency and the wavelet domains are given. The resulting detectors offer exceptional performance and are extremely easy to implement. There are no parameters to tune, and they may be considered "plug-in" solutions to the transient detection problem.

Detecting signals that are long, weak, and narrowband is a well known and important problem in acoustic signal processing. In this paper an ad hoc scheme is developed: its stages include the DFT, a multiresolution decomposition in the frequency domain, and a GLRT. The computational load is light, and the performance is remarkably good. This is so not just in the original narrowband situation, but also, due to an inherent adaptivity to the data, in the detection of signals that are relatively broadband in nature. Generalizations are given to CFAR operation in both prewhitened and unwhitened cases, and to the detection of multi-band signals. As regards the last, it is discovered that there is little loss from over-estimating the number of bands.

We (2001) previously showed that for solutions of the binary quadratic programming problem there exists an "efficient frontier" in the performance/speed domain among the algorithms which characterizes the relative performance of each algorithm. Here, in addition to the algorithms implemented previously, the Boltzmann machine, genetic algorithm and space alternating generalized EM (SAGE) receiver are implemented and results are given for much larger scale problems. Simulation results show that these and several other of the proposed methods can significantly outperform the decision feedback detector or its group counterpart.

We (2001) previously showed that for solutions of the binary quadratic programming problem there exists an "efficient frontier" in the performance/speed domain among the algorithms which characterizes the relative performance of each algorithm. Here, in addition to the algorithms implemented previously, the Boltzmann machine, genetic algorithm and space alternating generalized EM (SAGE) receiver are implemented and results are given for much larger scale problems. Simulation results show that these and several other of the proposed methods can significantly outperform the decision feedback detector or its group counterpart.

Binary quadratic programming (BQP) problems arise frequently in digital communication systems where online solutions are required. The multiuser detection (MUD) problem in code division multiple access (CDMA) communications, studied in the paper, is one such example. Due to the NP-hard nature of the BQP problem arising in MUD, only sub-optimal methods with polynomial complexities can be realistically considered. In the paper, a suboptimal algorithm based on the idea of probabilistic data association (PDA) is proposed. By treating the detection parameters as binary random variables, and by approximating the multi-modal Gaussian mixture by a single Gaussian noise, the PDA method provides near-optimal solution with a computational complexity of O(N/sup 3/), where N is the problem size. Several other algorithms for the MUD problem are also considered and compared in terms of computational efficiency and the degree of suboptimality.

The Bayesian data reduction algorithm is applied to a collection of thirty real-life data sets primarily found at the University of California at Irvine's Repository of Machine Learning databases. The algorithm works by finding the best performing quantization complexity of the feature vectors, and this makes it necessary to discretize all continuous valued features. Therefore, results are given by showing the initial quantization of the continuous valued features that yields best performance. Further, the Bayesian data reduction algorithm is also compared to a conventional linear classifier, which does not discretize any feature values. In general, the Bayesian data reduction algorithm outperforms the linear classifier by obtaining a lower probability of error, as averaged over all thirty data sets.

A class of coordinate descent methods is proposed for the joint detection of binary symbols of K users in a synchronous correlated waveform multiple-access (CWMA) channel with Gaussian noise. We consider the detection problem as one of optimizing a quadratic objective function with binary constraints on decision variables. The proposed coordinate descent methods, while still maintaining a low computational complexity, are shown to provide as much as two orders of magnitude improvement in the probability of error, especially in situations where the existing methods do not perform well. The paper concludes with a discussion of how the proposed methods can be further improved.

A model is developed to illustrate the effect that adapting correctly labeled training data with possibly incorrectly labeled data has on classification performance. The model is based on a previously developed model for mislabeled training data that uses the uniform Dirichlet distribution as a noninformative prior on the symbol probabilities of each class. Two versions of the model are developed under different a priori mislabeling assumptions for the data. In the first case, the probability of mislabeling is fixed and known, and in the second, the mislabeling is marginalized out, given it is a priori uniformly distributed from zero to one-half. A formula for the average probability of error is used to illustrate results that are plotted as a function of the quantization complexity, and for varying numbers of adapted mislabeled data. In general, it is shown that even for severe mislabeling, performance improves as more data are adapted to the training set.

In this paper the classical Westland set of empirical accelerometer helicopter data is analyzed with the aim of condition monitoring for diagnostic purposes. The goal is to determine features for failure events from these data, via a proprietary signal processing toolbox, and to weigh these according to a variety of classification algorithms. As regards signal processing, it appears that the autoregressive (AR) coefficients from a simple linear model encapsulate a great deal of information in a relatively few measurements; it has also been found that augmentation of these by harmonic and other parameters can improve classification significantly. As regards classification, several techniques have been explored, among these restricted Coulomb energy (RCE) networks, learning vector quantization (LVQ), Gaussian mixture classifiers and decision trees. A problem with these approaches, and in common with many classification paradigms, is that augmentation of the feature dimension can degrade classification ability. Thus, we also introduce the Bayesian data reduction algorithm (BDRA), which imposes a Dirichlet prior on training data and is thus able to quantify probability of error in an exact manner, such that features may be discarded or coarsened appropriately.

A simple yet effective statistic is proposed for detecting a transient buried in partially unknown ambient noise. The transient model is frequency scattered increased variance observations. We pose the transient detection problem as a homogeneity test and the statistic is derived as the (generalized) likelihood ratio test of overdispersion when the underlying observation sequence follows a double exponential distribution. Numerical testing focuses on the comparison of this scheme with the CFAR power-law detector.

The average probability of error is used to demonstrate the performance of a Bayesian classification test (referred to as the combined Bayes test (CBT)) given the training data of each class are mislabeled. The CBT combines the information in discrete training and test data to intersymbol probabilities, where a uniform Dirichlet prior (i.e., a noninformative prior of complete ignorance) is assumed for all classes. Using this prior it is shown how the classification performance degrades when mislabeling exists in the training data, and this occurs with a severity that depends on the value of the mislabeling probabilities. However, an increase in the mislabeling probabilities are also shown to cause an increase in M/sup */ (i.e., the best quantization fineness). Further, even when the actual mislabeling probabilities are known by the CBT, it is not possible to achieve the classification performance obtainable without mislabeling.

We develop an expression for the minimum extra bandwidth needed for a frequency-division multiple-access (FDMA) system to out perform its code-division (CDMA) counterpart uniformly (that is, for all rate n-tuples) in a Gaussian multiple-access channel (MAC). For equal-power sources, the behavior of this factor is as an iterated logarithm of the number of users; hence it increases slowly yet is unbounded. Asymmetric power cases are also studied and it is shown that the equal power scenario provides the least bandwidth expansion factor assuming constant constraint on total power.

For quickest detection of a permanent change in distribution of otherwise i.i.d. observations Page's test provides the optimal processor. Page's test has also been applied to the detection of transient (i.e. temporary) changes in distribution: it is easy to implement and has reliable performance, but as applied to the transient problem its optimality is questionable. In this paper we offer an alternative to the Page procedure which we call the iterated generalized sequential probability ratio test, or IGSPRT. While Page's test is itself an IGSPRT, its form and performance are constrained by its reliance on constant thresholds and biases. We demonstrate that with these time-varying, markedly increased detection probabilities are possible. The IGSPRT is easiest to understand and motivate in the Gaussian shift-in-mean problem, and we discuss this in detail, but since that problem is of limited practical interest, we also examine the effect of the IGSPRT in a more realistic situation.

Real time monitoring of complex systems requires a smart and efficient inference engine. TEAMS-RT is capable of monitoring up to 1000 tests in real-time. Even so, for larger systems, a centralized solution will be computationally infeasible. Here, we present a lattice architecture of multiple collaborative TEAMS-RTs that can be embedded in the different subsystems of an interconnected system. A signal processing toolkit has been developed to facilitate data acquisition, filtering, feature extraction and test decisions.

Page's (1954) test is optimal for detecting a permanent change in distribution, in the sense that it minimizes the worst case average delay to detection given an average distance between false alarms. When used to detect transient signals, however, it in fact becomes the generalized likelihood ratio test (GLRT). Since a GLRT is in almost all cases ad hoc, Page's test used as such cannot be said to be optimal in any explicit sense. This article discusses the development of the min-max test, via the new ideas of Baygun and Hero (see ibid., vol.41, p.688-703, 1995) for the detection of a transient.

For the problem of weak signal detection, the locally optimum test statistic for a known signal in independent and identically distributed (i.i.d.) noise of probability density function f(/spl middot/) is given. We show that the logistic distribution is the only example for which the locally-optimal nonlinearity has a uniform distribution.

Page's (1954) test is optimal for detecting a permanent change in the distribution, in the sense that it minimizes the average delay to detection given an average distance between false alarms. When used to detect transient signals, however, it in fact becomes the generalized likelihood ratio test (GLRT). Since a GLRT is in almost all cases ad hoc, Page's test used as such cannot be said to be optimal in any explicit sense. The subject of this paper is the development of the min-max test for the detection of a transient.

We introduce a discrete model for classifying a target that combines the information in training and test data to infer about the true symbol probabilities. Two tests are derived given that the symbols are distributed as a multinomial. The robustness of these tests lies in their ability to effectively use all of the information in the training and test data before making a classification decision. This is demonstrated by comparing their performance to a standard hypothesis test for a classification problem involving transmission of quantized data to a fusion center.

A steepest descent gradient algorithm prewhitens the signal received by a uniform planar array. Previously developed methods work only on single line arrays. A novel model facilitates algorithm development by reducing problems dimensionality associated with exact multi-dimensional autoregressive (AR) modeling. The discrete source model, based on a Kronecker product of the received signals between the vertical and horizontal elements of the array, agrees exactly with the classical sinusoidal model. The colored noise source Kronecker product model agrees approximately with a physical geometric one constructed from spherical surface harmonics. The algorithm uses a stacked vector parameterization of the vertical and horizontal AR parameters and optimizes them over a low order whiteness functional. Application of the algorithm with MUSIC demonstrates enhanced performance in terms of angular resolution and detection of low SNR sources. The algorithm allows extensibility and solves the general problem of the three-dimensional volumetric array with arbitrary geometry.

The performance of Page's (1954) test for the detection of a permanent change in distribution is reasonably well understood. However, there are few parallel results on its application to the detection of a temporary (i.e., transient) change, and this is the paper's subject. Specifically, a lower bound on detectability is developed using a quantization approach; and a pair of approximations are presented, one based on a Brownian motion analogy, which yields an upper bound in the Gaussian case, and the other again on quantisation. The correspondence between these and simulation appears good in both Gaussian and non-Gaussian cases with heavier tail probability.

Here we analyze the tracking characteristics of a new data-association/tracking algorithm proposed by Streit and Luginbuhl, the probabilistic multi-hypothesis tracker (PMHT). The algorithm uses a recursive method (known amongst statisticians as the expectation-maximization or EM method) to compute in an optimal way the associations between the measurements and targets. Until now, no comparative performance analysis has been done. We compare the performance of this new scheme to that of a commonly used tracking algorithm, the joint probabilistic data association filter (JPDAF).

It is common signal detection practice to base tests on quantized data and frequently, as in decentralized detection, this quantization is extreme: to a single bit. As to the accompanying degradation in performance, certain cases (such as that of an additive signal model and an efficacy measure) are well-understood. However, there has been little treatment of more general cases. In this correspondence we explore the possible performance loss from two perspectives. We examine the Chernoff exponent and discover a nontrivial lower bound on the relative efficiency of an optimized one-bit quantized detector as compared to unquantized. We then examine the case of finite sample size and discover a family of nontrivial bounds. These are upper bounds on the probability of detection for an unquantized system given a specified quantized performance, given that both systems operate at the same false-alarm rate.

A new daily of constant false alarm rate (CFAR) processors is introduced. An Ll-CFAR forms its noise power estimate by linearly filtering ranked samples from the reference set: the weights of this combination, however, depend not only on the rank, but also on the relative proximity of the sample to the cell under test. From the class of Ll-CFARs may be chosen members that effectively censor spurious targets, members that exhibit impressive control of false alarm in the presence of a clutter edge, and members that are robust against both such inhomogeneities. While the design of such schemes is involved, their implementation is not significantly more burdensome than that of plain order statistic (OS)-CFAR.>

The design of decentralized (or quantized) detection systems requires simultaneous optimization of quantizer mappings and ultimate fusion rule. It is shown that if the likelihood ratios of the unquantized (or raw) observations are independent and contain no point-masses of probability, the optimal test does not randomize; this is so despite the fact that the data to be fused can be considered discrete. The result is a considerable simplification in the design search.>