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.

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.

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.

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.

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.

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