PRIMEX (PRIME-based Graph Encoding and Extraction for Information Fusion) is a novel framework designed to enhance distributed information fusion while minimizing communication overhead and computational complexity. Traditional information graph (IG)-based approaches require frequent synchronization and large-scale graph updates, leading to significant communication demands. PRIMEX overcomes these challenges by encoding information pedigree of state estimates as products of distinct prime numbers, allowing fusion to be performed using lightweight arithmetic operations such as greatest common divisor (GCD) for redundancy removal and least common multiple (LCM) for data integration. This eliminates the need for transmitting complex graph structures and instead leverages prime factorization-based queries to efficiently identify shared information, significantly improving scalability. PRIMEX is particularly well-suited for edge computing environments and decentralized systems, where reducing communication, computation, and memory overhead is crucial. By supporting federated learning principles, PRIMEX enhances system adaptability while preserving data privacy, making it a practical solution for scalable, distributed information fusion in applications such as autonomous systems, multi-agent networks, and large-scale sensing platforms.

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.

This paper deals with the identification of the stochastic Ornstein-Uhlenbeck (OU) process error model, which is characterized by an inverse time constant, and the unknown variances of the process and observation noises. Although the availability of the explicit expression of the log-likelihood function allows one to obtain the maximum likelihood estimator (MLE), this entails evaluating the nontrivial gradient and also often struggles with local optima. To address these limitations, we put forth a sample-efficient global optimization approach based on the Bayesian optimization (BO) framework, which relies on a Gaussian process (GP) surrogate model for the objective function that effectively balances exploration and exploitation to select the query points. Specifically, each evaluation of the objective is implemented efficiently through the Kalman filter (KF) recursion. Comprehensive experiments on various parameter scenarios and sampling intervals corroborate that BO-based estimator consistently outperforms MLE implemented by the steady-state KF approximation and the expectation-maximization algorithm (whose derivation is a side contribution) in terms of root meansquare error (RMSE) and statistical consistency, confirming the effectiveness and robustness of the$\mathbf{B O}$for identification of the stochastic OU process. Notably, the RMSE values produced by the BO-based estimator are smaller than the classical CramérRao lower bound, especially for the inverse time constant, estimating which has been a long-standing challenge. This seemingly counterintuitive result can be explained by the data-driven prior for the learning parameters indirectly injected by BO through the GP prior over the objective function.

The Interacting Multiple Model (IMM) estimator is well accepted as the best algorithm for tracking maneuvering targets, when the computational cost is considered. The IMM estimator includes a model-conditioned estimator for each kinematic model and the switching between modes or models is assumed to be a finite state Markov chain. The two-model configuration of the IMM estimator, the most commonly used version, typically includes either two nearly constant velocity (NCV) motion models or one NCV model and one nearly constant acceleration (NCA) model. In this paper, the design of these two configurations of the IMM estimator is considered. In this case, design refers to the selection of the motion models (i.e., NCV or NCA) and the corresponding process noise variances. The design methods are first considered for single coordinate tracking with measurements of position, and simulation results are given to illustrate the effectiveness of the design methods. Then, the design methods are applied to radar tracking, and simulation results are given to demonstrate the effectiveness of the design methods.

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.

Electro-optical/Infrared (EO/IR) camera systems are commonly used in target detection and tracking applications. Such camera systems typically comprise a suite of sensors such as narrow/wide Field of View (FOV) cameras that provide target-originated angular measurements. To estimate the target position in Cartesian space, existing techniques in literature employ the non-linear measurement mapping from the Focal Plane Array (FPA) to azimuth and elevation space. A common assumption made in using this conversion is that azimuth and elevation measurement errors have the same standard deviation, are uncorrelated and are uniform across the camera’s FOV. This paper presents an approach to derive the azimuth and elevation statistics including the cross-correlation of their errors. This approach converts the raw target measurements and their covariance in the image space (FPA) to the angular space for subsequent use in Cartesian state filtering. This conversion has been validated to be unbiased and consistent, and results show that the Line of Sight (LOS) angle error variances and their correlations are in fact variable, with magnitudes dependent on the target’s location in the FPA. The correct LOS angle covariance matrices should be used in Cartesian state estimation and fusion rather than the assumed constant angle variances and uncorrelated errors between the azimuth and elevation.

In this paper, we develop an approach for measurement-to-track association (M2TA) in the presence of (unknown) camera panning and zooming from drone-captured video. Standard M2TA methods assume that the target motion can be used to predict the “measurement association regions” for the bounding boxes. However, if there is a sudden state change due to camera shift (panning) and zooming, it will lead to incorrect associations and poor tracking results. To solve this, the zoom ratio and panning in 2D coordinates are used to describe the camera motion parameters in each frame. The estimated parameters are obtained by a grid search combined with global assignment or directly solved using the linear least squares method, which is also combined iteratively with assignment. The goal is to achieve correct M2TA by adjusting the predicted measurements using the estimated camera parameters. These “improved” predictions can also be used to update the target state with filtering algorithms. Frames with panning or/and zooming from real data are used to illustrate the effectiveness of the proposed methods and compared with the validation gate method based on inflated covariances.

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.

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.

The problem addressed in this paper is the tracking a maneuvering target in a distributed sensor network using a real-world-motivated fusion configuration. The local node SL receives a track from the remote node SR generated by its Interacting Multiple Model (IMM) estimator, and the “inside information” such as motion models, mode probabilities and mode-conditioned estimates of the remote track is unknown. The local node SL has its own measurements which need to be fused with the remote IMM track. This problem can be solved using an existing technique with the following steps: 1) generate a SL track based on its own measurements; 2) perform Track-to-Track Fusion (T2TF) on SR and SL tracks. This paper will develop an alternative approach to fuse the remote IMM track and the local measurements directly. We called it the IMM Cumulated information Fusion (IMM-CFusion). The IMM-CFusion estimates the cumulated information of the local SLmeasurements with multiple models, and then fuses this cumulated information with the remote IMM track state. The IMM-CFusion shows better performance than the T2TF approach in a test case.

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.

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.

This paper considers the problem of target tracking using an asynchronous multistatic system with unknown transmitter positions. In such a system, the receiver is considered as the own sensor to perform passive tracking. It listens to the signals from at least two non-cooperative transmitters via direct and indirect (bouncing from targets) paths. The transmitters and targets are then tracked based on the measured bearings and the bistatic ranges (derived from the TDOA of the direct and indirect path signals). Since the transmitter positions are unknown, they have to be estimated, and their estimates will contain errors. To cope with these errors, we develop an iterated least squares estimator with covariance inflation (ILS-CI) for track initiation, and apply the covariance inflation filter (CIF) for track update. Four approaches, namely the optimal, simple, covariance inflation (CI) and combined approaches, with different strategies in track initiation and track update, are proposed to solve this tracking problem. Their performances are evaluated through simulation tests.

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

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.

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.

Acoustic propagation delay has not been investigated for a continuous wave multistatic sonar tracking system except for the recent study conducted by Jauffret et al. [4], which estimates the trajectory of a constant velocity target. The results showed that the estimate bias caused by the propagation delay is not negligible, especially for a bistatic system. This paper develops an interacting multiple model unscented Gauss-Helmert filter with numerical Jacobian (IMM-UGHF-NJ) to track a maneuvering target with propagation delay using a bistatic sonar system. The IMM-UGHF-NJ can overcome the two tracking challenges introduced by the delay, namely, implicit state transition model and lack of analytical expression of the Doppler shifted frequency in the measurement model. Simulation tests have been conducted, and the results show that the IMM-UGHF-NJ can reduce the estimation error significantly, especially for fast moving targets.

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.

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.

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.

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.

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.

Summary form only given. The problem of track-to-track association and track fusion has been considered in the literature where the local trackers assume the same target motion model and send their local state estimates to the fusion center on demand. Many issues arise when local trackers use different target motion models or even operate on different target state spaces. In this case, selecting an appropriate track association method at the fusion center is essential to the performance of the overall tracking system. In this paper, we examine several track association methods with different assumptions on the target distribution in a surveillance region. We found that the track association performance can be very different among these methods even when they have the same desired significance level of the correct association probability. We recommend to use the track association method that best approximates the likelihood ratio test with complete knowledge of the target distribution. In addition, existing track fusion techniques have to be modified to account for the model mismatch among some of the local trackers. The track association and fusion problem is illustrated by a two dimensional tracking example with both radar tracks and electronic support measures (ESM) tracks.

Summary form only given. The topic of multisensor tracking has been of interest to researchers for more than 30 years. However, the development and successful fielding of multisensor tracking systems have lagged significantly behind the research activities. In this presentation, a historical perspective of the key algorithmic developments associated with multisensor tracking will be given and their significance will be discussed. The technological advancements that have enabled the recent realizations of multisensor tracking will be discussed along with technological shortfalls that are limiting the realization of better multisensor tracking systems. Some thoughts on the future direction for multisensor tracking will be summarized.

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.

The problem of track-to-track association and track fusion has been considered in the literature where the fusion center has access to multiple track estimates and the associated estimation error covariances from local sensors, as well as their cross covariances. Due primarily to the communication constraints in real systems, some legacy trackers may only provide the local track estimates to the fusion center without any covariance information. In some cases, the local (sensor-level) trackers operate with fixed filter gain and do not have any self assessment of their estimation errors. In other cases, the network conveys a coarsely quantized root mean square (RMS) estimation error of each local tracker. Thus the fusion center needs to solve the track association and fusion problem with incomplete data from legacy local trackers. In this paper a robust track-to-track association and fusion algorithm is described for a distributed tracking system, which accounts for the cross correlation of the estimation error between local tracks in a practical way. Its applicability to real-time and different rate data sources is also discussed by generalizing the algorithms from the existing literature to the case of asynchronous sensors. The problem of track fusion with legacy track sources which lack covariance information is handled by approximating this information through a modified Lyapunov equation. The situation when a coarsely quantized RMS estimation error is available is also discussed. A two-sensor tracking example is used to illustrate the effectiveness of the proposed distributed track fusion algorithm and compared with a centralized interacting multiple model estimator

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.

This paper discusses several theoretical issues related to the score function for the measurement-to-track association/assignment decision in the track oriented version of the multiple hypothesis tracker (MHT). This score function is the likelihood ratio: the ratio of the pdf of a measurement having originated from a track, to the pdf of this measurement having a different origin. The likelihood ratio score is derived rigorously starting from the fully Bayesian (hypothesis oriented) MHT, which is shown to be amenable under some (reasonable) assumptions to the track oriented MHT. The latter can be implemented efficiently using multidimensional assignment. The main feature of a likelihood ratio is the fact that it is a (physically) dimensionless quantity and, consequently, can be used for the association of different numbers of measurements and/or measurements of different dimension. The explicit forms of the likelihood ratio are discussed both for the commonly used Kalman tracking filter, as well as for the interacting multiple model estimator. The issues of measurements of different dimension and different coordinate systems are also discussed.

In tracking targets with less-than-unity probability of detection in the presence of false alarms (FAs), data association-deciding which of the received multiple measurements to use to update each track-is crucial. Most algorithms that make a hard decision on the origin of the true measurement begin to fail as the FA rate increases or with low observable (low probability of target detection) maneuvering targets. Instead of using only one measurement among the received ones and discarding the others, an alternative approach is to use all of the validated measurements with different weights (probabilities), known as probabilistic data association (PDA). This paper presents an overview of the PDA technique and its application for different target tracking scenarios. First, it describes the use of the PDA technique for tracking low observable targets with passive sonar measurements. This target motion analysis is an application of the PDA technique, in conjunction with the maximum-likelihood approach, for target motion parameter estimation via a batch procedure. Then, the PDA technique for tracking highly maneuvering targets and for radar resource management is illustrated with recursive state estimation using the interacting multiple model estimator combined with PDA. Finally, a sliding window (which can also expand and contract) parameter estimator using the PDA approach for tracking the state of a maneuvering target using measurements from an electrooptical sensor is presented.

The focus of this paper is to present the results of our investigation and evaluation of various shared-memory parallelizations of the data association problem in multitarget tracking. The multitarget tracking algorithm developed was for a sparse air traffic surveillance problem, and is based on an Interacting Multiple Model (IMM) state estimator embedded into the (2D) assignment framework. The IMM estimator imposes a computational burden in terms of both space and time complexity, since more than one filter model is used to calculate state estimates, covariances, and likelihood functions. In fact, contrary to conventional wisdom, for sparse multitarget tracking problems, we show that the assignment (or data association) problem is not the major computational bottleneck. Instead, the interface to the assignment problem, namely, computing the rather numerous gating tests and IMM state estimates, covariance calculations, and likelihood function evaluations (used as cost coefficients in the assignment problem), is the major source of the workload. Using a measurement database based on two FAA air traffic control radars, we show that a "coarse-grained" (dynamic) parallelization across the numerous tracks found in a multitarget tracking problem is robust, scalable, and demonstrates superior computational performance to previously proposed "fine-grained" (static) parallelizations within the IMM.

We present a robust scalable parallelization of a multitarget tracking algorithm developed for air traffic surveillance. We couple the state estimation and data association problems by embedding an interacting multiple model (IMM) state estimator into an optimization-based assignment framework. A SPMD distributed-memory parallelization is described wherein the interface to the optimization problem, namely computing the rather numerous gating and IMM state estimates, covariance calculations, and likelihood function evaluations (used as cost coefficients in the assignment problem), is parallelized. We describe several heuristic algorithms developed for the inherent task allocation problem wherein the problem is one of assigning track tasks, having uncertain processing costs and negligible communication costs, across a set of homogeneous processors to minimize workload imbalances. Using a measurement database based on two FAA air traffic central radars, courtesy of Rome Laboratory, we show that near linear speedups are obtainable on a 32-node Intel Paragon supercomputer using simple task allocation algorithms.

In the authors' previous work Oron, Kumar, and Bar-Shalom (1993), they presented a method for precision tracking of a low observable target based on data obtained from imaging sensors. The image was divided into several layers of gray level intensities and thresholded. A binary image was obtained and grouped into clusters using image segmentation techniques. Using the centroid measurements of the clusters, the probabilistic data association filter (PDAF) was employed for tracking the target centroid. In this correspondence, the division of the image into several layers of gray level intensities is optimized by minimizing the Bayes risk. This optimal layering of the image has the following properties: (1) following the segmentation, a closed-form analytical expression is obtained for the noise variance of the centroid measurement based on a single frame; (2) in comparison to the previous paper, the measurement noise variance is smaller by at least a factor of 2, thus improving the performance of the tracker. The usefulness of the method for practical applications is demonstrated by considering a sequence of real target images (a moving car) of about 20 pixels in size in a noisy urban environment where the measurement noise was calculated as having 0.32 pixel RMS value. Filtering with the PDAF further reduces this by a factor of 1.6.>

The problem of target track detection and time delay estimation using cross-correlation of wideband signals has been analyzed. The concepts of target detection and (accurate) localization (TD&L), target detection (TD, with a possibly smeared measurement), and false detection (FD), have been defined in terms of resolution cell exceedances. Receiver operating curves relating to P/sub TD&L/ to P/sub FD/ and P/sub TD/ to P/sub FD/ have been presented. A generalized maximum likelihood estimate of the time delay based on the main peak and spillover cells of the cross-correlation has been presented. The accuracy of this estimate has been derived using the Cramer-Rao lower bound in terms of the resolution cell, signal-to-noise ratio (SNR), and the number of samples per observation interval. This accuracy has been verified via simulations for SNR as low as -6 dB for a 128-sample window.>

The reversion in time of a stochastic difference equation in a hybrid space with a Markovian solution is presented. The reversion is obtained by a martingale approach, which previously led to reverse time forms for stochastic equations with Gauss-Markov or diffusion solutions. The reverse time equations follow from a particular noncanonical martingale decomposition, while the reverse time equations for Gauss-Markov and diffusion solutions followed from the canonical martingale decomposition. The need for this noncanonical decomposition stems from the hybrid state-space situation. Moreover, the nonGaussian discrete-time situation leads to reverse time equations that incorporate a Bayesian estimation step. The latter step is carried out for linear systems with Markovian switching coefficients, and the result is shown to provide the solution to the problem of fixed-interval smoothing. For an application of this smoothing approach to a trajectory with sudden maneuvers, simulation results are given to illustrate the practical use of the reverse time equations obtained.>

The authors present a Markov-chain-based performance evaluation technique for a two-stage sliding-window cascaded logic (2/2*m/n) for track formation in a cluttered environment. The main features of this technique are that it avoids the need for extensive simulations and it is more realistic than previous methods in that it accounts for the variation of the association gate size. The gates are obtained from a Kalman filter and fully account for its transient following the two-point initiation from the first stage of the logic. The proposed technique can also be used to select logic parameters that meet system requirements such as, for example, the true track detection and false track acceptance probabilities.>

A model developed for optimal allocation of sampling resources in a surveillance system designed to enforce certain environmental standards is described. While the presentation is done in the specific context of a wastewater effluent pollution surveillance system, the methodology developed is potentially useful in other environmental areas. The surveillance system considered is one applicable to a finite number of sources, each containing one or more contaminants. A source can be sampled to determine whether any of its contaminants exceeds a maximum allowed value. If such an excess is detected, then the source is said to be in violation. The objective is to allocate the sampling resources for each source during a certain monitoring period such as to minimize a certain performance index, subject to a budget constraint. This performance index is taken as the expected environmental damage due to the undetected violations. The resulting optimization problem, which is of the integer programming type, is shown to be amenable to solution via the method of maximum marginal return.