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Detection and tracking of divers have become an important factor in port protection against underwater intruders. A problem arises from divers with open breathing systems because detections of the air bubbles they produce can mislead the tracking filter and sometimes result in a lost track. In this paper a probabilistic model is developed which reflects the probability that a false measurement originates from the bubbles. The novel contribution of this paper is the integration of this model in the probabilistic data association filter (PDAF) to improve the track continuity. The bubble detections may also cause confusion in the track initiation. To prevent this problem, a clustering method is proposed based on morphological operators which allows tracks to be initialized based on two-point differencing of the cluster centroids from succeeding scans. This morphological clustering method is included in a cell averaging constant false alarm rate (CA-CFAR) detector in such a way that both the point detections and their corresponding clusters can be fed to the tracking filter. These techniques are implemented and applied to real data of two divers, one with an open breathing system and the other with a closed breathing system, operating simultaneously in a coastal area. The real data were recorded from an active 90 kHz narrowband multibeam imaging sonar.

In multisensor tracking systems that operate in a centralized or distributed information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence due to system latencies. In order to avoid either a delay in the output or the need for reordering and reprocessing entire sequences of measurements, such latent measurements have to be processed by the tracking filter as out-of-sequence measurements (OOSM). Recent work developed a 'one-step' procedure for incorporating OOSM with multiple-time-step latency into the tracking filter, which, while suboptimal, was shown to yield results very close to those obtained by reordering and reprocessing an entire sequence of measurements. The counterpart of this problem is the need to remove (revocate) measurements that have already been used to update a track state. This can happen in real-world systems when such measurements are reassigned to another track. Similarly to the problem of update with an OOSM, it is desired to carry out the removal of an earlier measurement without recomputing the track estimate (and the data association) using possibly a long sequence of subsequent measurements one at a time. A one-step algorithm is presented for this problem of removing a multistep OOSM.

When the size of targets is comparable to the range resolution of monopulse radars, these targets should be considered as extended rather than point targets. If several closely-spaced targets fall within the same radar beam and between adjacent matched filter samples in range, the full monopulse information from all of these samples can and should be used to resolve these targets, i.e., estimate the number of targets and their respective angles-of-arrival and ranges. To detect and localize multiple unresolved extended targets, we establish a model for monopulse radar returns from extended objects, and present a maximum likelihood estimator (MLE) to localize the targets. Rissanen's minimum description length (MDL) criterion will be used to decide the number of existing extended objects. We also derive the upper limit on the number of targets and their scattering centers that can be resolved, and we provide necessary conditions for these targets to be uniquely identified. We compare the new extended target monopulse processing scheme with previously developed point-target monopulse techniques in the simulations.

In passive sensor target tracking, there are applications that require converting the angle-only measurements into Cartesian space. Multisensor methods can be used to convert the raw measurements into Cartesian measurements by finding the intersection of lines of sight. This method contains significant nonlinearity in its conversion; therefore, it is subject to corresponding errors such as a conversion bias and an improper covariance. The proposedmethod uses a secondorder Taylor series expansion to accurately account for the conversion nonlinearities. This results in an explicit (noniterative) expression of the Cartesian position based on two line-of-sight measurements in three dimensions. This paper investigates the severity of the conversion biases from nonlinearity and the efficiency of the unbiased conversion with regard to compensating for them. [ABSTRACT FROM AUTHOR]

This paper develops three-dimensional (3D) Cartesian tracking algorithms for a high-resolution wide field of view (FOV) camera surveillance system. This system consists of a network linking multiple narrow FOV cameras side-by-side looking at adjacent areas. In such a multi-camera system, a target usually appears in the FOV of one camera first, and then shifts to an adjacent one. The tracking algorithms estimate target 3D positions and velocities dynamically using the angular information (azimuth and elevation) provided by multiple cameras. The target state (consisting of position and velocity) is not fully observable when it is detected by the first camera only. Once it moves into the FOV of the next camera, the state can then be fully estimated. The main challenge is how to transfer the state information from the first camera to the next one when the target moves across cameras. In this paper, we develop an approach, designated as Cartesian state estimation with full maximum likelihood information transfer (fMLIT), to cope with this challenge. Since the fMLIT consists of an implicit state relationship, the conventional Kalman-like filters (for explicit constraints) are not suitable. We then develop three Gauss-Helmert filters, and test them with simulation data. [ABSTRACT FROM AUTHOR]

Successful track-to-track data association in a multisensor, muititarget scenario is predicated on a proper cost function. The cost function for associating two tracks is well established. This paper investigates different versions of the likelihood that more than two tracks represent the same target. These likelihoods lead to different cost functions for the general track-to-track association problem. Two of the likelihoods are approximations based on ad-hoc extensions of the well-known two-track expression. The next approximation is the generalized likelihood (GL), where the true state is replaced by the maximum likelihood (ML) estimate of the target state in the true likelihood. The final likelihood is derived exactly from a diffuse prior of the target state and is referred to as the diffuse prior likelihood (DPL). This paper reveals the connection between the DPL and GL. The last two likelihood expressions incorporate the cross-track error covariance matrices, which are not readily available in distributed track fusion. Therefore, the paper considers three forms of the DPL or GL: 1) the correlated tracks (CT) form by using the actual cross-covariance matrices, 2) the independent tracks (IT) form by assuming the cross-covariance matrices are zero, and 3) the approximated correlated tracks (ACT) form by approximating the cross-covariance matrices. Simulations compare the performance of all likelihood versions.

Recent advances are described in detecting and estimating the location of more than one target within a single monopulse radar beam. A quickest detection procedure based on sequential processing of the likelihood ratios is used for deciding on a change in the target model as an indication of a newly spawning target.

In this paper the problem of tracking multiple spawning targets with multiple finite-resolution sensors is considered and a new algorithm for measurement-to-track association with possibly unresolved measurements is presented. The goal is to initialize new tracks of spawned targets before they are resolved from the mother platform so that one has the ability to carry out early discrimination when they become resolved. The multiple scan data association problem is first formulated as a multidimensional assignment problem with explicit new constraints for the unresolved measurements. Then the top M hypotheses tracking (TMHT) is presented where the state estimates and their covariances are modified based on the M best hypotheses through the assignment solutions. A modification to the assignment problem is developed that leads to a linear programming (LP) where the optimal solution can be a noninteger in [0, 1]. The fractional optimal solution is interpreted as (pseudo) probabilities over the N - 1 frame sliding window. The best hard (binary) decision assignment solution and the M best via TMHT are compared with the soft decision solution for 2-D tracking scenarios with various sensor configurations. Based on the simulation results, the soft assignment approach has better track maintenance capability than the single best hard assignment and a performance nearly as good as the TMHT. Its computational load is slightly higher than the single best hard assignment but much lighter than TMHT.

We examine large-sample properties of the maximum-likelihood estimator (MLE) in the vicinity of points where the Fisher information measure (FIM) equals zero. Under mild regularity conditions the MLE is asymptotically efficient and therefore lower hounded by the Cramer-Rao lower hound (CRLB) [5], which diverges for such points. When a linear sensor array is used for angle-of-arrival (AOA) estimation, the CRLB diverges as the AOA approaches [tau]/2. We provide new results characterizing the MLE performance in the AOA problem.

Two procedures for validating track estimate obtained using the maximum-likehood probabilistic data association (ML-PDA) algorithm is presented.

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 probability density function (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 MHT (hypothesis oriented, based on combinatorial analysis of the general multitarget problem), which is shown to be amenable under some (reasonable) assumptions to the track-oriented MHT (TOMHT). The latter can be implemented efficiently using multidimensional assignment (MDA). 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 (IMM) estimator. The issues of measurements of different dimension and different coordinate systems together with the selection of certain MHT design parameters--the spatial densities of the false measurements and new targets--are also discussed.

In this paper, multisensor-multitarget tracking performance with bias estimation and compensation is investigated when only moving targets of opportunity are available. First, we discuss the tracking performance improvement with bias estimation and compensation for synchronous biased sensors, and then a novel bias estimation method is proposed for asynchronous sensors with time-varying biases. The performance analysis and simulations show that asynchronous sensors have a slightly degraded performance compared with the 'equivalent' synchronous ones. The bias estimates as well as the corresponding Cramer-Rao lower bound (CRLB) on the covariance of the bias estimates, i.e., the quantification of the available information on the sensor biases in any scenario are also given. Tracking performance evaluations with different sources of biases--offset biases, scale biases, and sensor location uncertainties, are also presented and we show that tracking performance is significantly improved with bias estimation and compensation compared with the target tracking using the original biased measurements. The performance is also close to the lower bound obtained in the absence of biases.

Recently, there have been several new results for an old topic, the Cramer-Rao lower bound (CRLB). Specifically, it has been shown that for a wide class of parameter estimation problems (e.g. for objects with deterministic dynamics) the matrix CRLB, with both measurement origin uncertainty (i.e., in the presence of false alarms or random clutter) and measurement noise, is simply that without measurement origin uncertainty times a scalar information reduction factor (IRF). Conversely, there has arisen a neat expression for the CRLB for state estimation of a stochastic dynamic nonlinear system (i.e., objects with a stochastic motion); but this is only valid without measurement origin uncertainty. The present paper can be considered a marriage of the two topics: the clever Riccati-like form from the latter is preserved, but it includes the IRF from the former. The effects of plant and observation dynamics on the CRLB are explored. Further, the CRLB is compared via simulation to two common target tracking algorithms, the probabilistic data association filter (PDAF) and the multi-frame (N-D) assignment algorithm.

The special feature of the interacting multiple model (IMM) estimator that distinguishes it from other suboptimal multiple model (MM) estimators is the 'mixing/interaction' between its 'mode-matched' base state filtering modules at the beginning of each cycle. This note shows that the same feature is exactly what it has in common with the optimal estimator for hybrid (MM) systems and this can be seen as the main reason for its success.

In most conventional tracking systems, only the target kinematic information from, for example, a radar or sonar or an electro-optical sensor, is used in measurement-to-track association. Target class information, which is typically used in postprocessing, can also be used to improve data association to give better tracking accuracy. The use of target class information in data association can improve discrimination by yielding purer tracks and preserving their continuity. In this paper, we present the simultaneous use of target classification information and target kinematic information for target tracking. The approach presented integrates target class information into the data association process using the 2-D (one track list and one measurement list) as well as multiframe (one track list and multiple measurement lists) assignments. The multiframe association likelihood is developed to include the classification results based on the 'confusion matrix' that specifies the accuracy of the target classifier. The objective is to improve association results using class information when the kinematic likelihoods are similar for different targets, i.e., there is ambiguity in using kinematic information alone. Performance comparisons with and without the use of class information in data association are presented on a ground target tracking problem. Simulation results quantify the benefits of classification-aided data association for improved target tracking, especially in the presence of association uncertainty in the kinematic measurements. Also, the benefit of S-D (or multiframe) association versus 2-D association is investigated for different quality classifiers. The main contribution of this paper is the development of the methodology to incorporate exactly the classification information into multidimensional (multiframe) association.

Here we discuss intervisibility (the existence of an unobstructed line of sight (LOS) between two points) accounting for the vertical and horizontal errors in the estimated locations of both points as well as elevation errors in the database of the terrain that could obstruct the LOS between these points. The errors are first simply treated as a 'white' noise sequence: we assume no correlation between the intervisibility at two different times, and the probability of an instantaneous intervisibility event is in this case developed. This is useful; but perhaps of greater concern is whether or not a target remains visible long enough and/or often enough that its motion can be tracked? Consequently, we present a second treatment in which the errors are stochastic processes of a certain bandwidth, and both the probability density function (pdf) of an intervisibility interval and the average number of intervisibility intervals over a certain time period are developed.

Maximum likelihood (ML) estimator is used for providing angles and sub-bin range estimates for targets between the monopulse returns from two-or more consecutive matched filter sampling points. Five targets are identified and isolated with the help of two matched filter samples.

In multisensor tracking systems that operate in a centralized information processing architecture, measurements from the same target obtained by different sensors can arrive at the processing center out of sequence. In order to avoid either a delay in the output or the need for reordering and reprocessing an entire sequence of measurements, such measurements have to be processed as out-of-sequence measurements (OOSMs). Recent work developed procedures for incorporating OOSMs into a Kalman filter (KF). Since the state of the art tracker for real (maneuvering) targets is the interacting multiple model (IMM) estimator, the algorithm for incorporating OOSMs into an IMM estimator is presented here. Both data association and estimation are considered. Simulation results are presented for two realistic problems using measurements from two airborne GMTI sensors. It is shown that the proposed algorithm for incorporating OOSMs into an IMM estimator yields practically the same performance as the reordering and in-sequence reprocessing of the measurements. Also, it is shown how the range rate from a GMTI sensor can be used as a linear velocity measurement in the tracking filter.

Most present-day radar systems use monopulse techniques to extract angular measurements of subbeam accuracy. The familiar 'monopulse ratio' is a very effective means to derive the angle of a single target within a radar beam. For the simultaneous estimation of the angles of two closely-spaced targets, a modification on the monopulse ratio was derived in [7], while [21] presented a maximum likelihood (ML) technique via numerical search. In this paper it is shown that the ML solution can in fact be found explicitly, and the numerical search of [21] is unnecessary. However, the ML solution requires the signal to noise ratio (SNR) for each target to be known, and hence we generalize it so it requires only the relative SNR. Several versions of expectation maximization (EM) joint angle estimators are also derived, these differing in the degree to which prior information on SNR and on beam pattern are assumed. The performances of the different direction-of-arrival (DOA) estimators for unresolved targets are studied via Monte Carlo, and it is found that most hove similar performance: this is remarkable since the use of prior information (SNR, relative SNR, beam pattern) varies widely between them. There is, however, considerable performance variability as a function of the two targets' off-boresight angles. A simple combined technique that fuses the results from different approaches is thus proposed, and it performs well uniformly.

The problem of joint detection and estimation for track initiation under measurement origin uncertainty is studied. The two well-known approaches, namely the maximum likelihood estimator with probabilistic data association (ML-PDA) and the multiple hypotheses tracking (MHT) via multiframe assignment, are characterized as special cases of the generalized likelihood ratio test (GLRT) and their performance limits indicated. A new detection scheme based on the optimal gating is proposed and the associated parameter estimation scheme modified within the ML-PDA framework. A simplified example shows the effectiveness of the new algorithm in detection performance under heavy clutter. Extension of the results to state estimation with measurement origin uncertainty is also discussed with emphasis on joint detection and recursive state estimation.

The development of a general framework for the systematic management of multiple sensors in target tracking in the presence of clutter is described. The basis of the technique is to quantify, and subsequently control, the accuracy of target state estimation. The posterior Cramer-Rao lower bound (PCRLB) provides the means of achieving this aim by enabling us to determine a bound on the performance of all unbiased estimators of the unknown target state. The general approach is then to use optimization techniques to control the measurement process in order to achieve accurate target state estimation. We are concerned primarily with the deployment and utilization of limited sensor resources. We also allow for measurement origin uncertainty, with sensor measurements either target-generated or false alarms. An example in which the aim is to track a submarine by deploying a series of constant false-alarm rate passive sanobuoys is presented. We show that by making some standard assumptions, the effect of the measurement origin uncertainty can be expressed as a state-dependent information reduction factor which can be calculated off-line. This enables the Fisher information matrix (FIM) to be calculated quickly, allowing Cramer-Rao bounds to be utilized for real-time, dynamic sensor management. The sensor management framework is shown to determine deployment strategies that enable the target to be accurately localized, and at the same time efficiently utilize the limited sensor resources.

In multisensor target tracking systems measurements from the same target can arrive out of sequence. Such 'out-of-sequence' measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting problem--how to update the current state estimate with an 'Older' measurement--is a nonstandard estimation problem. It was solved first (suboptimally, then optimally) for the case where the OOSM lies between the two last measurements, i.e, its lag is less than a sampling interval--the 1-step-lag ease. The real world has, however, OOSMs with arbitrary lag. Subsequently, the suboptimal algorithm was extended to the case of an arbitrary (multistep) lag, but the resulting algorithm required a significant amount of storage. The present work shows how the 1-step-lag algorithms can be generalized to handle an arbitrary (multistep) lag while preserving their main feature of solving the update problem without iterating. This leads only to a very small (a few percent) degradation of MSE performance. The incorporation of an OOSM into the data association process is also discussed. A realistic example with two GMTI radars is presented. The consistency of the proposed algorithm is also evaluated and it is found that its calculated covariances are reliable.

Many radar systems use the monopulse ratio to extract angle of arrival (AOA) measurements in both azimuth and elevation angles. The accuracies of each such measurement are reasonably well known: each measurement is, conditioned on the sum-signal return, Gaussian-distributed with calculable bias (relative to the true AOA), and variance. However, we note that the two monopulse ratios are functions of basic radar measurements that are not entirely independent, specifically in that the sum signal is common to both. The effect of this is that the monopulse ratios are dependent, and a simple explicit expression is given for their correlation; this is of considerable interest when the measurements are supplied to a tracking algorithm that requires a measurement covariance matrix. The system performance improvement when this is taken into account is quantified: while it makes little difference for a tracking radar with small pointing errors, there are more substantial gains when a target is allowed to stray within the beam, as with a rotating (track-while-scan) radar or when a single radar dwell interrogates two or more targets at different ranges. But in any case, the correct covariance expression is so simple that there is little reason not to use it. We additionally derive the Cramer-Rao lower bound (CRLB) on joint azimuth/elevation angle estimation and discover that it differs only slightly from the covariance matrix corresponding to the individual monopulse ratios. Hence, using the individual monopulse ratios and their simple joint accuracy expression is an adequate and quick approximation of the optimal maximum likelihood procedure for single resolved targets.

Track-to-track fusion is an important part in distributed multisensor-multitarget tracking. The centralized and distributed tracking configurations were studied in [7] using simulated air-to-air scenarios, and in [5] with analytical results based on [alpha]-[beta] filters. The current work generalizes the results in [5] to the cases with more than 2 sensors. As the number of sensors increases, the performance of the distributed tracker is shown to degrade compared with the centralized estimation even when the optimal track-to-track fusion is used. An approximate track-to-track fusion is presented and compared with the optimal track-to-track fusion with performance curves for various numbers of sensors. These performance curves can be used in designing a fusion system where certain trade-offs need to be considered. Finally, these results are compared with simulation results for a realistic air-to-air encounter scenario.

The goal of this article is to provide a real-time implementable algorithm to estimate the launch point (LP) of a thrusting object using angle-only measurements. The measurements are obtained in the object’s thrusting stage and from a single passive sensor (fixed or moving with constant velocity). It is assumed that one has a delayed acquisition, which means that the measurements are available only at some point after the launch time and the target’s mass decreases (i.e., its acceleration increases) due to fuel burn/ejection. Previous works on this problem mainly estimate the target’s state, which, for a passive sensor, requires a long batch of measurements, is sensitive to noise, and is ill-conditioned. In the present article, we only use a set of measurements (azimuth and elevation angles) to estimate the LP without motion state estimation. A polynomial fitting with the least-squares method is used to estimate the LP-based zero angular rate (which determines the launch time) and known LP altitude. Statistical analysis is provided to choose the optimal polynomial order, including overfitting and underfitting evaluation. Then, the estimated launch time is obtained by the “weighted average”. Compared with a more complicated state-of-the-art technique that relies on state estimation, the proposed approach provides a much simpler and effective way to implement in a real-time system. [ABSTRACT FROM AUTHOR]

In target tracking systems measurements are typically collected in 'scans' or 'frames' and then they are transmitted to a processing center. In multisensor tracking systems that operate in a centralized manner, there are usually different time delays in transmitting the scans or frames from the various sensors to the center. This can lead to situations where measurements from the same target arrive out of sequence. Such 'out-of-sequence' measurement (OOSM) arrivals can occur even in the absence of scan/frame communication time delays. The resulting 'negative-time measurement update' problem, which is quite common in real multisensor systems, was solved previously only approximately in the literature. The exact state update equation for such a problem is presented. The optimal and two suboptimal algorithms are compared on a number of realistic examples, including a GMTI (ground moving target indicator) radar case.

The conventional approach for tracking system design is to treat the detection and tracking subsystems as completely independent units. However, the two subsystems can be designed jointly to improve system (tracking) performance. It is known that different radar signal waveforms result in very different resolution cell shapes (for example, a rectangle versus an eccentric parallelogram) in the range/range-rate space, and that there are corresponding differences in overall tracking performance. We develop a framework for the analysis of this performance. An imperfect detection process, false alarms, target dynamics, and the matched filter sampling grid are all accounted for, using the Markov chain approach of Li and Bar Shalom. The role of the grid is stressed, and it is seen that the measurement-extraction process from contiguous radar 'hits' is very important. A number of conclusions are given, perhaps the most interesting of which is the corroboration in the new measurement space of Fitzgerald's result for delay-only (i.e., range) measurements, that a linear FM upsweep offers very good tracking performance.