A novel Nonlinear Adaptive Doppler Shift Estimation Technique (NADSET) is introduced in this paper. The quality of Doppler shift and power estimations by conventional Fourier-transform-based spectrum estimation methods deteriorates rapidly in low signal-to-noise-ratio (SNR) environment. The new NADSET algorithm compensates such deterioration in the quality of wind parameter estimates by adaptively utilizing the statistics of Doppler shift estimate in strong SNR ranges and identifying sporadic range bins where good Doppler shift estimates are found. NADSET is based on the nature of continuous wind profile and significantly improves the accuracy and the quality of Doppler shift estimates in low SNR ranges. The authenticity of NADSET is established by comparing the trend of wind parameters with and without NADSET applied to the lidar returns acquired over a long period of time by the coherent Doppler lidar system VALIDAR at NASA Langley Research Center in Virginia.

In this paper, we seek to study the impact of subbanding on blind source separation (BSS) as it could apply to radar and audio signals. We will focus on comparing wavelet-based subbanding, uniform subbanding, and no subbanding. For performing the BSS, we will use two common algorithms: joint approximate diagonalization of eigen-matrices (JADE) [4] and second-order blind identification (SOBI) [6]. As the measure of performance, we will use the interference to signal ratio.

In recent years, closed circuit cameras have become a common feature of urban life. There are environments however where the movement of people needs to be monitored but high resolution imaging is not necessarily desirable: rooms where privacy is required and the occupants are not comfortable with the perceived intrusion. Examples might include domiciliary care environments, prisons and other secure facilities, and even large open plan offices. This paper discusses algorithms that allow activity within this type of sensitive environment to be monitored using data from low resolution cameras (ones where all objects of interest are sub-pixel and cannot be resolved) and other non-intrusive sensors. The algorithms are based on techniques originally developed for wide area reconnaissance and surveillance applications. Of particular importance is determining the minimum spatial resolution that is required to provide a specific level of coverage and reliability.

In non-monopulse mechanically scanned surveillance radars, each target can be detected multiple times as the beam is scanned across the target. To prevent redundant reports of the object, a centroid processing algorithm is used to associate and fuse multiple detections, called primitives, into a single object measurement. At the 2001 SPIE conference,¹ Part I of this paper was presented wherein a new recursive least squares algorithm was derived that produces a single range-bearing centroid estimate. In this Part II paper, the problem is revisited to address one important aspect not previously considered. We develop a new algorithm component that will parse merged measurements that result from the presence of closely-spaced targets. The technique uses tracker feedback to identify the number of constituents in which to decompose the identified merged measurement. The algorithm has two components: one is a decomposition group formation algorithm, and the second is the expectation-maximization based centroid decomposition algorithm. Simulation results are presented that show the algorithm improves tracker completeness as well as measurement accuracy in scenarios with closely spaced objects.

The current nonlinear algorithm of the coherent Doppler lidar system VALIDAR at NASA Langley Research Center estimates wind parameters such as Doppler shift, power, wind velocity and direction by locating the maximum power and its frequency from the periodogram of the stochastic lidar returns. Due to the nonlinear nature of the algorithm, mathematically tractable parametric approaches to improve the quality of wind parameter estimates may pose a very little influence on the estimates especially in low signal-to-noise-ratio (SNR) regime. This paper discusses an alternate approach to accurately estimate the nonlinear wind parameters while preventing ambiguity in decision-making process via the subspace decomposition of wind data. By exploring the orthogonality between noise and signal subspaces expanded by the eigenvectors corresponding to the eigenvalues representing each subspace, a single maximum power frequency is estimated while suppressing erroneous peaks that are always present with conventional Fourier-transformbased frequency spectra. The subspace decomposition approach is integrated into the data processing program of VALIDAR in order to study the impact of such an approach on wind profiling with VALIDAR.

In order to reduce the time jitter and increase the speed of the sampling circuits for Analog-to-Digital Converters (ADCs), optical techniques can be used since high speed optical pulses can be generated (in the order of GHz) with pulse width in the regime of femtoseconds. In this paper, we present an optoelectronic sampling circuit for an optical ADC with an aggregate 5.12 Gigasample/s and a time jitter of 80 fs. The RF signal to be sampled is connected to 8 sampling circuit in parallel. Each sampling channel consists of a reverse-biased photodiode that acts as a fast optoelectronic switch in series with a load resistor. A bias tee was used to couple the RF signal to be sampled, and the d.c. voltage to reverse bias the photodiodes. The DC offset RF signals was then connected to each channel and was sampled by actuating the photodiodes with a modelocked optical pulses having repetition rate of 640 MHz. A relative delay of 0.195 ns was set between the sampling clocks. Thus the sampling circuits sampled different phases of the RF. The outputs of the eight sampling circuits were multiplexed together to give an aggregate sampling rate of 5.12GSPS. Finally, a synchronizer trigger circuits was designed in order that all eight sampling circuits can be triggered for simultaneous measurement.

Weak target inspecting and recovering are very important in IR detecting systems. In this paper, triple correlation peak inspecting techniques (TCPIT) are adopted for the signal processing of IR systems in detecting sub-pixel or point targets. Investigations show that the signal-to-noise ratio (SNR) improvement of approximate 23dB can be obtained with the input peak SNR of 0.84 and the input power SNR of -0.93dB. The triple correlation overlapping sampling technique (TCOST) is advanced for restoring signal waveforms of IR detection systems. Investigations show that signal waveforms can effectively be restored in the low signal-to-noise ratio circumstances using this approach.

In multitarget tracking alongside the problem of measurement to track association, there are decision problems related to track confirmation and termination. In general, such decisions are taken based on the total number of measurement associations, length of no association sequence, total lifetime of the track in question. For a better utilization of available information, confidence of the tracker on a particular track can be used. This quantity can be computed from the measurement-to-track association likelihoods corresponding to the particular track, target detection probability for the sensor-target geometry and false alarm density. In this work we propose a multitarget tracker based on a track quality measure which uses assignment based data association algorithm. The derivation of the track quality is provided. It can be noted that in this case one needs to consider different detection events than that of the track quality measures available in the literature for probabilistic data association (PDA) based trackers. Based on their quality and length of no association sequence tracks are divided into three sets, which are updated separately. The results show that discriminating tracks on the basis of their track quality can lead to longer track life while decreasing the average false track length.

A multiple-model tracker; e.g., the Gaussian Wavelet Estimator (GWE), employs a family of linear, local models to represent the motion of a maneuvering target over a range of operating modes. The state estimate generated by the GWE is a distribution with diffuse support. A road map provides contemporaneous, albeit circumscribed, information that can be integrated into the GWE to improve location estimation. However, fusing the inelastic restrictions of a road grid with the broad state estimates generated from conventional kinematic measurement requires considerable care. This paper presents a modified version of the GWE which integrates a map grid into the state estimate. The result is a state estimate consisting of a set of singular Gaussian sub-estimates. It is shown by example that map-enhancement improves the accuracy of the location estimates and sharpens the calculated uncertainty region.

The reliable detection and tracking of missile plumes in sequences of infrared images is a crucial factor in developing infrared missile warning systems for use in military and civil aircraft. This paper discusses the development of a set of algorithms that allow missile plumes to be detected, tracked and classified according to their perceived motion in the image plane. The aim is to classify the missile motion so as to provide an indication of the guidance law which is being used and, hence, to determine the type of missile that may be present and allow the appropriate countermeasures to be deployed. The algorithms allow for the motion of the host platform and they determine the missile motion relative to the fixed background provided by the scene. The tracks produced contain sufficient information to allow good discrimination between several standard missile types.

This paper considers three nonlinear estimation algorithms for impact point prediction (IPP) of ballistic targets. The paper assumes measurements are available from a 3D surveillance radar or phased array radar over some portion of the ballistic trajectory. The ballistic target (BT) is tracked using an extended Kalman filter (EKF), an unscented Kalman filter (UKF), and a particle filter (PF). With the track estimate as an initial condition, the equations of motion for the BT are integrated to obtain a prediction of the impact point. This paper compares the performance of the EKF, UKF, and a particular choice of PF for impact point prediction. The traditional Extended Kalman Filter equations are based on a first-order Taylor series approximation of the nonlinear transformations (expanded about the latest state estimate). Both the Unscented Kalman Filter and the Particle Filter allow nonlinear systems to be modeled without prior linearizion. The primary focus of the analysis presented in this paper is comparing the performance and accuracy of the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), and the chosen Particle Filter implementation for impact point prediction. The three filtering techniques are compared to the theoretical Cramer-Rao lower bounds (CRLB) of estimation error.

The GMTI radar sensor plays an important role in surveillance and precision tracking of ground moving targets. A class of GMTI sensors which employs a linear antenna measures the range, path difference between the received beams, and range-rate. The path difference is equivalent to the cone angle between the axis of the antenna and the radar line-of-sight. The measurement errors for the range, cone angle, and range-rate are independent. The measurements for the conventional GMTI measurement model are range, azimuth, and range-rate. The azimuth is a derived measurement obtained from the range and cone angle measurements. Therefore, the errors in the range and azimuth are correlated. However, the conventional GMTI measurement model ignores this correlation. We derive an analytic expression for the cross-covariance between the range and azimuth errors and show that the cross-covariance is inversely proportional to the ground-range. Thus for a stand-off GMTI sensor, the approximation used in neglecting the cross-covariance is reasonable. We present a new algorithm for the geolocation of the target using the maximum likelihood estimator and range, cone angle, and surface height measurements. Along-track, cross-track, and vertical errors in the sensor position and errors in the antenna orientation are taken into account. We use a flat Earth approximation. An initial estimate of the target state and associated covariance are required in a tracking filter using the first GMTI report. We present an extended Kalman filter based algorithm for GMTI track initialization using the GMTI geolocation results. Numerical results are presented using simulated data.

This work deals with the following question: using passive (line-of-sight angle) observations of a multistage surface to air missile from an aircraft, how can one infer that the missile is or is not aimed at the aircraft. The observations are assumed to be made only on the initial portion of the missile's trajectory. The approach is to model the trajectory of the missile with a number of kinematic and guidance parameters, estimate them and use statistical tools to infer whether the missile is guided toward the aircraft or not. A mathematical model is presented for a missile under pure proportional navigation with a changing velocity (direction change as well as speed change), to intercept a nonmaneuvering aircraft. A maximum likelihood estimator (MLE) is used for estimating the missile's motion parameters and a goodness-of-fit test is formulated to test if the aircraft is the aim or not. Using measurement data from several realistic missiles - single stage as well as multistage - aimed at an aircraft, it is shown that the proposed method can solve this problem successfully. The key to the solution, in addition to the missile model parametrization, is the use of a reliable global optimization algorithm with a hierarchical search technique for the MLE. The estimation/decision algorithm presented here can be used for an aircraft to decide, in a timely manner, whether appropriate countermeasures are necessary.

Typically, the posterior Cramer-Rao lower bound (PCRLB) is the performance bound of choice in tracking applications. This is primarily due to the availability of a computationally efficient recursive formulation of the bound. It has been shown, however, that this bound is weak in certain applications. Weiss-Weinstein lower bound (WWLB) is another second-order error bound that is free from the regularity conditions and it is applicable in a wide range of problems. In addition, it has free variables that can be tuned to get tighter bounds. In this paper, we develop the WWLB for maneuvering target tracking. In particular, we utilize the ability of the WWLB to handle continuous and discrete random variables: target motion model is represented by a separate discrete variable and the bound is calculated over the continuous state and discrete motion model variables. The bound is tightened by optimizing with respect to the free variables.

Multiple hypothesis trackers (MHTs) are widely accepted as the best means of tracking targets in the presence of clutter. This research seeks to incorporate multiple model Kalman filters into an Integral Square Error (ISE) cost-function-based MHT to increase the fidelity of target state estimation. Results indicate that the proposed multiple model methods can properly identify the maneuver mode of a target in dense clutter and ensure that an appropriately tuned filter is used. During benign portions of flight, this causes significant reductions in position and velocity RMS errors compared to a single-dynamics-model-based MHT. During portions of flight when the mixture mean deviates significantly from true target position, so-called deferred decision periods, the multiple model structures tend to accumulate greater RMS errors than a single-dynamics-model-based MHT, but this effect is inconsequential considering the inherently large magnitude of these errors (a non-MHT tracker would not be able to track during these periods at all). The multiple model MHT structures do not negatively impact track life when compared to a single-dynamics-model-based MHT.

We describe a new particle filter that uses quasi-Monte Carlo (QMC) sampling with product measures rather than boring old Monte Carlo sampling or QMC with or without randomization. The product measures for QMC were recently invented by M. Junk and G. Venkiteswaran, and therefore we call this new nonlinear filter the "JV filter". Standard particle filters use boring old Monte Carlo sampling and suffer from the curse of dimensionality, and they converge at the sluggish rate of c(d)/√N in which N is the number of particles, and c(d) depends strongly on dimension of the state vector (d). Oh's theory and numerical experiments (by us) show that for good proposal densities, c(d) grows as d³, whereas for poor proposal densities c(d) grows exponentially with d. In contrast, for certain problems, QMC converges much faster than MC with N. In particular, QMC converges as k(d)/N, in which k(d) is logarithmic in N and its dependence on d is an interesting story.

For ballistic target tracking using radar measurements in the polar or spherical coordinates, various nonlinear filters have been studied. Previous work often assumes that the ballistic coefficient of a missile target is known to the filter, which is unrealistic in practice. In this paper, we study the ballistic target tracking problem with unknown ballistic coefficient. We propose a general scheme to handle nonlinear systems with a nuisance parameter. The interacting multiple model (IMM) algorithm is employed and for each model the linear minimum mean square error (LMMSE) filter is used. Although we assume that the nuisance parameter is random and time invariant, our approach can be extended to time varying case. A useful property of the model transition probability matrix (TPM) is studied which provides a viable way to tune the model probability. In simulation studies, we illustrate the design of the TPM and compare the proposed method with another two IMM-based algorithms where the extended Kalman filter (EKF) and the unscented filter (UF) are used for each model, respectively. We conclude that the IMM-LMMSE filter is preferred for the problem being studied.

Tracking performance is a function of data quality, tracker type, and target maneuverability. Many contemporary tracking methods are useful for various operating conditions. To determine nonlinear tracking performance independent of the scenario, we wish to explore metrics that highlight the tracker capability. With the emerging relative track metrics, as opposed to root-mean-square error (RMS) calculations, we explore the Averaged Normalized Estimation Error Squared (ANESS) and Non Credibility Index (NCI) to determine tracker quality independent of the data. This paper demonstrates the usefulness of relative metrics to determine a model mismatch, or more specifically a bias in the model, using the probabilistic data association filter, the unscented Kalman filter, and the particle filter.

A number of methods exist to track a target's uncertain motion through space using inherently inaccurate sensor measurements. A powerful method of adaptive estimation is the interacting multiple model (IMM) estimator. In order to carry out state estimation from the noisy measurements of a sensor, however, the filter should have knowledge of the statistical characteristics of the noise associated with that sensor. The statistical characteristics (accuracies) of real sensors, however, are not always available, in particular for legacy sensors. This paper presents a method of determining the measurement noise variances of a sensor by using multiple IMM estimators while tracking targets whose motion is not known-targets of opportunity. Combining techniques outlined in [1] and [3], the likelihood functions are obtained for a number of IMM estimators, each with different assumptions on the measurement noise variances. Then a search is carried out to bracket the variances of the sensor measurement noises. The end result consists of estimates of the measurement noise variances of the sensor in question.

An advent in the development of smart munitions entails autonomously modifying target selection during flight in order to maximize the value of the target being destroyed. A unique guidance law can be constructed that exploits both attribute and kinematic data obtained from an onboard video sensor. An optimal path planning algorithm has been developed with the goals of obstacle avoidance and maximizing the value of the target impacted by the munition. Target identification and classification provides a basis for target value which is used in conjunction with multi-target tracks to determine an optimal waypoint for the munition. A dynamically feasible trajectory is computed to provide constraints on the waypoint selection. Results demonstrate the ability of the autonomous system to avoid moving obstacles and revise target selection in flight.

Passive sonar depends on signals of opportunity to detect, track, and localize targets. These signals, typically from the target itself, are often very weak relative to the ambient sound levels, making them difficult to detect and track, resulting in a sonar picture cluttered with many intermittent track segments. An accurate estimate of the position, course, and speed of a target depends on the characteristics, including duration, of the available track. In early sonar systems, where operators detected signals visually and tracked them manually, the time of detection was ambiguous since operators searched for repetitive events and visually followed them as far backward as possible. In modern tracking systems using an m out of n detector, the arrival of the m^th event is considered the time of detection. A tracker is initiated at this time and updated as new data is acquired. Data prior to the detection is discarded and localization is delayed until sufficient post-detection data has been acquired to produce a suitable track often tens of minutes later. Initiating a second tracker in reverse time can reduce the localization delay by gleaning additional track information from the acoustic data acquired prior to the time of detection and often prior to the data that triggered the detection. Implementing reverse-time tracking requires a large data cache and significant processing power as well as data association to fuse sequential and/or concurrent forward-time and reverse-time tracks, but it can be an effective tool to rapidly extract additional information from narrowband passive sonar data.

The multitarget recursive Bayes nonlinear filter is the theoretically optimal approach to multisensor-multitarget detection, tracking, and identification. For applications in which this filter is appropriate, it is likely to be tractable for only a small number of targets. In earlier papers we derived closed-form equations for an approximation of this filter based on propagation of a first-order multitarget moment called the probability hypothesis density (PHD). In a recent paper, Erdinc, Willett, and Bar-Shalom argued for the need for a PHD-type filter which remains first-order in the states of individual targets, but which is higher-order in target number. In an earlier paper at this conference we derived a closed-form cardinalized PHD CPHD), filter, which propagates not only the PHD but also the entire probability distribution on target number. Since the CPHD filter has computational complexity O(m³) in the number m of measurements, additional approximation is desirable. In this paper we discuss a second-order approximation called the "binomial filter."

This paper is generally concerned with multiple target tracking with possibly unresolved or merged measurements, and is motivated by recent advances in signal processing, particularly radar signal processing, that enable the extraction of two or more targets from a single merged detection, under certain conditions. The output of such signal processing can be viewed as a result of a process of estimating an unknown number of objects with no particular meaningful ordering, i.e., mathematically best characterized as a simple finite point process or, equivalently, a random finite set, and a priori and a posteriori statistics can be described as a set of Janossy measures. However, since a sensor generally observes only a subspace of a target state space, it may not be possible to express the target detection results as a full-dimensional probability distribution on a target state space. In this paper, we will try to extend the concept of the Janossy measure density function to express information pertaining only to an instantaneously observable part of target state space, to formulate what we tentatively called the generalized Janossy density function, which may be viewed as an unnormalized or improper probability distribution. Based on this concept of the generalized Janossy measure, or the likelihood function concept, a tracking process can be formulated as a process of recursively updating, by the measurement likelihood functions, the a posteriori probability distribution expressed as a set of Janossy measure density functions.

The use of multiple scans of data to improve ones ability to improve target tracking performance is widespread in the tracking literature. In this paper, we introduce a novel application of a recent innovation in the SMC literature that uses multiple scans of data to improve the stochastic approximation (and so the data association ability) of a multiple target Sequential Monte Carlo based tracking system. Such an improvement is achieved by resimulating sampled variates over a fixed-lag time window by artificially extending the space of the target distribution. In doing so, the stochastic approximation is improved and so the data association ambiguity is more readily resolved.

Detection and estimation of multiple unresolved targets with a monopulse radar is limited by the availability of information in monopulse signals. The maximum possible number of targets that can be extracted from the monopulse signals of a single bin is two. Recently two approaches have been proposed in the literature to overcome this limitation. The first is joint-bin processing that exploits target spill-over among adjacent cells by modeling the target returns in the adjacent cells. In addition to making use of the additional information available in target spill-over, it handles a more practical problem where the usual assumption of ideal sampling is relaxed. The second approach is to make use of tracking information in detection through joint detection and tracking with the help of Monte Carlo integration of a particle filter. It was shown that the extraction of even more targets is possible with tracking information. In this paper, a new approach is proposed to combine make the best of these two approaches - a new joint detection and tracking algorithm with multibin processing. The proposed method increases the detection ability as well as tracking accuracy. Simulation studies are carried out with amplitude comparison monopulse radar for an unresolved target scenario. The relative performances of various methods are also provided.

The MHT/MFA approach to tracking has been shown to have significant advantages compared to single frame methods. This is especially the case for dense scenarios where there are many targets and/or significant clutter. However, the data association problem for such scenarios can become computationally prohibitive. To make the problem manageable, one needs effective complexity reduction methods to reduce the number of possible associations that the data association algorithm must consider. At the 2005 SPIE conference, Part I of this paper¹ was presented wherein a number of "gating algorithms" used for complexity reduction were derived. These included bin gates, coarse pair and triple gates, and multiframe gates. In this Part II paper, we provide new results that include additional gating methods, describe a hierarchical framework for the integration of gates, and show simulation results that demonstrate a greater than 95% effectiveness at removing clutter from the tracking problem.

In this paper, we present two practical modifications of the original Murty algorithm. First, the algorithm is modified to handle rectangular association matrix. The original Murty algorithm was developed for a square matrix. It is found that the expanding rules should be changed so that the cross-over pair within an assignment can be extended to the last column and can be repeated for the last column upon certain conditions. The second modification is the allowance of an "infeasible" assignment, where some tracks are not assigned with any measurements, therefore, good "infeasible" hypotheses are maintained and clutter seduced hypotheses are suppressed when the information evidence becomes stronger. Examples are used to demonstrate the modifications of the existing Murty algorithm for a practical implementation of an N-best Multiple Hypothesis Tracker.

In this paper, we consider the problem of sensor resource management in decentralized tracking systems. Due to the availability of cheap sensors, it is possible to use a large number of sensors and a few fusion centers (FCs) to monitor a large surveillance region. Even though a large number of sensors are available, due to frequency, power and other physical limitations, only a few of them can be active at any one time. The problem is then to select sensor subsets that should be used by each FC at each sampling time in order to optimize the tracking performance subject to their operational constraints. In a recent paper, we proposed an algorithm to handle the above issues for joint detection and tracking, without using simplistic clustering techniques that are standard in the literature. However, in that paper, a hierarchical architecture with feedback at every sampling time was considered, and the sensor management was performed only at a central fusion center (CFC). However, in general, it is not possible to communicate with the CFC at every sampling time, and in many cases there may not even be a CFC. Sometimes, communication between CFC and local fusion centers might fail as well. Therefore performing sensor management only at the CFC is not viable in most networks. In this paper, we consider an architecture in which there is no CFC, each FC communicates only with the neighboring FCs, and communications are restricted. In this case, each FC has to decide which sensors are to be used by itself at each measurement time step. We propose an efficient algorithm to handle the above problem in real time. Simulation results illustrating the performance of the proposed algorithm are also presented.

The Probabilistic Multi-Hypothesis Tracker (PMHT) is an emerging algorithm that has shown some success and is intriguing because of its elegance and extensibility in many different aspects. It is a tracking algorithm that offers an alternative to the Multiple Hypothesis Tracker (MHT) in the multiple-frame tracking arena. Instead of enumerating many of the possibilities of track-to-measurement assignments, the PMHT uses a probabilistic approach to assign the likely "weight" of each measurement to contribute to each track. This paper presents the ongoing results of research using the PMHT algorithm as a network-level composite tracker on distributed platforms. In addition, the methods necessary to implement the PMHT in a realistic simulation are discussed. It further describes the techniques that have been tried to ensure a single integrated air picture (SIAP) across the platforms.

Detecting and localizing a threat ballistic missile as quickly and accurately as possible are key ingredients required to engage the missile during boost phase over the territory of the aggressor, and rapid and accurate launch point determination is crucial to attack hostile facilities. Earlier research has focused on track initiation, boost phase tracking and rapid launch point determination using augmented IMM and Kalman-based techniques. This work extends that earlier research by comparing these IMM and Kalman-based trackers and backfitters with the newer particle filters to see what advantages particle filters might offer in this application. Simulations used in this research assume the ballistic missile target is in boost phase, transitioning to coast phase using a gravity turn and constant gravity. The rocket is assumed to be single stage. The IMM tracker performs well in tracking through booster cutoff. A smoothed estimate of the initial target state vector is used to backfit for launch point determination. Errors in this process are rather large and there appear to be biases in the estimates. These results are compared with a particle filter implementation. Here the correct nonlinear model of the missile dynamics was used, but the algorithm had to estimate engine thrust and the drag coefficient as well as position and velocity states. This algorithm proved to be a large disappointment because the number of particles required to generate reasonable results was large and the algorithm run time became unrealistically long.

Track fusion processing is complicated because the estimation errors of a local track and a fusion track for the same target are usually cross-correlated. If these errors are cross-correlated, that should be taken into account when designing the data association processing and the filter used to combine the track data. An approach to dealing with this cross-correlation is to use tracklets. One of the important issues in tracklet fusion performance is whether the dynamics are deterministic, e.g., no filter process noise and no target maneuver. A number of different tracklet methods have been designed. This paper presents a comparison a tracklets-from-tracks approach to a tracklets-from-measurements approach. Tracklet fusion performance is also compared to centralized measurement fusion performance. The emphasis is on performance with targets that exhibit deterministic dynamics and the possibility of measurements caused by false signals.

In this paper, we consider the problem of collaborative sensor management with particular application to using unmanned aerial vehicles (UAVs) for multitarget tracking. We study the problem of decentralized cooperative control of a group of UAVs carrying out surveillance over a region that includes a number of moving targets. The objective is to maximize the information obtained and to track as many targets as possible with the maximum possible accuracy. Uncertainty in the information obtained by each UAV regarding the location of the ground targets are addressed in the problem formulation. In order to handle these issues, the problem is presented as a decentralized operation of a group of decision-makers lacking full observability of the global state of the system. Recent advances in solving special classes of decentralized Markov Decision Processes (Dec-MDPs) are incorporated into the solution. In these classes of Dec-MDPs, the agents' transitions and observations are independent. Also, the collaborating agents share common goals or objectives. Given the Dec-MDP model, a local policy of actions for a single agent (UAV) is given by a mapping from a current partial view of a global state observed by an agent to actions. The available probability model regarding possible and confirmed locations of the targets is considered in the computations of the UAVs' policies. Simulation results are presented on a representative multisensor-multitarget tracking problem.

In this paper we compare the performance of two Multidimensional Assignment Algorithms (MDA), the Lagrangean Relaxation based S-D algorithm and the Sequential m-best 2-D algorithm, applied to a realistic problem in missile defense surveillance. The benchmark problem consists of a set of sources that provide "event" (track) estimates of multiple launches, via a number of communication networks to a Fusion Center (FC) which has to perform data association prior to fusion. The network model used "loses" the information tag that distinguishes reports from the same source transmitted through different networks, i.e., the track identity (ID) assigned by the source is not passed on. Only a track ID assigned by the network, and the source ID accompany the track. Thus detection and elimination of track duplications at the FC is needed. The proposed hierarchical approach to the problem requires the solution of several MDA problems before calculating the fused estimate, so accuracy of the solution of each is crucial. Examples with several launches, sources and networks are presented to compare the performance of the two assignment algorithms.

This paper develops models for centralized and distributed trackers that account for target fading effects. The models build on earlier work by the author, and introduce: (1) sensor performance statistics based on a standard Rayleigh amplitude assumption; (2) the impact of false contacts on true track formation and maintenance. We exercise the models in a number of ways, to illustrate the strengths and weaknesses of centralized and distributed fusion architectures. Our findings are qualitatively consistent with sea trial based performance analysis.

In many active sonar tracking applications, targets frequently undergo fading detection performance in which the target's detection probability can shift suddenly from a high to a low value. This characteristic is a function of the undersea environment. Using a multistatic active sonar problem, we examine the performance of track management (initiation and termination) routines where the target detection probability is based on an underlying Hidden Markov Model (HMM) with high and low detection states. Using a likelihood ratio test, we develop the optimum track initiation performance as measured by a System Operating Characteristic, similar to a Receiver Operating Characteristic, which plots the probability of initiating a true track versus the probability of initiating a false track. We show that near-optimal performance can be attained using track initiation logic that differentiates the measurements as to receiver source in an "M detections of N scans from C sensors" type of rule. Performance can further be improved by using a composite track initiation test that combines two or three such rules in a logical OR operation. We next show that the use of a Shiryaev-Roberts test for track termination yields the quickest detection of false tracks for a given duration of true target tracks when compared to a Page test and rule-based tests of the form "M or fewer detections from K scans".

We have developed a new nonlinear filter that is superior to particle filters in five ways: (1) it exploits smoothness; (2) it uses an exact solution of the Fokker-Planck equation in continuous time; (3) it uses an FFT to compute the effect of process noise at discrete times; (4) it uses the adjoint method to compute the optimal density of points in state space to represent the smooth conditional probability density, and (5) it uses Bayes' rule exactly by exploiting the exponential family of probability densities. In contrast to particle filters, which do not exploit smoothness, the new filter does not use importance sampling or Monte Carlo methods. The new non-particle filter should be superior to particle filters for a broad class of practical problems. In particular, the new filter should dramatically reduce the curse of dimensionality for many (but not all) important real world nonlinear filter problems.

The primary components of a target track are the estimated state vector and its error variance-covariance matrix (or simply the covariance). The estimated state indicates the location and motion of the target. The track covariance should indicate the uncertainty or inaccuracy of the state estimate. The covariance is computed by the track processor and may or may not realistically indicate the inaccuracy of the state estimate. Covariance Consistency is the property that a computed variance-covariance matrix realistically represents the covariance of the actual errors of the estimate. The computed covariance of the state estimation error is used in the computations of the data association processing function; consequently, degraded track consistency causes misassociations (correlation errors) that can substantially degrade track performance. The computed covariance of the state estimation error is also used by downstream functions, such as the network-level resource management functions, to indicate the accuracy of the target state estimate. Hence, degraded track consistency can mislead those functions and the war fighter about how accurate each target track is. In the past, far more attention has been given to improving the accuracy of the estimated target state than in improving the track covariance consistency. This paper addresses the importance and analyzes properties of covariance consistency. Monte Carlo simulation results illustrate the characteristics of covariance consistency and the performance with some simple methods for improving covariance consistency.

Advances in characterizing the angle measurement covariance for phased array monopulse radar systems that use adaptive beamforming to null out a jammer source allow for the use of improved sensor models in tracking algorithms. Using a detection probability likelihood function consisting of a Gaussian sum that incorporates negative contact measurement information, three tracking systems are compared when used to track a maneuvering target passing into and through standoff jammer interference. Each tracker differs in how closely it replicates sensor performance in terms of accuracy of measurement covariance and the use of negative information. Only the tracker that uses both the negative contact information and corrected angle measurement covariance is able to consistently reacquire the target when it exits the jammer interference.

Fusion of data from multiple sensors can be hindered by systematic errors known as biases. Specifically, the presence of biases can lead to data misassociation and redundant tracks. Fortunately, if an estimate of the unknown biases can be obtained, the measurements and transformations for each sensor can be debiased prior to fusion. In this paper, we present an algorithm that uses truth data for offline estimation of time invariant biases. Our approach is unique for two reasons. First, we explicitly avoid the use of fictitious "roll-up" biases and instead attempt to model the true sources of systematic errors. This leads to a highly nonlinear bias model that contains 18 unknown parameters. Second, we use the singular value decomposition (SVD) within our nonlinear least-squares estimator to automatically handle the issue of parameter observability. We also show how the SVD can be used to differentiate between absolute and relative bias estimates. Finally, we demonstrate that our algorithm can improve track accuracy, especially for mobile sensor platforms.

Closely-spaced (but resolved) targets pose a challenge for measurement-to-track data association algorithms. Since the Mahalanobis distances between measurements collected on closely-spaced targets and tracks are similar, several elements of the corresponding kinematic measurement-to-track cost matrix are also similar. Lacking any other information on which to base assignments, it is not surprising that data association algorithms make mistakes. One ad hoc approach for mitigating this problem is to multiply the kinematic measurement-to-track likelihoods by amplitude likelihoods. However, this can actually be detrimental to the measurement-to-track association process. With that in mind, this paper pursues a rigorous treatment of the hypothesis probabilities for kinematic measurements and features. Three simple scenarios are used to demonstrate the impact of basing data association decisions on these hypothesis probabilities for Rayleigh, fixed-amplitude, and Rician targets. The first scenario assumes that the tracker carries two tracks but only one measurement is collected. This provides insight into more complex scenarios in which there are fewer measurements than tracks. The second scenario includes two measurements and one track. This extends naturally to the case with more measurements than tracks. Two measurements and two tracks are present in the third scenario, which provides insight into the performance of this method when the number of measurements equals the number of tracks. In all cases, basing data association decisions on the hypothesis probabilities leads to good results.

The probability hypothesis density (PHD) filter, an automatically track-managed multi-target tracker, is attracting increasing but cautious attention. Its derivation is elegant and mathematical, and thus of course many engineers fear it; perhaps that is currently limiting the number of researchers working on the subject. In this paper, we explore a physical-space approach - a bin model - which leads us to arrive the same filter equations as the PHD. Unlike the original derivation of the PHD filter, the concepts used are the familiar ones of conditional probability. The original PHD suffers from a "target-death" problem in which even a single missed detection can lead to the apparent disappearance of a target. To obviate this, PHD originator Mahler has recently developed a new "cardinalized" version of PHD (CPHD). We are able to extend our physical-space derivation to the CPHD case as well. We stress that the original derivations are mathematically correct, and need no embellishment from us; our contribution here is to offer an alternative derivation, one that we find appealing.

It is widely accepted that Classification Aided Tracking (CAT) has the potential to maintain continuous tracks on important targets. Moreover, when augmented with target behavior, a joint tracking and ID system can enhance the data association process for ground tracking systems. It is also recognized that it is likely that some targets in any scenario may not be included in a database, and the presence of such confusers would diminish both tracking and ID performance. Moreover, even with ID information, tracks may switch targets. Thus, a joint tracking and identification architecture has been developed which addresses the issues of both confusers and track ID switching. These methods are being tested using simulated dynamic ground targets and radar High Range Resolution (HRR) data provided by the Moving and Stationary Target Acquisition and Recognition (MSTAR) project. The paper begins by giving an overview of the IMM/MHT tracker that has been designed to handle the unique characteristics (such as on-off road behavior) of the ground target tracking problem. Then, a joint tracking identification methodology is described. Implementing this approach, target behavior (such as being part of a group, speed, and on/off road motion) can be used both in the data association and for target type information. A Dempster-Shafer method is used for combining all classification-related data. In addition, confusers are taken into account by incorporating the information from targets that are in the database. The track score, required in all MHT data association decisions, is augmented with a feature-related term derived from the conflict term computed from an application of Dempster's Rule. The histories of the most likely ID for each track are checked to identify possible switches, and if tracks are believed to have switched IDs, then the state and the covariances of these tracks are exchanged so that future observations may be consistent with the original targets. Finally, the paper illustrates the proposed methods using results from a detailed simulation of target convoys, with and without confuser targets, that perform on and off road maneuvers. Results using MSTAR HRR data are presented for Classification-Aided (CAT) approaches to feature-aided tracking.