This PDF file contains the front matter associated with SPIE Proceedings Volume 6699, including the Title Page, Copyright information, Table of Contents, Introduction, and the Conference Committee listing.

Automatic acquisition of aerial threats at thousands of kilometers distance requires high sensitivity to small differences in contrast and high optical quality for subpixel resolution, since targets occupy much less surface area than a single pixel. Targets travel at high speed and break up in the re-entry phase. Target/decoy discrimination at the earliest possible time is imperative. Real time performance requires a multifaceted approach with hyperspectral imaging and analog processing allowing feature extraction in real time. Hyperacuity Systems has developed a prototype chip capable of nonlinear increase in resolution or subpixel resolution far beyond either pixel size or spacing. Performance increase is due to a biomimetic implementation of animal retinas. Photosensitivity is not homogeneous across the sensor surface, allowing pixel parsing. It is remarkably simple to provide this profile to detectors and we showed at least three ways to do so. Individual photoreceptors have a Gaussian sensitivity profile and this nonlinear profile can be exploited to extract high-resolution. Adaptive, analog circuitry provides contrast enhancement, dynamic range setting with offset and gain control. Pixels are processed in parallel within modular elements called cartridges like photo-receptor inputs in fly eyes. These modular elements are connected by a novel function for a cell matrix known as L4. The system is exquisitely sensitive to small target motion and operates with a robust signal under degraded viewing conditions, allowing detection of targets smaller than a single pixel or at greater distance. Therefore, not only is instantaneous feature extraction possible but also subpixel resolution. Analog circuitry increases processing speed with more accurate motion specification for target tracking and identification.

Target detection in hyperspectral imagery is a challenging task as the targets occupy only a few pixels or less. The presence of noise can make detection more complicated as spectral signature of pixels can change due to noise. In this paper, a novel technique for detection is proposed using one dimensional maximum average correlation height (MACH) filter. The MACH filter is trained using likely variations of target spectral signatures. The variations can be taken from data or can be generated by applying Gaussian noise. Each pixels of the input scene is then correlated with the detection filter. The MACH filter maximizes the relative height of correlation peak for target in comparison with background and noise. Thus, a target can be detected by analyzing the correlation peak values. Single or Multiple targets in a hyperspectral sequence can be detected simultaneously this approach. Test results using real life hyperspectral data are presented to verify the accomplishments of one dimensional MACH filter.

The performances of order statistic (OS) constant false alarm rate (CFAR) detectors are analyzed for non-Gaussian clutters modeled by heavy-tailed complex isotropic symmetric alpha-stable random processes whose amplitude is the generalized Rayleigh distribution. The detection and false alarm probabilities of the amplitude OS-CFAR detectors are presented assuming that the target signal is Rayleigh distributed. Exact closed-form solutions are derived for the special case of Cauchy-Rayleigh distribution where the characteristic exponent is 1. Numerical results are presented for detection and false alarm rates as functions of the generalized signal-to-noise ratio, reference window sizes, and rank order indexes. It is shown that the window size and rank order do not have significant effects on the performances. It is also shown that the amplitude detectors provide similar performances as the square-law detectors in the heavy-tailed clutter environment.

In this paper we address the problem of detecting and tracking a single dim target in unknown background noise. Several methodologies have been developed for this problem, including track-before-detect (TBD) methods which work directly on unthresholded sensor data. The utilization of unthresholded data is essential when signal-to-noise ratio (SNR) is low, since the target amplitude may never be strong enough to exceed any reasonable threshold. Several problems arise when working with unthresholded data. Blurring and non-Gaussian noise can easily lead to very complicated likelihood expressions. The background noise also needs to be estimated. This estimate is a random variable due to the random nature of the background noise. We propose a recursive TBD method which estimates the background noise as part of its likelihood evaluation. The background noise is estimated by averaging over nearby sensor cells not affected by the target. The uncertainty of this estimate is taken into account by the likelihood evaluation, thereby yielding a more robust TBD method. The method is implemented using sequential Monte Carlo evaluation of the optimal Bayes equations, also known as particle filtering. Simulation results show how our method allows detection and tracking to be carried out in an uncertain environment where current recursive TBD methods fail.

A method is presented where the foreground is enhanced by an relative focus-map estimation. In the case of moving patterns a Stauffer Grimson approach is used to suppress background. In case of small and subpixel target size statistical evaluation is used for a rough classification. A new solution is given by a combination of foreground separation, relative focus-map generation and histogram-based local evaluation to find the foreground objects.

In this paper real data from divers is analyzed for detection and tracking purposes. There are two divers, one with an open breathing system, and the other with a closed breathing system. The data were recorded from an active 90kHz narrowband multibeam imaging sonar. A target such as the open breathing system diver yields several detections of air bubbles, and should be handled as an extended target. Modeling the extended target with morphological operators like erosion and dilation is discussed and a model of the bubbles in the data association is developed. For this data the MCA (Morphological Cell Averaging)-CFAR is implemented in cojunction with an augmented probabilistic data association filter (PDAF) that incorporates an additional bubble model.

This paper deals with models of ballistic target (BT) motion during the boost phase for target tracking. Different options to improve the accuracy of modeling are discussed and several enhanced models are proposed. They include simple kinematic models of the so-called gravity turn (GT) target motion and more sophisticated models, accounting for the BT flight dynamics during boost, as well. Tracking simulations are presented.

This paper addresses the out-of-sequence measurement (OOSM) problem associated with multiple platform tracking systems. The problem arises due to different transmission delays in communication of detection reports across platforms. Much of the literature focuses on the improvement to the state estimate by incorporating the OOSM. As the time lag increases, there is diminishing improvement to the state estimate. However, this paper shows that optimal processing of OOSMs may still be beneficial by improving data association as part of a multi-target tracker. This paper derives exact multi-lag algorithms with the property that the standard log likelihood track scoring is independent of the order in which the measurements are processed. The orthogonality principle is applied to generalize the method of Bar- Shalom in deriving the exact A1 algorithm for 1-lag estimation. Theory is also developed for optimal filtering of time averaged measurements and measurements correlated through periodic updates of a target aim-point. An alternative derivation of the multi-lag algorithms is also achieved using an efficient variant of the augmented state Kalman filter (AS-KF). This results in practical and reasonably efficient multi-lag algorithms. Results are compared to a well known ad hoc algorithm for incorporating OOSMs. Finally, the paper presents some simulated multi-target multi-static scenarios where there is a benefit to processing the data out of sequence in order to improve pruning efficiency.

The new generation of high resolution radars now being developed present a nonlinear tracking problem due to a combination of long target ranges, small range errors, and relatively imprecise angle measurements. A variety of filtering techniques have been proposed for ameliorating the effects of this non-linearity, including the (debiased) converted measurements Kalman filter and the unscented filter. The benefits of these techniques are often described in terms of tracking error; however, for handover of a dense target complex to downrange sensors, it is as important that the errors be consistent with their ascribed covariance. The purpose of this paper is to identify when the nonlinear conversion bias effects covariance consistency by examining the relative performance of various filtering techniques.

In our previous work, we presented an algorithm to quantify the degree of nonlinearity of nonlinear filtering problems with linear dynamic models and nonlinear measurement models. A quantitative measure of the degree of nonlinearity was formulated using differential geometry measures of nonlinearity, the parameter-effects curvature and intrinsic curvature. We presented numerical results for a number of practical nonlinear filtering problems of interest such as the bearing-only filtering, ground moving target indicator filtering, and video filtering problems. In this paper, we present an algorithm to compute the degree of nonlinearity of a nonlinear filtering problem with a nonlinear dynamic model and a linear measurement model. This situation arises for the bearing-only filtering problem with modified polar coordinates and log polar coordinates. We present numerical results using simulated data.

This paper discusses the meaning of filter and covariance consistency and metrics for quantifying covariance consistency. Methodologies for testing and verifying (monitoring) covariance consistency will be explained and contrasted. Possible methodologies with simulated data sets representing hypothetical sensors tracking simulated targets will be demonstrated. One key methodology relies on statistical hypothesis testing of Mahalanobis distances computed for innovation vectors and state vectors. The focus will be on two important contributors to filter inconsistency: sensor bias and a "scaling factor," which can be an important source of inconsistency in a well-behaved unbiased filter. Using these simulated data sets the problems encountered with testing the innovation vectors in the presence of sensor biases will be demonstrated, underscoring the need to focus the tests for sensor biases on the state vectors instead. It will also be shown that tests of innovations can be reliable in determining the scaling factor. A way to remove bias effects in consistency tests applied to tracker state vectors will be demonstrated as well.

The state of the art of tracking has matured and consequently, the priorities for improved performance and expanded or new processing capabilities have changed. Future directions in algorithm development in tracking and related data processing are not easy to predict with accuracy. The future priorities of development tasks predicted in this presentation are subjective; that is, simply the author's view. While there will continue to be algorithm development to improve many aspects of tracking, the emphasis is expected to change in favor of expanded and new capabilities. This presentation will address not only those tracking algorithms that will have higher priority for continued algorithm development but also those aspects of tracking related processing that are expected to be of special interest. In addition, to facilitate this discussion, the categories of the state of the art of tracking are more finely decomposed. Many aspects of single sensor, multiple target tracking have matured during the last 20 years but room for improvement remains. In contrast, fusion of data from multiple distributed sensors is not as mature and interest is expected to continue to increase. Many fusion systems pose challenges that are not of much concern in tracking with data from a single sensor and algorithm development of those aspects of fusion will continue to be needed. The capability of the many functions and users of the output of trackers needs to be improved and expanded. Consequently, an increase is expected in the need to improve the content and quality of the output of both the single sensor and fusing trackers. The identified aspects of the new needs in tracker output are discussed and a dialog on this topic is encouraged.

A multiple model tracking algorithm has considerable advantage when the target is moving on a road grid. A map-enhanced algorithm magnifies this by excluding large regions of the 2D motion-space from search. However, integrating the grid of streets and junctions into a recursive algorithm is challenging. This paper presents a map-enhanced, tracker that uses local models tuned to motions on the four cardinal directions. Map compliance is achieved by re-initializing the local kinematic state when a model change occurs and by moving the local estimate to the map after a measurement update. Unfortunately, the transition dynamics of the model state depend upon the kinematic state. A proposed junction influence function is based upon a rapidly decaying measure of the distance from the target to the nearest compatible junction.

The problem of tracking with very long range radars is studied in this paper. An important feature of the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is that, beyond a certain limit, measurement conversion based on the second order Taylor expansion (CM2) is necessary (and sufficient) to guarantee the consistency of the converted measurements (see part II [1] for the details). Initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the Converted Measurement Kalman Filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the Range-Direction-Cosine Extended Kalman Filter (ruvEKF) and the Unscented Kalman Filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard Extended Kalman Filter (E1KF) is proposed. This leads to a new filtering approach, designated as Measurement Covariance Adaptive Extended Kalman Filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the Posterior Carmer-Rao Lower Bound for the scenarios considered.

The Probabilistic Multi-Hypothesis Tracker (PMHT) has been demonstrated to be an effective multi-target tracker while retaining linear computational complexity in the number of measurements and targets. However PMHT only provides a point estimate for target tracks. The "covariance" returned by the PMHT is a byproduct of applying the Expectation-Maximization algorithm to maximize the PMHT likelihood function and is not intended to be the track estimate covariance. In this paper we derive a consistent covariance estimator for PMHT. By re-introducing the constraint that the sum of the PMHT weights (posterior probabilities that a measurement is target-originated) across measurements sum to unity, a covariance based on Probabilistic Data Association (PDA) principles is derived. We show through simulations that the resulting covariance provides a consistent covariance for the PMHT track estimates. There has been some work both in the statistics and engineering literature that gives the posterior covariance for ML Gaussian-mixture estimation, and the PMHT can be viewed as a tracker whose genesis is of MAP Gaussian-mixture estimation with a Gaussian prior. The expressions and calculations are, unfortunately, complicated. Consequently we also report on a novel and intuitive way to derive these via calculus.

In this paper we describe computationally efficient assignment-based algorithms to solve the data association problem in synchronous passive multisensor tracking systems. A traditional assignment-based solution to this problem is to solve the measurement-to-measurement association using multidimensional (S-dimensional or SD with S sensors) assignment formulation and the measurement-to-track association using two-dimensional assignment formulation. Even though this solution has been proven to be effective, it is computationally very expensive. One of the reasons is that in calculating the assignment cost of each possible candidate association one requires to find the maximum likelihood (ML) estimate of the unknown target state. The algorithms proposed in this paper use prior information of the targets that are being tracked to reduce the requirement for the costly ML estimation. The first algorithm is similar to the traditional two step technique except that it uses the predicted track information to avoid building the whole assignment tree in the measurement-to-measurement association. In particular, based on the predicted track information first validation gates are constructed for every target. Then, when forming the assignment tree, only the branches connecting measurements that satisfy the validation gate requirement are constructed. The second algorithm is a one-step algorithm in that it directly assigns the measurements to the tracks. We pose the data association problem as an (S + 1)-D assignment with the first dimension being the predicted state information of the tracks, and the rest of the S dimensions are the lists of measurements from the sensors. The costs of each possible (S + 1)-tuple are calculated based on the predicted track information, hence, the requirement for an ML estimate is eliminated. Further, we show that when the target maneuvers are not very high, and when the sensor measurements are uncorrelated the (S+1)-D assignment approximately decomposes into S individual 2-D assignments, resulting in huge computational savings.

This paper discusses the problem of numerically evaluating multi-frame, data-association hypotheses in multiple-target tracking in terms of their a posteriori probabilities. We describe two approaches to the problem: (1) an approach based on K-best multi-frame data association hypothesis selection algorithms, and (2) a more direct approach to calculating a posteriori probabilities through Markov-chain-Monte-Carlo (MCMC) or sequential Monte Carlo (SMC) methods. This paper defines algorithms based on those two approaches and compares their performance, and it discusses their relative effectiveness, using simple numerical examples.

The optimal Bayesian multi-target tracking is computationally demanding. The probability hypothesis density (PHD) filter, which is a first moment approximation of the optimal one, is a computationally tractable alternative. By evaluating the PHD, one can extract the number of targets as well as their individual states. Recent sequential Monte Carlo (SMC) implementation of the PHD filter paves the way to apply the PHD filter to nonlinear non-Gaussian problems. It seems that the particle implementation of PHD filter is more dependent on current measurements, especially in the case of low observable target problems (i.e., estimates are sensitive to missed detections and false alarms). In this paper, a PHD smoothing algorithm is proposed to improve the capability of the PHD based tracking system. By performing smoothing, which gives delayed estimates, we will get not only better estimates for target states but also better estimate for number of targets. Simulations are performed on proposed method with a multi-target scenario. Simulation results confirm the improved performance of the proposed algorithm.

This paper presents a method for the realization of nonlinear/non-Gaussian Bayesian filtering based on spline interpolation. Sequential Monte Carlo (SMC) approaches are widely used in nonlinear/non-Gaussian Bayesian filtering in which the densities are approximated by taking discrete set of points in the state space. In contrast to the SMC methods, the proposed approach uses spline polynomial interpolation to approximate the probability densities as well as the likelihood functions. A good representation of the probability densities is an essential issue in the success of the filtering algorithm, especially in nonlinear filtering, since the probability densities in nonlinear filtering could be multi-modal. An advantage of the proposed approach is that it retains the accurate density information and thus a target probability at any region in the state space can easily be obtained by evaluating the integral of the polynomial. Further, the probability densities are represented with polynomials of fixed order and any further processing on probability densities could be performed with less computation. This paper uses the B-spline interpolation in order to maintain the positivity of probability density functions and likelihood functions. Simulation results are presented to compare the performance and computational cost of the proposed algorithm with an SMC method.

In a single-frame track-to-track association, due to the local sensors track swapping (switching of the track from an estimated target to another estimated target, under measurement uncertainty conditions), the identities of the fused tracks over several frames are not preserved. The main goal of the proposed track-to-track association method is to link the histories of fused tracks over several frames and avoid track swapping at the fusion center level (e.g. to preserve the continuity of the fused tracks through their identities). In this method, the previous association hypotheses are taken as priors in a multiple-hypothesis association chain. The continuity of the fused tracks over several frames is achieved through the prediction of the fused tracks obtained from a set of best association hypotheses at each frame. Through this, if in computing the fused tracks estimation errors, their identities are taken into account (e.g. the errors of a fused track over all the frames are computed with respect to the same true target), this procedure will improve also the fused track state estimation error. The method and implementation proposed is intended to be used to identify the histories of two or more tracks at the fusion center, and possibly to improve the track-to-track association.

Fusion of data from multiple sensors can be hindered by systematic bias errors. This may lead to severe degradation in data association and track quality and may result in a large growth of redundant and spurious tracks. Multi-sensor networks will generally attempt to estimate the relevant bias values (usually, during sensor registration), and use the estimates to debias the sensor measurements and correct the reference frame transformations. Unfortunately, the biases and navigation errors are stochastic, and the estimates of the means account only for the "deterministic" part of the biases. The remaining stochastic errors are termed "residual" biases and are typically modeled as a zero-mean random vector. Residual biases may cause inconsistent covariance estimates, misassociation, multiple track swaps, and redundant/spurious track generation; we therefore require some efficient mechanism for mitigating the effects of residual biases. We present here results based on the Schmidt-Kalman filter for mitigating the effects of residual biases. A key advantage of this approach is that it maintains the cross-correlation between the state and the bias errors, leading to a realistic covariance estimate. The current work expands on the work previously performed by Numerica through an increase in the number of bias terms used in a high fidelity simulator for air defense. The new biases considered revolve around the transformation from the global earth-centered-earth-fixed (ECEF) coordinate frame to the local east-north-up (ENU) coordinate frame. We examine not only the effect of bias mitigation for the full set of biases, but also analyze the interplay between the various bias components.

This paper describes a primal-dual distributed algorithm for managing communications in a bandwidth-limited sensor network for tracking and surveillance. The algorithm possesses some scale-invariance properties and adaptive gains that make it more practical for applications such as tracking where the conditions change over time. A simulation study comparing this algorithm with a priority-queue-based approach in a network tracking scenario shows significant improvement in the resulting track quality when using flow control to manage communications.

Target tracking in an urban environment presents a wealth of ambiguous tracking scenarios that cause a kinematic-only tracker to fail. Partial or full occlusions in areas of tall buildings are particularly problematic as there is often no way to correctly identify the target with only kinematic information. Feature aided tracking attempts to resolve problems with a kinematic-only tracker by extracting features from the data. In the case of panchromatic video, the features are often histograms, the same is true for color video data. In the case where tracks are uniquely different colors, more typical feature aided trackers may perform well. However, a typical urban setting has similar size, shape, and color tracks, and more typical feature aided trackers have no hopes in resolving many of the ambiguities we face. We present a novel feature aided tracking algorithm combining two-sensor modes: panchromatic video data and hyperspectral imagery. The hyperspectral data is used to provide a unique fingerprint for each target of interest where that fingerprint is the set of features used in our feature aided tracker. Results indicate an impressive 19% gain in correct track ID with our hyperspectral feature aided tracker compared to the baseline performance with a kinematic-only tracker.

This paper compares the performance of several algorithms for estimating relative sensor biases when two sets of sensor tracks from two sensor systems are to be fused to form system tracks. The primary focus of this paper is the algorithms' performance, particularly in terms of the mean-square estimation error criterion. The efficiency of the algorithms is not our focus for this study. We are especially interested in three estimation algorithms: (1) the joint track-association/ relative-bias-estimation maximum a posteriori (MAP) probability-density/probability-mass function algorithm; (2) the marginal MAP probability density estimation algorithm; and (3) the minimum-variance (MV) estimation algorithm. Those algorithms rely on the capability of generating and evaluating multiple significant track-to-track association hypotheses, which may be obtained by any of the recently developed k-best bipartite data assignment algorithms. Several other algorithms that have been considered in the past will also be discussed.

The Observable Operator Model (OOM) approach have been proposed as a better alternative to the Hidden Markov Model (HMM). However the basic modeling of OOMs assume that the data is generated by some discrete state variable which can take on one of several values which is unreasonable for most classification problems. Main limitation of existing OOM classification is that they require substantial training data, assumed to be similar to the data on which the algorithm is tested. In many applications the target is observed from multiple target-sensor orientations (or aspects), and the underlying feature information is highly aspect dependant and continuous variable. The multi-aspect target classification method presented based on continuous-valued Observable Operator Model (OOM), from which a full posterior distribution of a target class is inferred. It is possible to extend a discrete OOM as a continuous-valued OOM using a membership function. Further, predefined set of classes were used in training based joint target tracking and classification methods. These methods perform poorly, when new target present in the surveillance region which is not in the available class-set. In order to overcome this shortage, we propose an online training algorithm for OOM, which identifies new incoming target classes and add them into the available class-set. As the number of target class increases with the online learning procedure, there is a need for an adaptive class-set selection in order to reduce computational cost. An adaptive class-set approach for joint target tracking and classification is formulated via hypotheses testing, which reduces computation cost compared to calculating OOM likelihood for each target class. Simulation results are given to demonstrates the merits of continuous-valued Observable Operator Method (OOM) for target classification over discrete OOM, advantages of online training OOM and the efficiency of class-set adaptation algorithm.

This paper documents initial work into the development of a novel framework for sensor resource management: the Adaptive Horizon Sensor Management Framework (AHSMF). The concept at the core of AHSMF is that the optimal length of the planning horizon is dependent on the accuracy with which one can predict actual future performance, which is itself dependent on the level of uncertainty in the system (e.g. target state uncertainty). In the simplest case, in which there is no uncertainty (e.g. the target state and behavior are precisely known), a Dynamic Programming approach allows the planning horizon to extend far into the future as it is known precisely what the long-term impact of actions will be. However, we argue that in highly uncertain environments, the planning horizon should remain relatively short as the implications of actions on medium (and longer) term performance are hard to quantify. The basis of this paper is to validate this concept. We present two examples. The first is a simple toy problem in which we must plan over two time steps. We show that one step-ahead planning can perform better than two step-ahead planning if (i): the future impact of actions is highly variable, and (ii): the system controller has only limited information that does not capture this variability. The second example considers the problem of tracking a highly manoeuvring target using unmanned air vehicles (UAVs) that perform passive sensing. In this case, even more complex mechanisms influence the optimal length of the planning horizon. Two step-ahead planning outperformed one step-ahead planning (in terms of tracking accuracy) in many scenarios. However, in the most difficult, challenging and uncertain problems, with just one UAV tracking a target that frequently manoeuvred, one step-ahead planning was shown to perform significantly better. Future work will aim to identify the exact mechanisms responsible for the sub-optimality of multi-step-ahead planning in this, and other, pertinent applications. This will then provide a framework for adjusting the planning horizon online, in order to avoid unnecessary over-planning and maximize performance.

As the military continues to move forward with an increased number of sensor and fusion systems, it becomes necessary for these systems to be able to communicate efficiently and effectively. In these environments there are multiple sensor and fusion systems that in the past have operated independently of one another. As an increasing number of systems become available, eventually an overlap in the coverage area occurs between these fusion systems. This results in a need for coordination between these semi-autonomous fusion systems. Short of a complete redesign of all the fusion systems, a solution is required to address the handoff of data between these systems. The primary goal of this paper is to describe a data fusion handoff capability that is able to augment these existing systems. This is accomplished by the use of a Handoff Manager that is added to each fusion system. The Handoff Manager is responsible for developing a global representation the track information displayed onboard its own fusion system that is common with the other members of the federation of fusion systems. This is accomplished by using a global track numbering scheme that requires communication and adjudication between the multiple Handoff Manager components that are present on the different fusion systems within the federation. This paper will define the data fusion handoff problem and describe our approach for handling the data fusion handoff problem within the context of overlapping and non-overlapping sensor environments. We will conclude with a discussion of results for a sample problem and of the path forward.

Surveillance and ground target tracking using multiple electro-optical and infrared video sensors onboard unmanned aerial vehicles (UAVs) have drawn a great deal of interest in recent years due to inexpensive video sensors and sensor platforms. In this paper, we compare the convex combination fusion algorithm with the centralized fusion algorithm using a single target and two UAVs. The local tracker for each UAV processes pixel location measurements in the digital image corresponding to the target location on the ground. The video measurement model is based on the perspective transformation and therefore is a nonlinear function of the target position. The measurement model also includes the radial and tangential lens distortions. Each local tracker and the central tracker use an extended Kalman filter with the nearly constant velocity dynamic model. We present numerical results using simulated data from two UAVs with varying levels of process noise power spectral density and pixel location standard deviations. Our results show that the two fusion algorithms are unbiased and the mean square error (MSE) of the convex combination fusion algorithm is close to the MSE of the centralized fusion algorithm. The covariance calculated by the centralized fusion algorithm is close to the MSE and is consistent for most measurement times. However, the covariance calculated by the convex combination fusion algorithm is lower than the MSE due to neglect of the common process noise and is not consistent with the estimation errors.

In this paper, we consider the problem of sensor resource management in decentralized tracking systems with asynchronous communication and sensor selection. Due to the availability of cheap sensors, it is possible to deploy a large number of sensors and use them 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 maximum of certain number of sensors can be used by any fusion center at any one time. The problem is then to select the sensor subsets that should be used at each sampling time in order to optimize the tracking performance under the given constraints. In recent papers, we proposed algorithms to handle the above problem in centralized, distributed and decentralized architectures. However, in the paper for sensor subset selection for decentralized architecture, we assumed that all the fusion centers change their sensors at the same time, and their sensor change time interval is fixed and known. However, in general case, fusion centers may change their sensors at different time, and their sensor change intervals may not be fixed. In this case, the sensor management become more difficult. We have to decide when to change the subsets, and how to incorporate the changes made in the neighboring fusion centers in selecting the future sensor subsets. 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 problem of track-to-track association of local tracks from two disparate and dispersed sensor systems is considered. Typical approaches to this problem base the association upon the estimated target states. Bias, pointing, navigation and location errors among others often frustrate theses approaches and result in higher association error probabilities. Realizing that the state estimate represents on the first order statistics of the target trajectory, this paper augments those approaches with an association test based upon the second order statistics of the measurements. It is shown that in general, the cross-covariance of the measurements from two disparate and dispersed sensor systems will be nonzero if the measurements are from tracks on the same target. If the tracks are on different targets then the measurement crosscovariance will be zero. A test of the null hypothesis that the measurement cross-covariance is zero is derived and an implementation using sample statistics is developed. The probability density function of the test statistic is presented so that the test result can be combined with the association result based upon the estimated track state. Both absolute and relative tests are discussed. The effect of track length is analyzed and then examined in an example.

Radar systems have good radial resolution, but they have poor angular resolution that results in unresolved measurements. This problem can be mitigated by utilizing the spatial diversity of multistatic radar system. In this paper, the detection of unresolved targets with a hybrid radar system using signal level fusion is considered. The system consists of two receivers: one is co-located with the transmitter and the other is located far from the transmitter. The area of interest, where the transmitter is focused on, is divided into grids, which are formed by circular range bins of the monostatic receiver and elliptical range bins of the bistatic receiver. Assuming these grids are good enough to resolve the targets (i.e., each grid has at most one target and vice versa), the amplitudes of the targets (corresponding to all grids) that maximize the likelihoods of the signals obtained from both receivers are determined. These optimum values are then compared against a threshold for the final decision. Simulation studies are performed to demonstrate the proposed algorithm for hybrid radar system with unresolved targets. The simulation results confirm the enhancement in detection of unresolved targets by fusing coherently received signals from both monostatic and bistatic receivers.

In this paper, we consider the problem of collaborative sensor management with particular application to using unmanned aerial vehicles (UAVs) for multitarget tracking. The problem of decentralized cooperative control considered in this paper is an optimization of the information obtained by a number of unmanned aerial vehicles (UAVs) equipped with Ground Moving Target Indicator (GMTI) radars, carrying out surveillance over a region which includes a number of confirmed and suspected moving targets. The goal is to track confirmed targets and detect new targets in the area. Each UAV has to decide on the most optimal path with the objective to track as many targets as possible maximizing the information obtained during its operation with the maximum possible accuracy at the lowest possible cost. Limited communication between UAVs and 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. Markov Decision Processes (MDPs) are incorporated into the solution. Given the 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. The authors present multi-level hierarchy of MDPs controlling each of the UAVs. Each level in the hierarchy solves a problem at a different level of abstraction. Simulation results are presented on a representative multisensor-multitarget tracking problem.

The PHD filter has attracted much international interest since its introduction in 2000. It is based on two approximations. First, it is a first-order approximation of the multitarget Bayes filter. Second, to achieve closed-form formulas for the Bayes data-update step, the predicted multitarget probability distribution must be assumed Poisson. In this paper we show how to derive an optimal PHD (OPHD) filter, given that target number does not exceed one. (That is, we restrict ourselves to the single-target detection and tracking problem.) We further show that, assuming no more than a single target, the following are identical: (1) the multitarget Bayes filter; (2) the OPHD filter; (3) the CPHD filter; and (4) the multi-hypothesis correlation (MHC) filter. We also note that all of these are generalizations of the probabilistic data association (IPDA) filter of Musicki, Evans, and Stankovic.

The problem of joint maximum a posteriori (MAP) bias estimation and data association belongs to a class of nonconvex mixed integer nonlinear programming problems. These problems are difficult to solve due to both the combinatorial nature of the problem and the nonconvexity of the objective function or constraints. Algorithms for this class of problems have been developed in a companion paper of the authors. This paper presents simulations that compare the "all-pairs" heuristic, the k-best heuristic, and a partial A*-based branch and bound algorithm. The combination of the latter two algorithms is an excellent candidate for use in a realtime system. For an optimal algorithm that also computes the k-best solutions of the joint MAP bias estimation problem and data association problem, we investigate a branch and bound framework that employs either a depth-first algorithm or an A*-search procedure. In addition, we demonstrate the improvements due to a new gating procedure.

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 might cause 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 performance metrics of covariance consistency. Monte Carlo simulation results illustrate the characteristics of the proposed metrics of covariance consistency.

Tracking multiple targets in a cluttered environment is a challenging task. Probabilistic Multiple Hypothesis Tracking (PMHT) is an efficient approach for dealing with it. Essentially PMHT is based on the method of Expectation-Maximization for handling with association conflicts. Linearity in the number of targets and measurements is the main motivation for a further development and extension of this methodology. Unfortunately, compared with the Probabilistic Data Association Filter (PDAF), PMHT has not yet shown its superiority in terms of track-lost statistics. Furthermore, the problem of track extraction and deletion is apparently not yet satisfactorily solved within this framework. Four properties of PMHT are responsible for its problems in track maintenance: Non-Adaptivity, Hospitality, Narcissism and Local Maxima.^{1, 2} In this work we present a solution for each of them and derive an improved PMHT by integrating the solutions into the PMHT formalism. The new PMHT is evaluated by Monte-Carlo simulations. A sequential Likelihood-Ratio (LR) test for track extraction has been developed and already integrated into the framework of traditional Bayesian Multiple Hypothesis Tracking.³ As a multi-scan approach, also the PMHT methodology has the potential for track extraction. In this paper an analogous integration of a sequential LR test into the PMHT framework is proposed. We present an LR formula for track extraction and deletion using the PMHT update formulae. As PMHT provides all required ingredients for a sequential LR calculation, the LR is thus a by-product of the PMHT iteration process. Therefore the resulting update formula for the sequential LR test affords the development of Track-Before-Detect algorithms for PMHT. The approach is illustrated by a simple example.

We derive and test a new nonlinear filter that implements Bayes' rule using an ODE rather than with a pointwise multiplication of two functions. This avoids one of the fundamental and well known problems in particle filters, namely "particle collapse" as a result of Bayes' rule. We use a log-homotopy to construct this ODE. Our new algorithm is vastly superior to the classic particle filter, and we do not use any proposal density supplied by an EKF or UKF or other outside source. This paper was written for normal engineers, who do not have homotopy for breakfast.

Particle filter tracking, a type of sequential Monte Carlo method, has long been considered to be a very promising but time-consuming tracking technique. Methods have been developed to include a particle filter as part of a Variable Structure, Interactive Multiple Model (VS-IMM) structure and to integrate it into the Multiple Hypothesis Tracker (MHT) scoring structure. By integrating a particle filter as just one of many filters in Raytheon's MHT, the particle filter is applied sparingly on difficult off-road targets. This dramatically reduces the computation time as well as improves tracking performance in circumstances in which the other filters do not excel. Moreover, terrain information may be taken into account in the particle propagation process. In particular, an Unscented Particle Filter (UPF) was implemented in order to address the potential dominance of a small set of degenerate particles and/or poor prior distribution sampling from hampering the ability of the particle filter to accurately handle a maneuver. The Unscented Particle Filter treats every particle as its own Kalman filter. After the distribution of particles is adjusted in order to take into account the terrain, each particle is divided into sigma point states. These sigma points are propagated forward in time and then recombined to form a new composite particle state and covariance. These reformed particles are used in scoring and can be updated with a new observation. Since the Unscented Particle Filter includes the covariances in these calculations, this particle filter approach is more accurate and potentially requires fewer particles than an ordinary particle filter. By adding an Unscented Particle Filter to the other filters in an MHT tracker, the advantages of the UPF can be utilized in an efficient manner in order to enhance tracking performance.

This paper presents a multiple model procedure to estimate the state of a ballistic object in the atmosphere and identify it using radar measurements. The measurements are taken during the first part of its trajectory and the final state estimate is then predicted to its impact point on earth. This paper uses, for each model, a different extended Kalman filter for state estimation and then uses the model likelihoods to identify the projectile. Simulations are carried out on three mortar trajectories using 7-state models. It is shown from simulations carried out on several ballistic trajectories that the impact point is predicted to a high degree of accuracy and with a consistent covariance and that the projectile can be identified with a high probability.

ITT Corporation, Advanced Engineering and Sciences Division, is currently developing the Joint Contaminated Surface Detector (JCSD) technology under an Advanced Concept Technology Demonstration (ACTD) managed jointly by the U.S. Army Research, Development, and Engineering Command (RDECOM) and the Joint Project Manager for Nuclear, Biological, and Chemical Contamination Avoidance for incorporation on the Army's future reconnaissance vehicles. This paper describes the design of the chemical agent identification (ID) algorithm associated with JCSD. The algorithm detects target chemicals mixed with surface and interferent signatures. Simulated data sets were generated from real instrument measurements to support a matrix of parameters based on a Design Of Experiments approach (DOE). Decisions based on receiver operating characteristics (ROC) curves and area-under-the-curve (AUC) measures were used to down-select between several ID algorithms. Results from top performing algorithms were then combined via a fusion approach to converge towards optimum rates of detections and false alarms. This paper describes the process associated with the algorithm design and provides an illustrating example.

Sometimes radar targets cross and become unresolved; this is a concern, but with a reasonable track depth and an appropriate merged-measurement model the concern is considerably mitigated. Sonar targets, however, can become merged (in the same beam) for considerably longer, particularly with bearing-only measurements. In such cases the crossing times can be 100 scans long, and no reasonable depth exists for an multi-frame tracker that can "see" both ends of the merged period. Further, there is a demonstrable tendency for estimated targets to repel each other as they are being tracked. In this paper we explore the hypothesis-oriented multi-hypothesis tracker (HO-MHT), an MHT approach that uses the new "rollout" optimization insight and the to give an appropriate and cost-effective means to rank hypotheses, and also the PMHT tracker that operates on batches of scans with linear computational complexity in most quantities. We show results in terms of estimation error (RMSE), consistency (NEES) and computational effort in both linear and beam-space tracking scenarios.

Closely-spaced (but resolved) targets pose a significant challenge for single-frame unique measurement-to-track data association algorithms. This is due to the similarity of the Mahalanobis distances between the closely-spaced measurements and tracks. Contrary to conventional wisdom, adding target feature information (e.g., target amplitude) does not necessarily improve the probability of correctly assigning measurements to tracks. In this paper, the theoretical limitations of using radar cross section (RCS) data to aid in measurement-totrack association are reviewed. The results of a high-fidelity simulation assessment of the benefits of RCSaided measurement-to-track association (using the Signal-to-Noise Ratio) are given and other possibilities for RCS-aided tracking are discussed. Namely, we show the analytical results of our investigation into using RCS information to determine the presence of merged measurements.

The problem of joint maximum a posteriori (MAP) bias estimation and data association belongs to a class of nonconvex mixed integer nonlinear programming problems. These problems are difficult to solve due to both the combinatorial nature of the problem and the nonconvexity of the objective function or constraints. A specific problem that has received some attention in the tracking literature is that of the target object map problem in which one tries match a set of tracks as observed by two different sensors in the presence of biases, which are modeled here as a translation between the track states. The general framework also applies to problems in which the costs are general nonlinear functions of the biases. The goal of this paper is to present a class of algorithms based on the branch and bound framework and the "all-pairs" and k-best heuristics that provide a good initial upper bound for a branch and bound algorithm. These heuristics can be used as part of a real-time algorithm or as part of an "anytime algorithm" within the branch and bound framework. In addition, we consider both the A*-search and depth-first search procedures as well as several efficiency improvements such as gating. While this paper focuses on the algorithms, a second paper will focus on simulations.

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 targets of opportunity in the sensor field-of-view for online estimation of time-variant biases. The algorithm uses the singular value decomposition (SVD) to automatically handle the issue of parameter observability during tracking, allowing for shorter estimation windows and more accurate bias estimation. Our approach extends the novel methods proposed in the companion paper by Herman and Poore that used the SVD within a nonlinear least-squares estimator to handle the issue of parameter observability during offine estimation of time-invariant biases using truth data.

This paper describes experiences and results from developing a basic signal and data processing simulation for a pair of GEO IR sensors observing the boost phase of Theater Ballistic Missiles (TBM). The goal of such a system is the detection of launched TBM, also against a cloud background, and the tracking from cloud break ideally up to boost-end. Two GEO satellites are used for stereo view of one and the same non-global limited Field-of-Regard (FOR). They are positioned in such a way that both cover the FOR and provide a sufficient triangulation baseline. Signal Processing is applied for each of both passive IR sensors in order to detect and track the TBM on the focal plane. The applied approach can be summarized under the term 'velocity filtering'. Data Processing operates on the 2-D signal processing input from both IR sensors, i.e. azimuth and elevation line-of-sight (LOS) angles as well as their rates. The goal is to provide 3-D tracks of the targets, which can be used to cue early warning or fire control radars. The underlying simulation model constitutes a prototype and vehicle for further research. Nevertheless, even in its current stage it provides a first tool for the analysis and evaluation of corresponding sensor design concepts.

The measurement conversion from a radar's r-u-v coordinate system to a Cartesian coordinate system is discussed in this paper. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventional (first order) converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitable corrected version (with second order terms) of the conversion equations (CM2) eliminates the inconsistency. The decision between using the standard conversion and the second order version is based on a condition ratio, namely, for an r-u-v measurement whose condition ratio is lower than a certain threshold, CM2 should be used. Results on various tracking filter using these conversions are presented in part I [1].