The multirate processing of two-dimensional (2D) signals involves various types of sampling and matrices, due to different grid geometry. A more consistent theory is then needed in order to obtain better techniques and useful results in many areas, such as image and signal processing, biomedical, telecommunications, multimedia, remote sensing, optics. In this work, a 2-channel complementary filter banks theory, designed based on 2D multirate processing and complementary filters properties is presented with foundations for multiresolution levels methods modeling, for the processing of signals in two-dimensions, in nonseparable way. Signal analysis and synthesis using 2-channel complementary filter (CF) banks, the conditions under which the reconstruction of the 2D input signal is perfect and frequency division in the analysis part are developed. Since multiresolution decomposition of signals, wavelet representation and filter banks have a strong link, a relation of then with complementary filter banks is done. Other multiresolution levels methods can be derived from this theory and applications of them were found for compression, edge detection, 2D scaling and wavelets functions and digital TV systems.

In target detection and tracking applications with imagery data taken from a moving camera platform, it is necessary to segment potential targets in each image frame. This is typically done by preprocessing individual images to exploit some known attribute about the data. Often these methods make many false detections, particularly in the presence of additive noise, and the results thus require significant post-processing. A means of estimating the background in the imagery sequence under the formalism of the Kalman filter is suggested. This background estimate is then used to recast the segmentation problem as one of outlier detection, and the result of segmentation is used to modify the filter update. Ways of making the technique computationally benign are discussed. The technique is used to analyse a simulated image sequence, and the performance is compared to that of a single-frame background-estimation technique. The feasibility of target segmentation via background tracking is thus demonstrated.

In this study, the best engagement ordering for a friendly fire unit against multiple targets is considered. This target prioritization is performed by computing a priority function based on the range and direction of a target using the images from an optical device. We automatically obtain the features of a target like x, y coordinates, intensity and size from the image sequence by the help of a tracker software. These features are used to estimate the range and the direction of each target. In our range estimation algorithm, camera properties (focal length, angle of view) and the features of the target extracted from tracker are used to find the z coordinate of the target. We estimate the range by using the x, y and z coordinates of the target. We assumed the direction is given by the cosine value of the angle between the vector pointing to the friendly force from the target and the vector of the movement of the target. We apply the direction algorithm by the help of the x, y, z coordinates of the target. After the estimation of the range and the direction, we applied target prioritization techniques. In the prioritization process, an expected utility value is computed for each possible engagement ordering using some features of the forces like range, direction, and mean rate of fire; then the ordering which maximizes this value is chosen. The aim of the friendly fire unit may vary: In some cases he may want to annihilate as many targets as possible regardless of the threats they pose whereas in other cases he may prefer to maximize the removed threat. The utility value used in all these cases may vary between zero and one. The strength of these range and direction estimation algorithms on engagement ordering are tested through simulated data and the results are approximately the same with the correct range and direction values.

A Vertical-Strip Least Mean Squared (VSLMS) algorithm is proposed to enhance the detection of small moving targets in IR image sequences. This algorithm is an improvement over the Two-Dimensional LMS (TDLMS), which is designed to detect small targets within highly correlated background of static images. This paper focuses on processing IR image sequences with different background features with layers of sky, sea and land clutter. The VSLMS uses multiple LMS modules and a different scanning method to process individual lines in the IR image sequences. Simulation results show successful enhancement of very small targets in an IR mage sequence.

The proliferation of small, lightweight, 'micro-' and 'nanosatellite' (largest dimension < 1m ) has presented new challenges to the space surveillance community. The small size of these satellites makes them unresolvable by ground-based imaging systems. The core concept of using Non-Imaging Measurements (NIM) to gather information about these objects comes from the fact that after reflection on a satellite surface, the reflected light contains information about the surface materials of the satellite. This approach of using NIM for satellite evaluation is relatively new. In this paper, we discuss the accuracy of using these spectral measurements to match an unknown spectrum to a database containing known spectra. Several approaches have been developed and are presented in this paper. The first method is an artificial neural network designed to process central moments of real measured spectra. This spectrum database is the Spica database provided by the Maui Surveillance Site (MSSS), Hawaii USA and consists in spectra from more than 100 different satellites. The average rate of correct identification is 84%. The second approach is based on the ability of spectral signal processing to estimate relative abundances of materials from the measurement of a single spectrum; this method is called spectral unmixing. Material spectra were provided by the NASA Johnson Space Center (JSC) to create synthetic spectra. An approach based on the Expectation Maximization (EM) algorithm was used to estimate relative abundances and presence of materials in a synthetic spectrum. The results for material identification and abundance estimation are presented as a function of signal-to-noise ratio. For the EM method, the overall correct estimation rate is 95.1% and the average error on the fractional composition estimation is 19.7%.

Past attempts to use acoustic sensor performance predictions, typically probability of detection as a function of range, in naval undersea warfare tactical decision aids such as trackers and mission planning tools have met with great difficulty. These efforts have been hampered by the uncertainty often inherent in these predictions. In some cases, the use of incorrect predictions produced results or recommendations that were worse than not using the predictions at all. The goal of the work reported in this paper is to develop a Track-Before-Detect (TBD) system that accounts for this uncertainty and has the following features: (1) It produces results are at least as good as those obtained with no performance prediction information. (2) It produces a significant improvement in performance in some situations. In this paper we describe an extension of a TBD system called the Likelihood Ratio Tracker (LRT) that incorporates uncertainty in performance prediction. We have run LRT on data that simulate a multistatic active sonar detection system similar to one in use by the Navy. In these simulated cases, we have shown that using performance prediction improves LRT tracking and detection performance even in the presence of large prediction errors.

Tracking maneuvering targets has always been a significant challenge to the tracking community, so new approaches to this problem are always being pursued. One approach is to use multiple model filters as an attractive design logic for both maneuver detection and filter re-initialization. Common current practice in multiple model tracking uses a switching Markov model. A well known multiple model tracker that uses Markov switching model is the Interactive Multiple Model (IMM). This approach requires the a priori knowledge of the transition probability matrix (TPM) of the target state. Such knowledge may not be available unless one has combat identification, so one is usually dealing with target of unknown maneuver strategies. The objective of this paper is to introduce concepts from fuzzy sets to design a multiple model filter which is applicable to an arbitrary number of target models while at the same time not requiring the usage of the Markov switching to transition between the threat models. The essential concept is to treat each possible target dynamics as a fuzzy cluster, then to use the measurement information about the target to compute the degree of membership the target has relative to a particular fuzzy cluster. Such membership value would then be the equivalent of the switching gain when using IMM terminology. The target state is the weighted sum of the states provided by each individual filter.

In target tracking algorithms using Kalman filtering-like approaches, the standard assumptions are Gaussian process and measurement noise models. Based on these assumptions, the Kalman filter is widely used in single or multiple filter versions (e.g., in an Interacting Multiple Model-IMM-estimator). The over-simplification resulting from the above assumptions can cause severe degradation in tracking performance. Of particular concern is the simplistic white noise or Wiener process acceleration models used to handle maneuvering targets. Presence of heavy-tailed noise in the observation process is another concern. In this paper we explore the application of Kalman-Levy filter to handle maneuvering targets. This filter assumes a heavy tailed noise distribution known as the Levy distribution. Unlike in the case of Gaussian distribution, the existence of the covariance is not guaranteed in this case. Due to the heavy tailed nature of the assumed distribution, the Kalman-Levy filter is more effective in the presence of large errors that can occur, for example, due to the onset of acceleration or deceleration. However, for the same reason, the performance of Kalman-Levy filter in non-maneuvering portion of track is worse than a Kalman filter's. This motivates us to develop an IMM estimator incorporating a Kalman filter and a Kalman-Levy filter. The performance of this filter is compared with an IMM estimator with two standard Kalman filters in a scenario from the 4th Navy tracking benchmark problem. It is found that the IMM estimator with a Kalman-Levy filter performs better than the other IMM estimator in both maneuvering and non-maneuvering portion of target flight.

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the target number varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The Probability Hypothesis Density (PHD) filter, which propagates only the first-order statistical moment (or the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important, but current PHD implementations do not provide a mechanism for handling this. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-conditioned estimates in a manner similar to the one used in the Interacting Multiple Model (IMM) estimator. In this paper a multiple model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using Sequential Monte Carlo methods, is proposed. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.

In target tracking, the track filter is an important element. It is also quite important that it is implemented efficiently. This is even better seen if one thinks of it that a filter is running for each data association hypothesis and in a real multi target tracking application the number of hypotheses, that need to be updated every scan, may easily be in the order of thousands. A standard 'single model' building block for a track filter is the (Extended) Kalman Filter (EKF). Multiple model filters, such as the popular and widely used Interacting Multiple Model filter (IMM) or the recently developed Multiple Model Multiple Hypothesis filter (M3H), are based on banks of EKF's that run in parallel and interact according to an underlying Markov transition modeling assumption. It is well known that, in case of a single model filter, the standard Kalman Filter gains and covariances can be calculated off line, when the process noise covariance and the measurement noise covariance are known. Unfortunately, this does not hold for the two types of multiple model filters, mentioned before. The main reason for this is that these multiple model filters interact. In this paper we investigate several methods to (partially) do the calculations off line and thus use less computations, while at the same time aiming at a minimal loss of performance. We will compare such an approximate IMM or M3H filter with the full on line IMM or M3H filter, both in terms of computational load and performance.

The assumption of Gaussian noise in the system and measurement model has been standard practice for target tracking algorithm development for many years. For problems involving manoeuvring targets this is known to be an over-simplification and a potentially poor approximation. In this paper the use of heavy-tailed distributions is suggested as a means of efficiently modelling the behaviour of manoeuvring targets with a single dynamic model. We exploit the fact that all heavy-tailed distributions can be written as scale mixture of Normals to propose a Rao-Blackwellised particle filter (SMNPF) where particles sample the history of the continuous scale parameter and a Kalman filter is used to conduct the associated filtering for each particle. Schemes are proposed for making the proposal of new particles efficient. Performance of a heavy-tailed system model implemented via the SMNPF filter is compared against an IMM for a sample trajectory taken from a benchmark problem.

Most practical multi-platform data fusion systems use the distributed tracking architecture where each sensor platform has its own local tracker. A local tracker performs tracking using measurements from one or more sensors and sends its track data to a central fusion system. When the track data from a local tracker is transmitted to the central fusion system using a communication network, the track data can arrive out-of-sequence due to random delays in the communication network and different processing times at local trackers. Track-to-track fusion using the equivalent decorrelated pseudo-measurement approach is an efficient algorithm for the distributed tracking problem. In this paper, we use an existing multiple-lag out-of-sequence measurement (OOSM) algorithm and the decorrelated pseudo-measurement approach for track-to-track fusion of out-of-sequence track (OOST) data. We present numerical results using simulated data for a scenario where a global tracker processes track data from two local trackers. Each local tracker processes two-dimensional position and velocity measurements from a single sensor. We use Monte Carlo simulations to evaluate the performance of the algorithm.

The problem of tracking targets in clutter naturally leads to a Gaussian mixture representation of the probability density function of the target state vector. Modern tracking methods maintain the mean, covariance and probability weight corresponding to each hypothesis, yet they rely on simple merging and pruning rules to control the growth of hypotheses. This paper proposes a structured, cost-function-based approach to the hypothesis control problem, utilizing the Integral Square Error (ISE) cost measure. A comparison of track life performance versus computational cost is made between the ISE-based filter and previously proposed approximations including simple pruning, Singer's n-scan memory filter, Salmond's joining filter, and Chen and Liu's Mixture Kalman Filter (MKF). The results demonstrate that the ISE-based mixture reduction algorithm provides track life performance which is significantly better than the compared techniques using similar numbers of mixture components, and performance competitive with the compared algorithms for similar mean computation times.

Methods have been developed to apply Multiple Hypothesis Tracking (MHT) to a distributed multiple platform system for tracking missile targets. The major issue that must be addressed is the requirement for a single integrated air picture (SIAP) to be maintained across the multiple platforms. Communication delays and failures mean that the platforms will, in general, form different MHT hypotheses with resultant different output tracks presented to the users. Thus, logic, described in this paper, has been developed to ensure that similar data association decisions will be made across the multiple platforms.

The need to track closely-spaced targets in clutter is essential in support of military operations. This paper presents a Multiple Hypothesis Tracking (MHT) algorithm which uses an efficient structure to represent the dependency which naturally arises between targets due to the joint observation process, and an Integral Square Error (ISE) mixture reduction algorithm for hypothesis control. The resulting algorithm, denoted MHT with ISE Reduction (MISER), is tested against performance metrics including track life, coalescence and track swap. The results demonstrate track life performance similar to that of ISE-based methods in the single-target case, and a significant improvement in track swap metric due to the preservation of correlation between targets. The result that correlation reduces the track life performance for formation targets requires further investigation, although it appears to demonstrate that the inherent coupling of dynamics noises for such problems eliminates much of the benefit of representing correlation only due to the joint observation process.

This paper discusses the evaluation of data association hypotheses for a general class of multiple target tracking problems. We assume that the number of targets is unknown, and that given the number of targets, the joint target state distributions form a system of independent, identically distributed (i.i.d.) probability distributions. We are particularly interested in the case where the prior probability distribution of the number of targets is not necessarily Poisson. We will show that the Poisson assumption is not only sufficient but also necessary for the commonly used standard multiplicative hypothesis evaluation formula. Consequently, we claim that the use of the standard multiplicative hypothesis evaluation formula implies, either explicitly or implicitly, the Poisson assumption. We will also examine the Poisson assumption on the number of false alarms in each measurement set.

Multi-sensor management is concerned with utilising the available sensor resource in the most effective way possible to detect, classify or track targets. We are primarily concerned with utilising the sensor resource in order to track a target as closely as possible. Previous work in this area has focused on tracking targets whose motion is either governed by a pre-specified model, or manoeuvre at pre-specified times. In particular, targets do not adapt their behaviour in order to make tracking them more difficult. In this paper, we apply state of the art sensor management techniques to a scenario in which the target is actively trying to avoid being tracked. This creates a conflict between the aims of sensor network and the target, which these previous techniques are unable to resolve. We formulate the action (e.g. manoeuvre) of the sensor resource (the pursuer) and the target (the evader) as a two-player game. The "reward" each player receives is then dependent on the actions chosen and the ensuing tracking accuracy. We also allow multi-step planning, in which the action of each player takes into account the impact this will have on future expected rewards (i.e. future tracking performance). We show that, form the pursuer's perspective, tracking performance is significantly improved by multi-step planning. Conversely, the evader can substantially degrade tracking performance by following the strategies we recommend, when compared to either performing random manoeuvres or moving with constant velocity.

Association of observations and tracks is a fundamental component of most solutions to the tracking problem. Association is frequently formulated as a multiple hypothesis test. Typically, the test statistic, called the track score, is the likelihood or likelihood ratio of the observations conditioned upon the association hypotheses. Assuming that the test is reasonably efficient, further reduction in the association error probability necessitates the introduction of additional information into the track score. This additional information is embodied in quantities called track features which are to be included in the track score. In practice, the necessary conditional probabilities of the track features are unknown. The class of non-parametric hypothesis tests is designed to provide such a test in the absence of any probabilistic information about the data. However, the test statistics used in non-parametric tests cannot be used directly in the track score. The one probabilistic quantity generally available with non-parametric tests is the Type I error probability, the probability of failing to accept a true hypothesis. If the non-parametric test is distribution free then the Type I error probability is independent of the distribution of the track features. This paper presents a distribution free, non-parametric test of the track features that can be used to test the association hypotheses and a quantity that can be included in the track score is derived from the Type I error probability of the test.

The tracking goal is to reduce positional uncertainty. There are many ways to reduce tracking uncertainty: including classification data, using trafficability maps, and employing behavior information. We seek to extend tracking and identification modeling by incorporating intent to update prediction velocity vectors. A hybrid state space approach is formulated to deal with continuous-valued kinematics and discrete-valued target type, pose (inherently continuous but quantized), and intent behavior. The coupled tracker design is illustrated within the context of using ground moving target indicator (GMTI) and high range-resolution (HRRR) measurements as well as digital terrain elevation data (DTED), road map, and estimated goal states. The resulting Intent Coupled Tracking and Identification (ICTI) system is expected to outperform separately designed systems particularly during target maneuvers and recovering from temporary data dropout.

In this paper we consider the general problem of managing an array of sensors in order to track multiple targets in the presence of measurement origin uncertainty. There are two complicating factors: the first is that because of physical limitations (e.g., communication bandwidth) only a small number of sensors can be utilized at any one time. The second complication is that the associations of measurements to targets/clutter are unknown. It is this second factor that extends our previous work [14]. Hence sensors must be utilized in an efficient manner to alleviate association ambiguities and allow accurate target state estimation. Our sensor management technique is then based on controlling the Posterior Cramer-Rao Lower Bound (PCRLB), which provides a measure of the optimal achievable accuracy of target state estimation. Only recently have expressions for multitarget PCRLBs been determined [7], and the necessary simulation techniques are computationally expensive. However, in this paper we propose some approximations that reduce the computational load and we present two sensor selection strategies for closely spaced (but, resolved) targets. Simulation results show the ability of the PCRLB based sensor management technique to allow efficient utilization of the sensor resources, allowing accurate target state estimation.

Traditional missile warning systems (MWSs) have tended to use the ultra-violet waveband, where the ambient intensity levels tend to be low and the resultant false alarm rate is comparatively small. The development of modern infrared imagers has generated interest in the use of infrared imagers in MWSs. Infrared cameras can detect the heat signatures of missile plumes, which peak in the mid-wave (3-5 micron) infrared band, but they can also contain appreciable levels of noise: including intermittent defects that are of the same size as the potential targets. Typically, both missiles and defects will only occupy a few pixels in each image. This paper reviews a project concerned with developing an MWS algorithm toolbox for use in evaluating infrared MWSs. In particular, the paper discusses some of the main problems associated with detecting and tracking missiles in infrared imagery from a moving platform in the presence of localised image noise.

Tracking and initiating large numbers of closely spaced objects can pose significant real-time challenges to current state-of-the-art tracking systems. Cluster or group tracking has been suggested to reduce the computational complexity when closely spaced targets move with similar dynamical properties. While modern individual object tracking systems make association decisions over multiple frames of data, most cluster tracking systems make single-frame clustering decisions. In this paper we illustrate an extension of multiple frame assignment (MFA) individual object tracking to multiple frame cluster MFA tracking. In our approach, multiple single-frame clustering hypotheses are formed and the best clustering is selected over multiple frames of data. In recent work we formulated multiple frame cluster tracking assignment problems and demonstrated a single-frame cluster MFA tracking architecture. The work discussed in this paper extends the previous work and illustrates a multiple hypothesis clustering, multiple frame assignment (MHC-MFA), tracking system. We present simulations studies that motivate the benefits of the multiple frame cluster tracking approach over single-frame cluster tracking and discuss the computational efficiency of the multiple frame cluster tracking approach.

Effective and efficient approaches to monitor and manage maneuvering objects are of great importance in various applications, such as wide battlefields, traffics, and wireless communications. Modern airborne radar sensors can provide wide-area surveillance coverage of ground activities. The huge volume of radar data renders it impractical and inefficient to examine all the activities of individual moving object. Clustering moving objects and predicting motion tendencies of large groups are becoming a crucial issue for optimizing resource distribution and formulating sound decisions. However, most traditional clustering techniques are static-object-oriented and not effective at clustering maneuvering objects. In addition, the radar data intermittence and noise data, which are caused by extraneous objects and stationary clutter background, are major difficulties in clustering and predicting groups. In this paper, we present a dynamic-object-oriented clustering approach to detecting and predicting large group activities over time. We propose a "core member" concept to support dynamic-object-oriented clustering and to mitigate the effects of data intermittence and noise data. In general, some special targets always tend to remain in a constant group and stay near the center of that group. To a large extent, the movement of these targets represents the activity of the entire group. To exploit this characteristic, we consider these special targets to be core members of their own cluster. The movements of the core members can help us detect clusters and predict their future movements. The performance and results of the application of our approach to CASTFOREM data sets are also presented.

Performance Metrics (PMs) may be used to evaluate correlation and fusion algorithm performance, particularly in conjunction with Monte Carlo runs of candidate algorithms. These PMs, in some cases, have been used for many years by researchers; less often in industry applications. A survey of recent literature in tracking and fusion shows there are many PMs from which to choose. A few of the more popular metrics include: percent of miscorrelations, percent of correct correlations, total tracking time (tracking persistence), time on target, and percent of total targets tracked and correlated. These types of statistics may be obtained from Monte Carlo simulation test runs. Determination of and access to the truth data for comparison purposes are only part of the problem when using a performance metric. A versatile test tool which can be tailored to the application is also essential. Use of Monte Carlo simulation test results to compute performance metrics is reviewed. Recent experience with PM usage in algorithm development projects is recounted in case studies with appropriate tables and charts. Factors affecting algorithm performance and hence, PM values are considered and discussed. Several questions are posed (and partly answered) regarding ultimate use of PM results.

We propose a very generic Bayesian framework for the principled exploitation of probabilistic batch-learning technologies for real-time state estimation. To illustrate our concepts, we derive a nonlinear filtering/smoothing solution for a challenging case study in target tracking. We also demonstrate the application of Markov chain Monte Carlo (MCMC) sampling methods as a computational tool within our framework. Finally, we present simulation results, benchmarked against a comparable particle filter.

The multisensor-multitarget Bayes filter is the foundation for multi-sensor-multitarget detection, tracking, and identification. This paper addresses the question of principled implementation of this filter. Algorithms can always be cobbled together using catch-as-catch-can heuristic techniques. In formal Bayes modeling one instead derives statistically precise, implementation-independent equations from which principle approximations can then be derived. Indeed, this has become the accepted methodology for single-sensor, single-target tracking R&D. In the case of the multitarget filter, however, partisans of a so-called "plain-vanilla Bayesian approach" have disparaged formal Bayes modelling, and have protrayed specific, ad hoc implementations as completely general, "powerful and robust computational methods." In this and a companion paper I expose the speciousness of such claims. This paper reviews the elements of formal Bayes modeling and approximation, describes what they must look like in the multitarget case, and contrasts them with the "plain-vanilla Bayesian approach."

Hybrid models have proven useful for tracking targets with multiple motion modes. Most emphasis in the literature has been devoted to aircraft which transition from constant velocity motion to constant (or nearly constant) turns and back. Ground targets motions have received less attention despite similarities with aircraft. This paper presents a study of the ground-tracking problem using the Gaussian wavelet estimator as the basic algorithm. The sensor suite contains a matrix of range-bearing sensors of quality that is strongly range dependent. There also may be an acoustic sensor which provides an auxiliary speed measurement. It is shown that the high degree of partitioning of the kinematic state space provided by the algorithm is useful in this application.

In this paper we propose a new formulation for reliably solving the measurement-to-track association problem with a priori constraints. Those constraints are incorporated into the scalar objective function in a general formula. This is a key step in most target tracking problems when one has to handle the measurement origin uncertainty. Our methodology is able to formulate the measurement-to-track correspondence problem with most of the commonly used assumptions and considers target feature measurements and possibly unresolved measurements as well. The resulting constrained optimization problem deals with the whole combinatorial space of possible feature selections and measurement-to-track correspondences. To find the global optimal solution, we build a convex objective function and relax the integer constraint. The special structure of this extended problem assures its equivalence to the original one, but it can be solved optimally by efficient algorithms to avoid the cominatorial search. This approach works for any cost function with continuous second derivatives. We use a track formation example and a multisensor tracking scenario to illustrate the effectiveness of the convex programming approach.

A major challenge in tracking midcourse objects by means of an infrared (IR) sensor is that during a significant part of the trajectory they are closely spaced (Closely Spaced Objects, or CSO). The imprints of the CSOs on the IR focal plane create blurred unresolved clusters where the number, the coordinates, and the radiant intensities of the objects are not immediately apparent. This paper presents two methods for solving the problem of midcourse CSO resolution using IR focal plane data in the context of the Space Tracking and Surveillance System (STSS). Both approaches are based on dynamics/radiant intensity models of the focal plane objects, and use least squares-based minimization procedures. The first and more traditional baseline approach estimates the focal plane coordinates of the objects and their intensities on a frame-by-frame basis. The object tracks are then established by associating and fitting the estimates of all the frames to the postulated models. An alternative, multi-frame approach explored in this paper, uses the focal plane information from an entire sequence of frames, and, using least squares criteria over space and time and matched filtering, estimates the model parameters directly. With this "track-before-detect" approach, the association problem of objects to tracks is embedded in the estimation procedure.

Most maximum likelihood (ML) trackers based on measurement fusion (measurement-to-measurement or measurement-to-track) or track-to-track fusion produce a single data association hypothesis together with kinematic track state estimates. Uncertainty in the track states due to process and measurement noise is represented by covariance matrices, however uncertainty in the data association is either entirely neglected or representative of only limited types of association uncertainty. This paper presents a Bayesian-Network uncertainty management system for use in conjunction with maximum-likelihood trackers. The system, termed the Bayesian Network Tracking Database (BNTD) comprises algorithms for interactive access, whereby expectation values of arbitrary track properties can be calculated over all association hypotheses, and algorithms and data-structures for long-term storage, whereby the complete set of association hypotheses can be efficiently approximated, even over long time intervals. A conjoined MLE/BNTD system is thus capable of supporting target identification (ID), feature-aided tracking, and long-term track maintenance (LTTM).

A monopulse radar is able to derive accurate angular measurements via intelligent processing of its sum and difference channel returns. Recently there have emerged techniques for angular estimation of several unresolved targets, meaning targets that are, in principle, merged within the same radar beam, can be extracted separately. The key is the joint exploitation of information in several range bins. Here we show the performance of this approach in a high-fidelity simulation: we observe considerable improvement in track RMSE, but little corresponding gain in track completeness. Coupled with a hidden Markov model on target number, however, the performance is impressive.

Many tracking systems have the requirement to transfer information about a particular tracked object between two systems. The general approach to this involves generation of an object map by the system designating the particular track followed by receipt of the map and correlation to the local track picture of the second system. Correlation performance is in general limited by a number of factors: random track errors added by each system, miss-registration of the two systems' coordinate frames, and miss-match between the numbers of objects tracked by the two systems. Two correlation algorithms are considered for this problem: Global Nearest Neighbor (GNN) and Global Nearest Pattern (GNP). Four basic failure modes are identified for the GNP formulation, and three of these explain failures in the GNN formulation. Analytic expressions are derived for each of these modes, and a comparison of each to Monte-Carlo experiment is provided to demonstrate overall validity.

Over-the-horizon radar (OTHR) uses the refraction of high frequency radiation through the ionosphere in order to detect targets beyond the line-of-sight horizon. The complexities of the ionosphere can produce multipath propagation, which may result in multiple resolved detections for a single target. When there are multipath detections, an OTHR tracker will produce several spatially separated tracks for each target. Information conveying the state of the ionosphere is required in order to determine the true location of the target and is available in the form of a set of possible propagation paths, and a transformation from measured coordinates into ground coordinates for each path. Since there is no a-priori information as to how many targets are in the surveillance region, or which propagation path gave rise to which track, there is a joint target and propagation path association ambiguity which must be resolved using the available track and ionospheric information. The multipath track association problem has traditionally been solved using a multiple hypothesis technique, but a shortcoming of this method is that the number of possible association hypotheses increases exponentially with both the number of tracks and the number of possible propagation paths. This paper proposes an algorithm based on a combinatorial optimisation method to solve the multipath track association problem. The association is formulated as a two-dimensional assignment problem with additional constraints. The problem is then solved using Lagrangian relaxation, which is a technique familiar in the tracking literature for the multidimensional assignment problem arising in data association. It is argued that due to a fundamental property of relaxations convergence cannot be guaranteed for this problem. However, results show that a multipath track-to-track association algorithm based on Lagrangian relaxation, when compared with an exact algorithm, provides a large reduction in computational effort, without significantly degrading association accuracy.

Multiple target tracking requires data association that operates in conjunction with filtering. When multiple targets are closely spaced, the conventional approach (MHT/assignment) may not give satisfactory results. This is mainly because of the difficulty in deciding what the number of targets is. Recently, the probability hypothesis density (PHD) filter, which propagates the PHD or the first moment instead of the full multitarget posterior density, was proposed. In this approach, the integral of the PHD over a region in the state space is the expected number of targets within this region and the peaks in the PHD can be regarded as the estimated locations of the targets at a given time step. In this approach the data association problem is not considered, i.e., the PHD is obtained only for a frame at a time. In our paper, a data association method combined with the PHD approach is proposed for multitarget tracking, i.e., we keep a separate tracker for each target, use the PHD filter to get the estimated number and locations of the targets at each time step, and then perform the "peak-to-track" association, whose results can provide information for PHD peak extraction at the next time step. Besides, by keeping a separate tracker for each target, our approach provides more information than the standard PHD filter. Using our approach, the multitarget tracking can be performed with automatic track initiation, maintenance, spawning, merging and termination. Simulation results demonstrate that our approach is computationally feasible and effective.

We describe a new hybrid particle filter that has two novel features: (1) it uses quasi-Monte Carlo samples rather than the conventional Monte Carlo sampling, and (2) it implements Bayes' rule exactly using smooth densities from the exponential family. Theory and numerical experiments over the last decade have shown that quasi-Monte Carlo sampling is vastly superior to Monte Carlo samples for certain high dimensional integrals, and we exploit this fact to reduce the computational complexity of our new particle filter. The main problem with conventional particle filters is the curse of dimensionality. We mitigate this issue by avoiding particle depletion, by implementing Bayes' rule exactly using smooth densities from the exponential family.

Track-before-detect (TBD) refers to a tracking scheme where detection of a target is not made by placing a threshold on the sensor data. Rather, the complete sensor data is used to detect and track a target in the absence of a data threshold. By using all of the sensor data a TBD algorithm can detect and track targets which have a lower signal power than could be detected by using a standard detection and tracking scheme. This paper presents an efficient particle filter TBD algorithm, which models the signal processing stages which may be found in a sensor such as radar. In this type of sensor the noise is modelled as the magnitude of a complex Gaussian process, which is Rayleigh distributed. This noise model and the model of the sensor signal processing is incorporated into the filter derivation. It is shown that in a simple simulation the algorithm can detect and track targets with a signal-to-noise ratio as low as 3dB.

Cetin has applied non-quadratic optimization methods to produce feature enhanced high range resolution (HRR) radar profiles. This work concerned ground based targets and was carried out in the temporal domain. In this paper, we propose a wavelet-based-half-quadratic technique for ground-to-air target identification. The method is tested on simulated data generated by standard techniques. This analysis shows the ability of the proposed method to recover high-resolution features such as the locations and amplitudes of the dominant scatterers in the HRR profile. This suggests that the technique potentially may help improve the performance of HRR target recognition systems.

An obvious use for feature and attribute data is for classification and in combat identification. The term classification is used broadly here to include discrimination, detection, target typing, identification, and pattern recognition. An additional use is in the data (or track) association process to reduce the misassociations, often called feature aided tracking. Previous papers discussed the integration of features and attributes into target track processing in addition to their use in multiple target classification. The distinction is made between feature and attribute data because they are processed differently. The term features applies to data from continuous sample space and attributes applies to data from discrete sample space. The primary concern of this paper is to address processing of attributes when there is incomplete data. For example in fusion of sensor data from distributed sensors, a sensor processor might make a hard decision on whether a target exhibits a specific target class (or attribute value) or not (without providing additional information such as likelihoods or probabilities). In another example, a sensor might distribute the likelihood of the most likely target class (or attribute property) and no information on the other possibilities. Both classification and attribute aided tracking is addressed for these examples of incomplete data. The purpose of this paper is to show the feasibility of a simple approach to dealing with incomplete data.

This paper considers the optimal resolution cell (pixel) size in detection and tracking IR targets. Using refined resolution can help localizing the position of the targets precisely. However, along with a smaller resolution cell the signal power in each resolution cell becomes lower, because a point target is recorded as a blur according to the point spread function (PSF). Meanwhile, since the noise power is proportional to the area of the pixel, the noise is also lower. On the other hand, using coarse resolution (which is the result of opting for a high signal power in the resolution cell) renders less accurate target position estimates together with higher noise power. That is, as the pixel size changes there is a trade-off in terms of detection performance versus estimation accuracy. We submit that the only defensible way to rationalize this is from system level concerns: what is best for tracking? We will first look at the initial state estimation of a constant velocity target. Relationships between the Cramer-Rao lower bound for the initial state estimation and the resolution cell size will be established. Then, from a general target tracking perspective, the pixel-size effects on the probability of detection and the target location centroiding accuracy will be analyzed.

Our theory is based on the mapping between two Fokker-Planck equations and two Schroedinger equations (see [1] & [2]), which is well known in physics, but which has not been exploited in filtering theory. This theory expands Brockett's Lie algebra homomorphism conjecture for characterizing finite dimensional filters. In particular, the Schroedinger equation generates a group, whereas the Zakai equation (as well as the Fokker-Planck equation) does not, owing to the lack of a smooth inverse. Simple non-pathological low-dimensional linear-Gaussian timeinvariant counterexamples show that Brockett's conjecture does not reliably predict when a nonlinear filtering problem will have an exact finite dimensional solution. That is, there are manifestly finite dimensional filters for estimation problems with infinite dimensional Lie algebras. There are three reasons that the Lie algebraic approach as originally formulated by Brockett is incomplete: (1) the Zakai equation does not generate a group; (2) Lie algebras are coordinate free, whereas separation of variables in PDEs is not coordinate free, and (3) Brockett's theory aims to characterize finite dimensional filters for any initial condition of the Zakai equation, whereas SOV for PDEs generally depends on the initial condition. We will attempt to make this paper accessible to normal engineers who do not have Lie algebras for breakfast.

The combinatorial optimization problem of multidimensional assignment has been treated with renewed interest because of its extensive application in target tracking, cooperative control, robotics and image processing. In this work we particularly concentrate on data association in multisensor-multitarget tracking algorithms, in which solving the multidimensional assignment is an essential step. Current algorithms generate good suboptimal solutions (with quantifiable accuracy) to these problems in pseudo polynomial time. However, in dense scenarios these methods can become inefficient because of the resulting dense candidate association tree. Also, in order to generate the top m (or ranked) solutions these algorithms need to solve a number of optimization problems, which increases the computational complexity significantly. In this paper we develop a Randomized Heuristic Approach (RHA), in which, in each step, instead of choosing the best solution indicated by the heuristic, one of the solutions is chosen randomly depending on the "probability" associated with it. The resulting algorithm produces solutions that are as good as or better than those produced by Lagrange relaxation-based algorithms that have much higher computational complexity. This method also produces other ranked best solutions with no further computational requirement.

A method is presented that circumvents the combinatorial explosion often assumed to exist when summing probabilities of joint association events in a multiple target tracking context. The approach involves no approximations in the summation and while the number of joint events grows exponentially with teh number of targets, the computational complexity of the approach is substantially less than exponential. Multiple target tracking algorithms that use this summation include mutual exclusion in a particle filtering context and the Joint Probabilistic Data Association Filter, a Kalman Filter based algorithm. The perceived computational expense associated with this combinatorial explosion has meant that such algorithms have been restricted to applications involving only a handful of targets. The approach presented here makes it possible to use such algorithms with a large number of targets.

Cluster Tracking (also called group tracking) is a key approach to greatly reducing the required data communication and processing loads that can result from the extreme amount of ambiguous data that might be generated by radar and IR sensors in the early post boost phase of a ballistic missile. Cluster tracking is especially appropriate in tracking a mixture of resolved and unresolved objects as a cluster and simplifies the processing for initiating individual tracks when many of the target measurements are resolved. This paper presents the bibliography that resulted from a literature search on cluster tracking using data from one or more sensors. Although the focus was on cluster tracking, the literature search also uncovered papers on formation tracking and track partitioning (track clustering) and those papers are included in the bibliography. The paper also includes an introduction that provides an overview of cluster tracking and the advantages of tracking clusters. This includes a discussion of the four major types of cluster tracking and the uses and distinction between cluster tracking, formation tracking, and track clusters (partitions).

This paper presents a new hybrid and hierarchical algorithm for aligning two partially overlapping aerial images. This computationally efficient approach produces accurate results even when large rotation and translation have occurred between two images. The first step of the approach is coarse matching where transformation parameters are estimated using the partial Hausdorff distance measure for maximally feature consensus. For feature extraction, it applies a modified phase congruency model to effectively locate feature points of local curvature discontinuity, structural boundaries, and other prominent edges. Our proposed coarse matching doesn't require explicit feature correspondence, and the partial Hausdorff distance measure can tolerate well the presence of outliers and feature extraction errors. In the second step, the pairwise matching of the feature points detected from both images is performed, where the initial estimate obtained in the first step is used to dramatically facilitate the determination of feature point correspondence. This two-step approach compensates deficiencies in each step and it is computationally efficient. The first step dramatically decreases the size of the search range for correspondence establishment in the second step and no direct pairwise feature matching is required in the first step. Experiment results demonstrate the robustness of our proposed algorithm using real aerial photos.

The problem of accurately registering an aerial video image to geo-referenced imagery has become more important in recent years. To achieve high efficiency, we propose a guided hierarchical searching scheme to augment the current geo-registration framework. The algorithm consists of three major steps. In the first step, the reference image and video frames are projected to a common coordinate system based on the telemetry. In the second step, feature points are extracted in the video and reference, and the coarse searching for the best match was performed on a feature points image pyramid, where the comparison process is only applied to the regions with feature points. In the final step, the precise transformation parameters are estimated using the Levenberg-Marquardt techniques, which results in a precise alignment of the video and reference. Compared with conventional blind comparison based on the normalized cross-correlation measure, the proposed approach differes because it applies a feature-based hierarchical searching scheme to quickly lead the matching process to the most likely protion in the reference and speed up the matching process. Experimental results that evaluate the developed approach using real world aerial video will be presented. The obtained results demonstrate that our proposed method can be used in a complete geo-registration system to provide accurate registration of the video frames.

In this paper, a moving object tracking algorithm for infrared image sequences is presented. The tracking algorithm is based on the mean-shift tracking method which is based on comparing the histograms of moving objects in consecutive image frames. In video obtained after visible light, the color histogram of the object is used for tracking. In forward looking infrared image sequences, the histogram is constructed not only from the pixel values but also from a highpass filtered version of the original image. The reason behind the use of highpass filter outputs in histogram construction is to capture structural nature of the moving object. Simulation examples are presented.

This paper compares six different algorithms for target maneuver detection in a number of typical maneuvering target tracking scenarios. Measurement residual based chi-square test, input estimate based chi-square test, input estimate based significance test, generalized likelihood ratio, cumulative sum, and marginalized likelihood ratio detectors are examined. Maneuver onset detection times and ROC curves are presented and performance measures are discussed through simulations. Further, the effect of different window sizes on detection performance is evaluated.

This is a part of Part VI (nonlinear filtering) of a series of papers that provide a comprehensive survey of techniques for tracking maneuvering targets without addressing the so-called measurement-origin uncertainty. Part I [52] and Part II [48] deal with target motion models. Part III [49], Part IV [50], and Part V [51] cover measurement models, maneuver detection based techniques, and multiple-model methods, respectively. This part surveys approximation techniques for point estimation of nonlinear dynamic systems that are general, applicable to a wide spectrum of nonlinear filtering problems, especially those in the context of maneuvering target tracking. Three classes of such techniques are survey here: function approximation, moment approximation, and stochastic model approximation.

The effect of the crosscovariance in track-to-track fusion has been studied in [2] [3] [4] [5]. Ignoring the crosscovariance of the local track estimation errors leads to optimistic covariance for the fused state estimates. However, evaluation of this crosscovariance is too demanding. Consequently, we approximate the crosscovariances between two sensors' track estimation errors in a manner similar to one of the procedures presented in [2], namely, with constant crosscorrelation coefficients. The results of using this in a practical naval surveillance system are discussed by comparing the exact covariances of the fused tracks, the covariances obtained with the approximation and the covariances obtained by completely ignoring the crosscorrelations.

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