The DARPA MUSIC program is presently collecting data to support multi-spectral infrared target detection in clutter. The plan of the MUSIC program is discussed first, followed by the theoretical basis of multi-spectral and recursive moving target indicator (RMTI) processing. An example using data from the MUSIC sensor is presented. In this example spectral-spatial processing of two bands is compared to registration and temporal processing of a single band.

Terrain images taken from an unstabilized platform by a line CCD camera are often distorted as a result of angular motion of the line of sight (LOS). Distortions appear as stretching, shrinking and twisting of an image. Distorted images can be corrected by image processing techniques. Reconstruction of distorted images is based solely on information contained in the image and does not include inertial measurements of the LOS angular motion. The purpose of this work was to provide a useable image of the scanned terrain, containing minimal distortions, to enable the user correct orientation in the image, and the detection and recognition of viewed objects. The reconstruction algorithm is based on crosscorrelation between sequential image lines. Correlation coefficients calculated for each sampled image line serve to determine the three components of the displacement vector, namely, lateral shift, advance rate and rotation of image lines. Reversing of the camera scanning direction is detected by locating an image line, which constitutes the symmetry line of a mirror image in the received image. The performance level of the algorithm was tested on simulated distorted images, and real images taken by a line CCD camera. The distortion levels at which the algorithm was tested were: Lateral shift of sequential image lines: 0 -< 3 pixels/line, with total accumulated shift of up to 250 pixels; sampling rate density of image lines: 0.5 -< 10 lines/pixel; rotation rate of image line: 0 -< 0.05 degrees/line, with total accumulation of up to 10 degrees. Reconstruction errors of 5-7% of a pixel in lateral shift correction, 15% in line sampling rate determination and 2-8 10e-2 degrees in line rotation calculation were obtained. The ability to successfully reconstruct distorted images with various distortion levels within the expected dynamic range of real systems was demonstrated. The algorithm was also shown to perform successfully under conditions of different terrain textures.

A new approach is described for detecting small targets in natural background clutter using multiple time and/or spectral-band imagery. The target detection problem is formulated as a composite hypothesis test in which the alternative hypothesis set is parameterized by the target amplitude and location within the image set. Thus, the size and shape of the target are assumed to be known, but nothing is assumed for the amplitude or trajectory of the target. The probability density function for the image set is taken to be a multivariate normal density whose covariance is a function of the clutter spatial, temporal, and/or spectral degrees of freedom. The assumption of small targets allows the clutter statistics to be estimated directly from the input imagery. The resulting processor is a generalized likelihood ratio test in which the unknown target amplitude and location are replaced by their maximum likelihood estimates. The assumption of spatially stationary background clutter allows the test statistic to be expressed as a set of spatially filtered images in which each spatial frequency component is processed independently in time and/or spectral band by a linear transfonnation operating on the input image set. The algorithm can be implemented either as a block or recursive processor. The latter form requires less storage and allows the clutter statistics to be adaptively updated frame by frame. The approach has been successfully applied to a variety of synthetic and real imagery, including HI-CAMP I and II data. Performance estimates and samples of unclassified processed imagery are presented.

Intercepting an object in mid-flight is quite a complex task but we see examples of it in nature all the time. Insects recognize prey, follow it, and intercept it using relatively simple neural systems. At the same time, sophisticated computer algorithms fail to match the degree of robustness and accuracy displayed by insects. This paper provides a scheme to utilize the optic flow characteristics and the geometrical properties of the sensor configuration to perform fast, reliable target tracking, and system stabilization, from crude visual inputs. Artificial neural networks are used to implement the algorithms because of their excellent generalization capabilities which can provide an adequate response in situations where a response would not be expected using conventional computer algorithms. Other advantages offered are the speed of computation, the simplicity of schemas and algorithms, and robustness

The detection of small targets in infrared (IR) clutter is a problem of critical importance to Infrared Search and Track (IRST) systems. This paper presents techniques for analyzing and improving the detection performance of IRST systems. Only spatial, or single-frame, processing will be addressed. For clutter with spatially slowly varying statistics, our approach is based on linear filtering. Models of target and clutter are developed and used to analyze matched filter performance and sensitivity. This sensitivity analysis is used to improve filter bank design. A clutter classification scheme which can separate clutter of different types is presented. Finally, to improve system performance in the presence of large intensity gradients, such as cloud edges, an improved adaptive threshold scheme is presented.

The detection of weak targets with an infrared surveillance system is often complicated not only by a severe clutter environment but also by background and platform motion effects. Conventional sequentially applied algorithms combining frame—to—frame registration, clutter rejection filtering, and adaptive thresholding detection simply overwhelm the track processor in a weak target scenario, due to the required lowering of detector block thresholds. To address this problem, we have developed a 3—D filter/"track—before—detect" signal processing approach in which an adaptive spatio—temporal filter is used for clutter suppression and a Viterbi "track—before—detect" block is used for noncoherent target integration. This paper discusses a 3—D adaptive filtering technique which combines time and spatial filtering (in both azimuth and elevation directions) to achieve simultaneous frame—to-frame registration, background clutter suppression, and target preservation/enhancement. In addition, this 3-D filtering procedure whitens the data, thus greatly facilitating the "track-before—detect" processing block task. Unlike other commonly employed procedures, this technique neither entails the suboptimal sequential application of filtering procedures (e.g., spatial followed by temporal filtering) nor demands very accurate subpixel-level registration or exact knowledge of the target's velocity characteristics. The only requirements are that data frames should be roughly aligned (so the offsets are contained within the filter window) and that the assumption of the moving target indicator (MTI) is valid. In this paper simulation results of the 3—D filtering procedure using real, scanned sensor array data are presented, and the procedure performance and implementation complexity are traded off versus adaptive spatial filtering, adaptive temporal, and sequentially applied time/spatial filtering techniques. Also, modification and simulation results are presented for an extension of the 3—D adaptive spatiotemporal filtering technique, which accommodates both MTI and non-MTI case scenarios.

A hierarchical data structure is presented to organize the various types of informational entities available from infrared (IR) sensor data. This provides a common framework in which to discuss alternate techniques applicable to the problem of automatic acquisition and tracking of small targets. Of these techniques, the Hierarchical Pattern Recognition (HPR) algorithm processes all available information for the acquisition. Targets of interest are typically unresolved by sensor optics at acquisition ranges and appear against highly cluttered background scenes. Performance of the HPR algorithm is demonstrated by simulation using various types of pattern classifiers, with and without the benefit of feature data inputs representing scene context. The Viterbi algorithm is utilized to resolve ambiguous observation-to-track pairings while tracking an acquired target. Its performance is characterized by the expected number of frames required to resolve such ambiguities.

Studied in this paper is the problem of achieving the optimum MTI detection performance in strong clutterof unknown spectrum, when the set of data available to the estimation of clutter statistics is small due to a severely nonhomogeneous environment. A new adaptive implementation, called the Doppler Domain Localized Generalized Likelihood Ratio processor (DDL—GLR), is ProPosed and its detection performance-derived. It is shown that the DDL-GLR is a data-efficient implementation of the high-order optimum detector, together with several advantages of practical importance over other adaptive processors.

Optical autodyne detection is a direct detection method for measuring relative Doppler frequency shifts induced by laser illuminated object. The method is of interest in laser radars for its relative simplicity and robustness. In this paper we discuss the estimation of ranges, relative velocity, and amplitudes for a two point target, when laser backscattered radiation is collected with a photon- bucket receiver, and registered by an incoherent autodyne detector. An analytical framework is developed to establish the fundamental limits on the resolution of such a system, and to obtain a quantitative understanding of the dependence of estimation accuracy on target separations, relative velocity, and on the number of photons available. The value of a priori knowledge for obtaining a desired estimation accuracy of a parameter of interest is discussed for selected cases. The analysis is carried out for Poisson photon statistics. The performance of various estimators is evaluated by utilizing the Cramér-Rao bound, for both signal and background shot noise limited conditions. The results presented have applications for mbust laser radars, and contribute to a better understanding of the perfonnance and potential of an autodyne detection system.

Linear, finite-impulse-response (FIR) filters are efficient for detecting point sources in data generated by a scanning detector array. In particular, matched filters have been widely used for detection and initial estimation of isolated sources. When separate sources have overlapping signals the matched filter does not work as well. Others have applied deconvolution filters to this case and shown good performance with high signal-to-noise ratios (SNR). The deconvolution filter is examined here in the context of general FIR filters. The novel aspect of this paper is the definition and application of an optimality concept for resolving arbitrary numbers of sources. A "resolution" attribute is defined which measures the difference between filter peak response and minimum response between adjacent peaks. A "max_min" filter is derived which has maximal resolution for given requirements on SNR and source separation distance. Its performance is compared with that of deconvolution.

In detection systems (e.g. radar) , the effect of interference patterns (clutter) from the environment are partially unknown and/or varying in terms of their statistical properties. In such instances, the performance of the optimal detector deteriorates significantly, and a nonparametric or constant false alarm rate (CFAR) detector which is designed to be insensitive to changes in the underlying density functions of the clutter is needed. Order Statistic (OS) filters have been shown to perform effectively in detection systems when the observations are independent and identically distributed. When the assumptions about the observations are violated or the underlying distribution of the clutter is altered, only certain ranks of the OS filter show robust performance. This study analyzes the performance of OS filters in the framework of nonparametric detection for cases in which the observations do not contain equivalent statistical information or observations are not independent. Through computer simulation, the extent of robustness that can be obtained from different ranks is illustrated.

Algorithms involving ranking are used to suppress noise induced in IR detectors by gamma radiation, based on enhanced response to gamma photons relative to other excitation. An analytic expression for the characteristic function of detector response to signal plus Gaussian noise plus gamma noise is derived; it is used to compute second moments of order statistics corresponding to ranked groups of redundant detector samples of an image pixel. These are used to illustrate a simple method of 'quantifying noise-suppression potential of simple ranking algorithms, as a function of gamma noise and ranking parameters. Ranking suppresses noise from all sources, and selection of low-order ranked data yields substantial SNR gain when the probability of one gamma photon per detector sample approaches 1.0.

Temperature discrimination of closely spaced objects (CSO's) may be a difficult problem for passive sensors with limited spatial resolution. In this paper, we establish limits on the accuracy of temperature estimation of two closely spaced point targets having different temperatures, when such targets are observed in several spectral bands. The effect of a priori knowledge (e.g., emissivities, areas, earthshine) on temperature estimation is discussed. An analytical framework is developed to establish the fundamental limits on temperature resolution of a passive system, and to obtain a quantitative understanding of the dependence of estimation accuracy on parameters describing the targets (e.g., temperatures, emissivities), and on the number of photons available. We examine the sensitivity of temperature estimation to target parameters and the selection of the number and location of the spectral bands in which the measurements are made. The advantage of partial resolution of targets in one or more spectral bands is examined. The analysis is carried out for Poisson photon statistics. The Cramr-Rao bounds (CRB) are computed for the estimation of various parameters describing a two point source, and to the sensitivity of the CRB to different parameter values, changes in the number of unknown parameters, and the selection of spectral bands is examined. The results presented provide a more comprehensive definition of temperature resolution and can be useful in astronomy, multispectral scene analysis, and other commercial and military applications.

A new pipeline approach is addressed for the task of detecting and tracking pixel-sized moving targets from a time sequence of dynamic images of a high-noise environment. The trajectories of the moving targets are unknown, but continuous and smooth. The image sequence contains significant, randomly drifting background clutter, and is also contaminated by random sensor noise. The Pipeline Target Detection Algorithm (PTDA) uses the temporal continuity of the smooth trajectories of moving targets, and successfully detects and simultaneously tracks all the target trajectories by re-constructing them from the time sequence of noisy images in a single targetframe in real time. The pipeline approach breaks the constraint of straight line trajectory that most other algorithms require for the similar tasks and detects and tracks any trajectories of arbitrary shapes as long as they are continuous and smooth. The pipeline fashion of the aigorithm is a complete parallel distributedprocessing (PDP) type process, and therefore is highly time efficient. It also agrees with the pattern that real image sequences are acquired, so is ideal for real-time target detection and tracking.

This paper describes the Knowledge-Based Tracking (KBT) algorithm for which a real-time flight test demonstration was recently conducted at Rome Air Development Center (RADC). In KBT processing, the radar signal in each resolution cell is thresholded at a lower than normal setting to detect low RCS targets. This lower threshold produces a larger than normal false alarm rate. Therefore, additional signal processing including spectral filtering, CFAR and knowledge-based acceptance testing are performed to eliminate some of the false alarms. TSC's knowledge-based Track-Before-Detect (TBD) algorithm is then applied to the data from each azimuth sector to detect target tracks. In this algorithm, tentative track templates are formed for each threshold crossing and knowledge-based association rules are applied to the range, Doppler, and azimuth measurements from successive scans. Lastly, an M-association out of N-scan rule is used to declare a detection. This scan-to-scan integration enhances the probability of target detection while maintaining an acceptably low output false alarm rate. For a real-time demonstration of the KBT algorithm, the L-band radar in the Surveillance Laboratory (SL) at RADC was used to illuminate a small Cessna 310 test aircraft. The received radar signal wa digitized and processed by a ST-100 Array Processor and VAX computer network in the lab. The ST-100 performed all of the radar signal processing functions, including Moving Target Indicator (MTI) pulse cancelling, FFT Doppler filtering, and CFAR detection. The VAX computers performed the remaining range-Doppler clustering, beamsplitting and TBD processing functions. The KBT algorithm provided a 9.5 dB improvement relative to single scan performance with a nominal real time delay of less than one second between illumination and display.

Sensitivity to low—observable targets—-given a sequence of N frames of pre—processed (e.g., spatial/time-filtered) but unthresholded data—may be enhanced by selecting, from among all possible paths traversing these frames, those containing any indication that a target may be present. However, since only upper bounds regarding target velocities are usually known, explicit formulation of all feasible paths (and accompanying confidence factors) becomes a formidable task even for small values of N. In this paper we address this problem by utilizing a Dynamic Programming ("Viterbi") algorithm to efficiently generate and evaluate, in an unthresholded fashion, all possible paths through the N frames. Trajectories are traced recursively by assigning accumulated trajectory scores to each entry in a given frame of data so as to maximize that entry's updated score. This Viterbi Track- Before—Detect procedure differs from standard Multiple Hypothesis Testing (MHT) methods in two ways. First, while in the MHT method the number of plausible paths grows exponentially (hence the need for introducing thresholds), in the Viterbi approach they remain constant, equal to the number of data entries in a frame. Second, whereas in the MHT method trajectories are updated by selecting for each existing trajectory the best current (thresholded) detection, in the Viterbi approach each current data value is updated with the best trajectory up to that point. Simulation results show that application of the Viterbi Track-Before-Detect algorithm over ten frames of IR data yields roughly a 7 dB improvement in detection sensitivity over conventional thresholding/peak-detection procedures.

A dynamic programming (DP) technique has been developed for the detection of subpixel-sized, low-SNR targets observed by mosaic imaging sensors. The primary advantages of DP are its sensitivity to weak targets along with its robustness to target maneuvers and sensor instabilities. Such enhancements are achieved by performing target data association and detection in a single optimization procedure. To the extent that the target motion and noise behavior can be accurately modeled, the DP algorithm is shown to be optimal for this task. A prototype JR tracking system based on the DP approach was developed and tested for a step-staring IR camera application. Performance analysis indicates a sensitivity improvement of several dB over conventional sequential detection tracking approaches.

This paper describes the evolutionary development of adaptive signal processing algorithms which utilize spatial and spectral information provided by a passive infrared sensor to enhance the detectability of targets in clutter. Key parameters affecting the performance of multi-spectral detection processors are identified and discussed. Adaptive filtering algorithms are presented which can achieve near-optimum detection performance with no prior knowledge of the target and background spectral properties.

Entropy and its generalization, the Kuliback-Leibler measure can be useful in characterizing the relationships that exist between measurements. The relationships that exist when a target is present provide a means of distinguishing these measurements from a set of measurements due to noise alone. We utilize these ideas in developing a detection procedure that first develops a score based on measurements using the Significance Test and then calculates the relationship between the measurements. This relationship is the "effective number" of measurements entering into the Significance Test score and is computed from the entropy of the normalized measurements; both a high score and "effective number" are needed for a detection. The "effective number" is used to discriminate against false detections, i.e., high scores, caused by a relatively few, strong, noisy measurements. We compare the performance of this detector to more conventional detectors in the problem of detecting a target in Weibull clutter.

When Oliver (Drummond) asked me to moderate a Panel discussion this year, I felt that this would be a great opportunity to address a subject that has been uppermost in my mind for some time

A neural network solution to the data association problem in multitarget tracking is presented. This requires position and velocity measurements of the targets over two consecutive time frames. A quadratic neural energy function results that is suitable for an optical processing implementation. Realistic target trajectories are simulated, yielding several different scenarios with spurious measurements (clutter) and measurement noise, which are used to test the tracking ability of the neural network. Simulation results are presented, and an overall tracking system using the neural net, Kalman filters, and a Hough transform subsystem is discussed.

Conventional practice in single-sensor passive track is to fit azimuth-elevation object observations with polynomials in the early stages of track initialization. At least three and usually more observations are fitted to quadratic polynomials before they are accepted for testing with a six dimensional model. This paper develops an alternative to these polynomials based on closed-form solutions of the trajectories in angle-space. This paper is applicable when both the sensor and target are in free fall. The approach relies on a flat-earth assumption to achieve the solutions. Experimental comparisons are made with the polynomial fit method.

This paper describes a PC software package for the following problem : We are given multiple passive sensors, each with a number of detections at a given time. With each detection, there is an associated line-of-sight measurement originating from a source. The source can be either a real target, in which case the measurements are azimuth and elevation angles of the target, plus some measurement noise, or a spurious one, i.e., a false alarm. Position estimates of targets can be formed by associating measurements originating from it. Mathematically, the measurement-target association problem leads to a generalized assignment problem. The problem of forming position estimates of multiple targets in a dense cluster, from passive sensor measurements at a given time, require at least three sensors. However, for three sensors, the three-dimensional assignment is known to be NP-complete, i.e., the complexity of the optimal algorithm increases exponentially with the size of the problem. The association problem is solved as a maximum likelihood estimation procedure; the likelihood function is maximized through the use of a near-optimal, iterative, and polynomial-time three dimensional assignment algorithm which employs Lagrangian relaxation technique that successively solves a series of (polynomial time) generalized two-dimensional assignment subproblems. The algorithm is coded in Fortran and available as an interactive PC software package PASSDAT. In this paper we present performance results and graphical scenario description of a representative test case solved by PASSDAT.

This paper is generally related to analytic methods for evaluating tracking performance, in particular for predicting track accuracy in dense target environments. A very simple analytic expression is derived to predict the effects of mis-associations on track accuracy. The paper analyzes an optimal track-to-measurement assignment algorithm in track continuation phases, i.e., when tracks are well established.

This paper discusses the application of a particular implementation of Multiple Hypothesis Tracking (MHT) to the problem of detection and tracking of dim targets in a heavy clutter or false alarm background. The MHT method and the performance improvement associated with MHT for these applications is well documented [1—6], but the actual implementation has been limited due to the computational load and complexity associated with "traditional" implementations. We present an approach (Structured Branching) that offers significant computational savings as compared with alternative approaches, and can maintain hundreds of "possible" tracks that are initiated in a dense clutter or false alarm background without overwhelming computational or memory requirements. Further, this method can be applied to much more limited implementations according to the computational resources available—there is minimal "overhead" associated with Structured Branching (SB) since hypotheses are not propagated explicitly. The SB algorithm is described, highlighting the ways in which computational savings are achieved, and simulation results are presented. Then, approximate techniques are developed for predicting the performance of MHT (any implementation, not just SB), and results comparing predicted performance with simulation results are presented.

Over the last ten years a number of computer programs have been developed which do symbolic and algebraic operations as well as numeric calculations and graphics. Mathematica is the latest entry into this arena. This report gives a brief introduction into its capabilities and illustrates its power for engineering applications, including an example of static covariance analysis.

Real-time measuring problem about temporal locations and trajectories of multi—objects in space is discussed. A correlation recognition method about real—time interactive measurement is provided to solve the temporal location of object points in space. Corresponding mathe— iatic model is established. Relation of error with bland area and fast algoritha are discussed. Finally, the experimental results are given.

In target environments that include Electronic Countermeasures (ECM), vhere the availability of radar range measurements is severely reduced, an integration of ESM into a multi-sensor tracker provides an inexpensive but effective approach to augmenting radar tracking systems. Tracking filter equations are presented for a multi heterogeneous-sensor tracking system consisting of radars and ESM sensors. Measurement time-based track updating is performed, due to non—periodicity of ESM measurement acquisition times, instead of usual track—based updates. Track updating using ESM measurements is accomplished via an EKF-based algorithm and radar measurements via an tracking algorithm. The integration of data from different sensor types is a logical response to increasingly hostile airborne threats. The technique described in this paper is a straight forward and costeffective approach for accomplishing that integration.

Plot/track association consists of assigning radar plots to predicted track positions and is an important feature of all track while scan systems. We demonstrate the feasibility of applying neural network technology to the plot/track association problem in such a way as to achieve good global solutions. The plot/track association problem can be structured in a basic framework very similar to that of the classic Travelling Salesman Problem (TSP). Hopfield organization networks have been applied to the TSP by various researchers, but with varying degrees of success because of recurring instability problems. The network presented here seeks to minimize a global cost which is a function of the distances between plots in a given scan of data and the predicted track positions. Additionally, in this paper a novel technique is introduced for helping to alleviate the instability of Hopfield networks.

This paper describes an application of Bayesian Networks, or Influence Diagrams, to the multitarget tracking problem of a single, angles only, scanning sensor. The Bayesian Network combines the continuous track state vectors and discrete report-to-track association hypotheses into one network which is then used to perform track state vector prediction and update, and to generate, score and prune association hypotheses. The advantages of operating on the network are discussed via an example in which a track resolves into two tracks. The example demonstrates that the network operations provide a highly flexible, numerically stable, computationally efficient. mechanism for calculating the state vectors, covariances and intertrack correlations of the resolved tracks. It is shown that these intertrack correlations, which are somewhat cumbersome to maintain in the usual track filter formulations, are automatically maintained in the network formulation and can improve track accuracy and resolution.

This paper develops a group tracking algorithm for the tracking of clusters of closely spaced targets as viewed by passive sensors. This problem is complex because the size and shape of the observed cluster will differ from sensor to sensor. Since a passive sensor provides projection of the objects, possible sensors in different locations will provide different projections of the 3-dimensional (3-D) shape of a cluster. Furthermore, the number of resolved objects in a cluster can vary as closely spaced targets may appear to a sensor as a single extended object. In order to track the target clusters with multiple sensois, a method is needed to characterize the size, shape and location of each cluster. The method described in this paper models the target cluster in 3-D as an effipsoid with the projection in 2-D being an effipse. The centroid and parameteis of the ethpsoid are tracked over time using measurements from widely spaced passive sensors. The filtering methods are described and performance is presented based upon tracking simulations. Application of this method to tracking extended objects with multiple sensors is also discussed

In this paper target tracking as an hierarchical information extraction process is defined and spatio-temporal factors in vision affecting motion detection are briefly discussed. The relativistic aspects of motion perception which quantify perceived extent, time, and velocity of moving objects are introduced. A systems approach to the operator-display interaction is also investigated and the role of the human operator as an optimal position and velocity estimator and controller is presented.

This paper treats the problem of source dynamic motion evaluation in underwater applications using recursive prediction error estimation techniques. The issue of compensating for underwater motion effects arises in a number of areas of current interest such as control and operations of autonomous remotely operated vehicles, underwater seismic exploration, and buoy wave data analysis. Earlier treatments of the problem relied on frequency response methods and Kalman filtering. The present paper discusses the compensation problem using an alternative discrete model of the process and proposes use of the recursive prediction error algorithm for its solution. The algorithm is simpler than Kalman filtering in terms of the required knowledge of noise statistics and provides an attractive alternative to Kalman Filtering

An attempt is made to combine a deterministic digital filter and a stochastic filter. The state equation is the standard form used for a Kalman filter deriva— tion and the output equation is of the finite impulse response filter. An optimal estimator is derived for this combined structure, called a finite impulse response estimator (FIRE) which permits processing of a signal contaminated by deterministic and random noises. Derivation of the FIRE utilizes the state augmentation technique and the innovation technique. The proposed method is straight forward and easy to implement and it can be applied to areas such as time varying signal processing or target tracking where radar 'returns are contaminated by low frequency noises. Full derivation and a tracking application are presented.

The paper centers on the continued development of the symmetric measurement equation (SME) filter developed by Kamen' for track maintenance in multiple target tracking. In this approach there is no need to correctly associate measurements and targets before target state estimation can take place. Rather the data association problem is embedded in the process of target state estimation. The "first order" version of the SME filter is an extended Kalman filter (EKF), and thus the computational requirements for filter implementation are comparable to that for a standard Kalman filter. In addition, in contrast to probabilistic data association filters, the estimator does not rely on the computation of probabilities for correct measurement/target associations. The SME filter is based on a standard state model for the target state trajectories. However, in contrast to existing approaches, the measurements are defmed in terms of nonlinear symmetric functionals of the target positions, except for one of the measurements which is defmed to be a scaled sum of the target positions. The measurement functions are defmed so that in the noise-free case, the target position vector for each coordinate can be determined up to a permutation of elements from knowledge of the measurements. In this paper, we define the measurements in terms of sums of products of the target coordinate positions. The performance of the SME filter is investigated via a computer simulation of the six-target case.

An algorithm for tracking highly maneuvering targets is presented in this paper. The algorithm provides optimal state estimates for non-maneuvering targets and robust tracking performance during target maneuvers. This technique does not make any assumptions about the probability for the jumps between target state models and requires less computations than the algorithm described in reference [3]. Various simulation results are provided to show the performance of the algorithm for maneuvering and non-maneuvering targets and for targets with multiple maneuvers. Simulation results have shown good tracking performance for target maneuvers in the order of 10 g's.

The Bayesian solution of the problem of tracking a target in random clutter gives rise to Gaussian mixture distributions, which are composed of an ever increasing number of components. To implement such a tracking filter, the growth of components must be controlled by approximating the mixture distribution. A popular and economical scheme is the Probabilistic Data Association Filter (PDAF), which reduces the mixture to a single Gaussian component at each time step. However this approximation may destroy valuable information, especially if several significant, well spaced components are present.

In this paper, two new algorithms for reducing Gaussian mixture distributions are presented. These techniques preserve the mean and covariance of the mixture, and the fmal approximation is itself a Gaussian mixture. The reduction is achieved by successively merging pairs of components or groups of components until their number is reduced to some specified limit. Further reduction will then proceed while the approximation to the main features of the original distribution is still good.

The performance of the most economical of these algorithms has been compared with that of the PDAF for the problem of tracking a single target which moves in a plane according to a second order model. A linear sensor which measures target position is corrupted by uniformly distributed clutter. Given a detection probability of unity and perfect knowledge of initial target position and velocity, this problem depends on only twç non-dimensional parameters. Monte Carlo simulation has been employed to identify the region of this parameter space where significant performance improvement is obtained over the PDAF.

High-level algorithms are needed to take tracking sensor reports as input and produce continuous, labeled, target tracks as output. These algorithms will aid human track analysts in sorting through ever-increasing numbers of sensors and targets. The action of such a system is similar to that of computer vision systems; that is, it performs intelligent reasoning about sensed data to infer the characteristics of a spatially organized set of objects. Some of the issues that must be resolved in such a system are knowledge representation, control schemes, uncertainty management, and timeliness. Although progress has been made in establishing a framework for such a system, further work is necessary before a totally automated track analysis system is realized.