In signal processing applications it is common to assume a Gaussian problem in the design of optimal signal processors. However, non-Gaussian processes do arise in many situations. When the possibility of a non-Gaussian problem is encountered, the question as to which probability distributions should be utilized in a specific situation for modeling the data needs to be answered. In practice, the underlying probability distributions are not known a priori. Consequently, an assessment must be made by monitoring the environment to subdivide for each patch. In this paper, an automatic statistical characterization and partitioning of environments process, previously used on simulated data, is applied to real data of an IR image. Two separate procedures are used to determine all homogeneous patches and subpatches in the IR image. The first procedure, referred to as the mapping procedure, is used to separate contiguous homogeneous regions by segregating between their power levels. The second procedure, referred to as the statistical procedure, separates contiguous homogeneous regions by segregating between their probabilistic data distributions. The latter procedure makes use of Ozturk algorithm, a newly developed algorithm for analyzing random data. Furthermore, the statistical procedure identifies suitable approximations to the probability density function for each homogeneous patch and determines the location of outliers. Convergence of the procedures is controlled by an expert system shell.

In the companion paper, two algorithms for tracking point targets in consecutive frame staring IR imagery with evolving cloud clutter are described and compared by using representative example scenes. Here, our total data base of local airborne scenes with targets of opportunity are used for a more quantitative and comprehensive comparison. The use of real world data as well as our focus on temporal filtering over large number of consecutive frames triggered a search for more relevant metrics than those available. We present two new metrics which have most of the attributes sought. In each metric, gain is taken as a ratio of output to input signal to clutter. Maximum values rather than statistical measures are used for clutter. In the variation metric (VM), a temporal standard deviation for each pixel over 95 consecutive frames is computed and the maximum non-target result is taken as the input clutter. The input signal, a real target moving with sub-pixel velocity through sampled imagery, is estimated by a reference mean technique. Output signal and clutter are taken as maximum target and clutter affected pixels in algorithm filtered outputs. In the second metric, the use of an anti-median filter (AM) provides symmetric treatment of input and output as well as signal and clutter. The maximum target and non-target response to the AM filter on input frames and output frames defines the signal and clutter measures. Our set of real-world data is plotted as output versus input signal to clutter for each metric and each algorithm and the pros and cons of each metric is discussed. With either metric, the signal to clutter gain ratios are approximately 5 - 6 dB greater with the temporal filter algorithm than with the velocity filter algorithm.

We treat the problem of long range aircraft detection in the presence of evolving cloud clutter. The advantages of a staring infrared camera for this application include passive performance, day and night operation, and rapid frame rate. The latter increases frame correlation of evolving clouds and favors temporal processing. We used targets of opportunity in daytime imagery, which had sub-pixel velocities from 0.1 - 0.5 pixels per frame, to develop and assess two algorithmic approaches. The approaches are: (1) banks of spatio-temporal velocity filters followed by dynamic programming based stage-to-stage association, and (2) a simple recursive temporal filter suggested by a singular value decomposition of the consecutive frame data. In this paper, we outline the algorithms, present representative results in a pictorial fashion, and draw general conclusions on the relative performance. In a second paper, we quantify the relative performance of the two algorithms by applying newly developed metrics to extensive real world data. The temporal filter responds preferentially to pixels influenced by moving point targets over those influenced by drifting clouds and thus achieves impressive cloud clutter suppression without requiring sub-pixel frame registration. It is roughly twice as effective in clutter suppression when results are limited by cloud evolution. However when results are limited by temporal noise (close to blue sky conditions), the velocity filter approach is roughly twice as sensitive to weak targets in our velocity range. Real-time hardware implementation of the temporal filter is far more practical and is underway.

New results are presented for optimum coherent detection of signals with random parameters in non-Gaussian clutter. The spherically invariant random vector (SIRV) model is used to characterize the correlated, non-Gaussian clutter samples. A new canonical form for the optimal nonlinear receiver structure is presented. This form incorporates the conventional matched filter which maximizes signal-to-clutter ratio. Closed form solutions for the optimum receivers in Student-t SIRV clutter are presented for the known signal case and in the case of a signal with U(0,2(pi) ) initial random phase. The Student-t clutter example is used to demonstrate the significant improvement in detection probability of the non-Gaussian receiver for the weak signal problem, when compared to conventional Gaussian-based receivers.

Detecting the presence of small weak targets in nonstationary clutter backgrounds is a fundamental problem in representative IR surveillance and tracking systems. In this paper, a system is proposed using spatiotemporal adaptive matched filtering to suppress the effects of clutter and enhance target detection. Shortfalls in conventional adaptive systems lead to a multiple parallel scanning approach to eliminate transients resulting from suboptimal filtering at clutter edges. Simulation results are provided which demonstrate that this approach provides substantially superior performance to a non-adaptive matched filter detection system design using global clutter statistics and, in some cases, can even achieve performance approximating that of an ideal fully-adaptive detector design from the complete statistical knowledge of the nonstationary clutter.

The comparative analysis of experimental results of the optimal detector synthesized on the basis of the generalized signal detection algorithm is accomplished. Signal detection criterions by the generalized detector are defined. A greater informativeness of the generalized detector in comparison with the optimal one is marked.

The detection, recognition and tracking of point targets are the critical technology to lengthen the action distance of detection system. To discriminate the targets in same space orbit with same coating but have different shell thickness, the characteristic in infrared band is discussed in this paper. The algorithm for the computation of the radiation characteristics is presented at first. And then, on the basis of a large amount of infrared radiation data, the features for discriminating the targets are recommended. Finally, an ANN method is put forward to implement the discrimination.

This article characterizes asymptotic limits for the error probabilities that arise while testing for the detection of targets in the presence of clutter. The hypothesis test decision regions are determined by the discrimination function. The function is the basic measure of the information contained in the measurements. While the Neyman-Pearson Theorem specifies the optimum decision regions, it does not specify the detection performance in terms of the error probabilities. Asymptotic bounds expressed as analytical functions allows us to determine the effect of the decision threshold, the clutter density, and the number of measurements on the error probabilities; thus indicating the effectiveness of the testing procedure.

Infrared multispectral sensors are being investigated as a means for day and night target detection. Infrared multispectral sensors would exploit high spectral band-to-band correlation to reject high background clutter. An infrared Fourier transform spectrometer-based field measurement system was used to collect spectral signature data of targets and desert scrub and sand backgrounds from a 100 foot tower at White Sands Missile Range. The measurements include target-to-background spectral contrast, subpixel targets, background spectral correlation, and background spatial power spectra. The measurements have been analyzed to determine multispectral signal-to-clutter ratios versus target, background, diurnal, and weather variations, background correlation versus temperature clutter variations, and spectral correlation versus spatial scale. These measurements contribute to the expanding target and background infrared hyperspectral signature database. The results of the analysis demonstrate the utility and robustness of infrared multispectral techniques for target detection.

In this paper we address the problem of tracking low-SNR targets in an environment of heavy, stationary clutter (e.g., ground clutter). The processing approach is Bayesian field tracking, in which a posterior target distribution is developed over the entire position-velocity state space. Development of the Bayesian posterior probabilities is recursive and is driven by likelihood fields evaluated from successive measurement observations. This track-before-detect approach has a demonstrated capability to track at SNR levels below those for which the usual Kalman- based tracker is functional. We have applied two clutter mitigation techniques that correspond individually to the following clutter characteristics: (1) the occurrence of high-amplitude (non- Gaussian) events and (2) the stationary nature of clutter features. The first characteristic is treated by a composite Gaussian environment model and the second by active discrimination against features tracked (by the Bayesian field tracker) at zero velocity. Both mitigation techniques combine to provide a decision theory test of signal versus noise or clutter, and the net impact is rigorously integrated into the Bayesian tracker processing through the likelihood- ratio field that drives the recursive update. Evaluation of ROC curves for simulated and real environments show both mitigation techniques to be highly effective.

Small-target (single/sub-pixel) detection techniques that use non-Fourier-based whitening approaches are presented for inputs consisting of a time series of images in one or more data channels. Backgrounds are assumed to be complicated by spatial correlation (Gaussian clutter) that is further correlated over time and across channels and may be further corrupted by highly localized non-Gaussian interference terms (`spikes') that appear target-like. For signals of known shape in Gaussian clutter, the Neyman-Pearson criterion leads to an optimal test that employs a self-consistent whitening approach based upon a time-dependent, multichannel linear predictive filtering kernel estimated from the data via least squares. Additionally, an adaptation of iterative scaling is shown to be an effective tool for partitioning correlated and uncorrelated elements of a time series of images. The partitioning of correlated from uncorrelated data, in turn, leads to an approach for isolating targets in Gaussian clutter corrupted by random spikes or for editing spikes in Gaussian clutter without affecting correlated signals or `punching holes' in correlated backgrounds. When possible, results are compared to theoretical predictions and/or optimal processing.

The detection and recognition of targets in infrared wide area surveillance systems is made difficult by clutter background and low resolution. Recent advances in technology have made available small and lightweight hyperspectral imaging sensors. Hyperspectral sensors can facilitate the detection of targets in clutter because natural vegetation clutter has a different statistical distribution of radiant energy in the spectral bands than targets. Natural clutter from vegetation can be characterized as a grey body, but man made objects (i.e. targets) are selective radiators. Compared to blackbody radiators, targets emit radiation more strongly at some wavelengths than at others. The approach taken in this paper is to partition the bands into two groups. The targets exhibit substantial color signatures in one group but look like grey bodies in the other group. A generalized formation for combining the hyperspectral bands is derived using maximum likelihood techniques. The algorithm is a generalization of the weighted spectral difference algorithm, and reduces to that form if the image data is preprocessed to make it spatially white. It is also shown that the algorithm is optimum for non- Gaussian noise when the criterion is to minimize the mean square error between the two groups of bands. The algorithm is applied to TIMS multispectral and SMIFTS hyperspectral data to illustrate the algorithm performance.

This paper presents a new method for detection of small moving targets from noisy image sequences using a recursive filter, which contains a local maximum filter in the feedback loop. Since all the procedures contained in this method can be implemented by fully parallel algorithm, this method can be realized by a neural network and real-time processing is possible for image sequences at high frame rates. First we investigate the performance of the method on the assumption that the targets move randomly in an image plane and the background noise is white both in time and space. The results show that the proposed method has the ability to suppress the background noise and enhances small moving targets, and that the targets are detected only by thresholding after the processing of the recursive filter. There can be other backgrounds such as clutters and stationary objects. It is also shown that the above method is applicable after preprocessing of conventional time difference method, and is able to suppress these backgrounds. Next we analyze the performance of the method using the property of order statistics. The performance measure is the output signal-to-noise ratio and is represented analytically as a function of input SNR and the parameters included in the method. Finally, the recursive filter is optimized using the result of the analysis.

Studies show that vigilance decreases rapidly after several minutes when human operators are required to search live video for infrequent intrusion detections. Therefore, there is a need for systems which can automatically detect targets in live video and reserve the operator's attention for assessment only. Thus far, automated systems have not simultaneously provided adequate detection sensitivity, false alarm suppression, and ease of setup when used in external, unconstrained environments. This unsatisfactory performance can be exacerbated by poor video imagery with low contrast, high noise, dynamic clutter, image misregistration, and/or the presence of small, slow, or erratically moving targets. This paper describes a highly adaptive video motion detection and tracking algorithm provides good performance under stressing data and environmental conditions. Features of the algorithm include: reliable detection with negligible false alarm rate of variable velocity targets having low signal-to- clutter ratios; reliable tracking of targets that exhibit motion that is non-inertial, i.e. varies in direction and velocity; automatic adaptation to both infrared and visible imagery with variable quality; and suppression of false alarms caused by sensor flaws and/or cutouts.

The development and evaluation of signal and data processing algorithms for IR surveillance systems is critically dependent on realistic simulations of targets and background. The Advanced Surveillance Testbed has been developed by GRC to perform such simulations. It has recently been upgraded to include models for the scattering of sunlight from high-altitude clouds of ice-crystals. The ice cloud models in the Advanced Surveillance Testbed are designed primarily for the SWIR and MWIR bands. The ice clouds are assumed to have nominally flat upper surfaces, and to be composed of hexagonal crystals (plates, columns, or intermediates), with any of several alternative distributions of shapes and sizes. The ice- crystals are assumed to rotate randomly about their hexagonal axes, but the user can choose from several models for the orientation of this axis: random isotropic, random horizonal, or nominally vertical. A single scattering model is used, with the small-angle forward scattering removed by renormalization. The scattering is calculated by geometrical optics, using algorithms based on the papers published by Liou, Takano, Cai, and Coleman. However, the GRC implementation includes some innovations that greatly increase its computational efficiency. In the SWIR band, the refractive index is highly variable. Its imaginary part varies by orders of magnitude, and its real part can be less than unity, causing total external reflections. Therefore, it is necessary to perform the computations for multiple IR wavelengths and combine the results. The calculations include two-way atmospheric transmission for the relevant wavelengths and the assumed cloud altitude. The model and its utility will be discussed.

This paper presents simulations of IR and radar surveillance sensors to support an ongoing Multi Sensor Data Fusion (MSDF) performance evaluation study for potential application to the Canadian Patrol Frigate midlife upgrade. The surveillance sensor models are used in an algorithm-level testbed that allows the investigation of advanced MSDF concepts. The sensor models take into account sensor's design parameters and external environmental effects such as clutter, clouds, propagation and jamming. The latest findings regarding the dominant perturbing effects affecting the sensor detection performance are included. The sensor models can be used to generate contacts and false alarms in scenarios for multi-sensor data fusion studies while the scenarios is running.

Innovative approach to signal processing of the small targets under complicated conditions including low-contrast and maneuvering targets with backgrounds is presented. Its essence is dealt with the use of intelligent solid-state photosensor, so-called photoelectric structures with memory (PESM). PESM is integrated multilayer heterostructure, which combines the main capabilities of photodetector, imager, memory media and parallel processor. Optical information signal is detected in photosensitive layer, recorded and stored as 2D charge pattern in memory layer, read out from reading layer, and processed due to charge, potential and electric field pattern interactions throughout the PESM layers. PESM performs such parallel image processing as summation, subtraction, contouring, convolution and correlation, which may be effectively applied to numerous tasks of diverse photonic systems. It is essential, that PESM performs such multifunctional operations in a real time without any additional processors and computers.

This paper considers the effectiveness of different registration algorithms in an air surveillance radar tracking environment. The evaluation is based on real data collected from an operating radar network in Canada. The existing real time quality control (RTQC) routine in the network requires targets to be on both sides of the line between the radars; this type of distribution is usually not available in the area with low air traffic density. The least squares (LS) algorithm which solves for the least squares biases is an alternative to handle this problem. Two algorithms that are considered as being more rigorous in the literature are the maximum likelihood (ML) and generalized least squares (GLS). The ML algorithm is a solution of the registration problem that uses a calculated covariance matrix of the measurement noise. The GLS algorithm is a variation of the ML algorithm where only the variances of the measurement noise are used. Based on the real data analysis, the track separation after registration are identical for the LS and ML algorithm, with the GLS being close most of the time. The result of the RTQC algorithm is close when the radar returns are split evenly between the two sides of the line between the radars. If the data in unevenly distributed, then the RTQC algorithm provides less accurate estimates. Comparing their computational complexities, the RTQC and LS algorithm are very efficient while the ML and GLS algorithm are about hundred times slower in terms of computational speed.

This paper assesses tracking performance of a number of commonly-used data association techniques, including the nearest-neighbor (NN) data association with optimal and sub-optimal assignments, the weighted-average and nearest-neighbor version of the probabilistic data association (PDA), joint probabilistic data association (JPDA), cheap JPDA, and sub-optimal JPDA. The real radar tracking data used for the performance evaluation in this paper contain multiple maneuvering and non-maneuvering air targets in various clutter conditions. The study shows that all the data association methods perform well when the targets are well separated with near straight-line trajectories. In the case of closely spaced and maneuvering targets, the NN and NN version of JPDA methods are more effective than the weighted-average PDA and JPDA methods.

A method of point target detection for real-time image processing is presented. It is simple and practical. It is easy for hardware implementation and cost is low for real-time image processing.

This paper will introduce an approach to eliminate the image quivering, that is called phase correlation approach. The method can effectively measure the pixel offsets and correct it. Its accuracy is up to subpixel. Through the processing, we can use energy accumulation method to detect out the dim point target easily.

The performance of a commonly employed linear array of sonar sensors is assessed for point- target localization. Two different methods of combining time-of-flight information from the sensors are described to estimate the range and azimuth of the target: pairwise estimate method and the maximum likelihood estimator. The biases and variances of the methods are investigated and their combined effect is compared to the Cramer-Rao Lower Bound. Simulation studies indicate that in estimating range, both methods perform comparably; in estimating azimuth, maximum likelihood estimate is superior at a cost of extra computation.

Description of a class of heuristical algorithms for the time-coordinate data sequential analysis providing continuous output of data and eliminating the image blur is presented. The time- coordinate data make up a flux of coordinates and detection moments of input radiation photons detected by the lately developed new generation of photo-receivers.

This paper describes a Directional High-order Correlation Method (DHCM) for detecting dim Point-Source Target (PST) in IR noise. By exploiting the directional characteristics and the consecutive temporal-spatial dependencies of the points on a track, the DHCM computes the correlations between different frames and identifies targets' tracks among noisy images. Theoretical analyses and simulation results show that the DHCM has high capability in noise rejection. A DHCM-based scheme has been proposed for tracking initiation and updating. The presented simulation results for PST detecting in low SNR (<EQ 2) indicates the effectiveness of the proposed DHCM in detecting dim moving PST.

This paper presents a practical algorithm and system for automatic detecting and tracking small targets in IR image sequences. A recursively adaptive detection is designed to improve SCR and deal with the unknown background clutter. Then the algorithm labels the candidate targets with a new method which can be done rapidly, and locks the real target based on a multi-frame concept. The system includes two processors, CoreModule and TMS320C30. They constitute a flexible multi-bus architecture which can perform the algorithm parallelly. Experiment results demonstrate that the system can detect and track low intensity small targets successfully in real time.

In this paper, a real-time detection algorithm for small moving target in FLIR image sequence was proposed, it is based on certain-factor (CF) and composed of two components: a predetector and a trace matcher. The predetector implements a N-P test on each pixel of the input image and outputs a record denoting the pixel's information for each detected pixel. The trace matcher matches the detected pixels in image with previously formed traces. Two certain-factors were introduced to traces. According to the value of CF, the matcher can identify the target in the image sequence. Performance analysis and simulation results were presented.

This paper describes a Neural Network (NN) aided Kalman Filter (KF) for tracking Point- Source Target in IR images. To improve the Kalman estimates and tracking accuracy, we introduce multi-layer backpropagation neural networks into the normal Kalman filter. The performance improvement of NNKF estimations with quantization noise presence has been investigated. This NNKF uses the coordinates of the detected targets in every frame as the measurement data, and estimates the targets' motion parameters which are used as the decision statistics for rejecting/maintaining a target. If the parameters related to an individual possible target have gone beyond a given bound, this `target' will be set aside, and related tracking ended. Simulation results have shown that the performance and accuracy of the NNKF tracker have been improved a lot than that without the aid of neural networks.

This paper studies the performance of least mean square (LMS) adaptive filters for prewhitening noise and multiframe accumulation algorithm for the detection of point target in IR image data. The object of interest is assumed to have a very small spatial spread and is obscured by correlated clutter and noise of much larger spatial extent, and the signal-to-noise ratio (SNR) is very low (SNR < 2). Traditional target detection algorithms involve background suppression/target enhancement that usually requires spatial and temporal prewhitening. In our scheme, adaptive Prediction Filters are employed as prewhitening filters to enhance the dim target and suppress the correlated background. According to the correlation of noise and clutter, 1D least mean square adaptive filters are adopted, which update filter weights based on the spatial coherence between the signal and noise components of the data. As a result of prewhitening the SNR has been increased a lot. In our scheme, the dim target moves very slowly (v < 0.5 pixel/frame), so an effective algorithm to enhance target is to sum up target energy through successive frames. Considering low speed of the target, summing operation may be operated by directly adding N consecutive frames under the assumption that the point target stays at a pixel at least in N frames. The summed-up result image is then processed by a proper threshold to pick out candidate target points with high summed energy. The above N-frame adding and thresholding procedure is recursively done as the image sequences are continually input from infrared sensor. All the thresholded result images are added up to form a new result image, in which the picked-out candidate target points embody target trajectories with continuous points, while noisy false targets with non- continuous points. In IR image, there are some stationary objects. To discriminate moving targets from almost stationary objects in background, the intensity time sequence on trajectories are used to extract their different intensity features.

A method for managing agile sensors to optimize detection and classification based on discrimination gain is presented. Expected discrimination gain is used to determine threshold settings and search order for a collection of discrete detection cells. This is applied in a low signal-to-noise environment where target-containing cells must be sampled many times before a target can be detected or classified with high confidence. Bayes rule is used to compute the expected discrimination gain for each sample region using estimated probability that it contains a target. This gain is used to select the optimal cell for the next sample. The effectiveness of this approach was assessed in a simple test case by comparing the result of discrimination optimized search with direct search. For a single 0 dB Gaussian target, the error rate for discrimination optimized search was similar to the direct search result against a 6 dB target.

Surprisingly, fuzzy sets (in the guise of equivalence classes of random sets) arises naturally in a Bayesian analysis of bounds on performance for tracking in a dense multiple target environment. This talk will explain the connection between these ideas. Moreover, the use of fuzzy sets as `primitives' has promise to reduce the computational complexity of real-time approximate multiple hypothesis tracking algorithms.

The tracking of resident space objects (RSO) by space-based sensors can lead to engagements that result in stressing backgrounds. These backgrounds, including hard earth, earth limb, and zodiacal, pose various difficulties for signal processing algorithms designed to detect and track the target with a minimum of false alarms. Simulated RSO engagements were generated using the Strategic Scene Generator Model and a sensor model to create focal plane scenes. Using this data, the performance of several detection algorithms has been quantified for space, earth limb and cluttered hard earth backgrounds. These algorithms consist of an adaptive spatial filter, a transversal (matched) filters, and a median variance (nonlinear) filter. Signal-to-clutter statistics of the filtered scenes are compared to those of the unfiltered scene. False alarm and detection results are included. Based on these findings, a suggested processing software architectures design is hypothesized.

This paper briefly reviews the development of the mean-field event-averaged maximum likelihood estimation (MFEAMLE) tracker and compares its tracking performance with that of a joint probabilistic data association (JPDA) filter. The JPDA and MFEAMLE approaches are similar in that they both average over measurement to track associations. However, there are several features of MFEAMLE that improve its estimation performance at high target and clutter densities while simplifying the required computation enough to make real-time performance feasible. To enhance tracking of close targets, the filter explicitly models the error correlations that occur between such target pairs, rather than assuming that they are independent. These error correlations arise from the measurement to track association ambiguity present when target separations are comparable to the measurement errors in the sensors. In order to reduce the computational load, a mean-field approximation is used to perform the summation over all associations. In performance comparison on simulated data, smaller average errors and less track loss were obtained for the MFEAMLE tracker than with JPDA.

A CFAR detector commonly used for the detection of unresolved targets normalizes the background variance by dividing the detection filter output by the local sample standard deviation. A number of researchers have measured the experimental false alarm probability of this detector and found it to be higher than the probability predicted by a Gaussian density function. This is the case even when the filter output statistics are known to be Gaussian distributed. A number of attempts have been made to heuristically construct distributions which exhibit the heavy tails associated with the measured false alarm probability (e.g. sum of two Gaussian densities or the modified gamma density). This paper presents a first principle derivation of the detector false alarm density function based upon the assumption that the filter output is Gaussian distributed. The resulting false alarm density function is very nearly Gaussian out to about 3.5 standard deviations. Past 3.5 standard deviations the tails of the derived density function are markedly heavier than the corresponding Gaussian tails. The parameters of this new density function are easily estimated from the filter outputs. The analytic results are validated using a Chi-Square goodness-of-fit test and experimental measurements of the false alarm density.

Low observable targets pose a unique challenge to both civilian and military surveillance systems. Since `detection densities' received at surveillance centers may be significantly reduced when attempting to track low observable target types, the amount of noise filtering performed at each level of the surveillance system (primary, secondary, and tertiary) must be reduced in an effort to establish and maintain track on the low observable target. This paper discusses specific modifications that may be made to the various primary, secondary, and tertiary processes to allow for enhanced low observable target tracking and their resulting impact on potential tracking performance.

The two most popular solutions to the nonlinear filtering problem are the Extended Kalman filter (EKF) and the Iterated Extended Kalman filter (IKF). Both are sub-optimal algorithms which employ a first-order, Taylor-series approximation to adapt the linear, Kalman filter to the nonlinear problem. While the Taylor-series approximation makes an implementation realizable, its accuracy depends heavily on the stability of the Jacobian matrix. In practice the Jacobian matrix is often numerically unstable, resulting in filter divergence and, in the case of the IKF, slowed or even non-convergence of the iterates. This paper identifies inadequacies inherent to the EKF and IKF, discusses their detrimental effect on performance, and then proposes a solution which uses the Julier et al. time update and a new iterated procedure for computing the measurement update. The resulting new iterated filter is believed to be a robust alternative to prevailing methods. Examples involving target tracking are considered.

This paper describes a new exact nonlinear filter which generalizes the Kalman filter. The filter will be explained using block diagrams, for maximal clarity, in addition to detailed equations. A comparison with the Kalman filter will be given, highlighting the similar structure and low computational complexity. Using this block diagram comparison, engineers who are familiar with the Kalman filter will readily grasp the new nonlinear filter technique.

This paper presents a solution to a second benchmark problem for tracking highly maneuvering targets in the presence of False Alarms (FA) and Electronic Counter Measures (ECM) and involves beam pointing control of a phased array radar. The proposed solution utilizes an Interacting Multiple Model (IMM) algorithm in conjunction with the Integrated Probabilistic Data Association Filter (IPDAF) when there are measurements of uncertain origin. The output of the IMM algorithm is used to compute the time for the next measurement in order to maintain a given level of tracking performance which was established to prevent track loss. A testbed simulation program that includes the effects of target amplitude fluctuations, beamshape, missed detections, target maneuvers, FA, ECM, and track loss was used to evaluate performance. For this benchmark problem, the `best' tracking algorithm is the one that requires a minimum amount of radar energy while satisfying a 5% lost track constraint.

A Multirate Interacting Multiple Model tracking algorithm is developed in this paper. The algorithm is based on a reformulation of the interacting multiple model (IMM) filter under the assumption that each model operates at an update rate proportional to the model's assumed dynamics. A wavelet transform is used to generate equivalent multirate measurements, which exhibit the additional property of lower equivalent measurement noise for low-rate data. Using this filtering approach performance virtually equivalent to a full IMM filter can be realized but with only a moderated increase in computational complexity over a single Kalman filter.

Estimation of the specular sea-reflection coefficient is carried out while simultaneously tracking a low-flying target with an `Extended Kalman Filter'. The error in the determination of target elevation is reduced by compensating the measurement for the corruption caused by the multipath reflection using an estimate of the sea-reflection coefficient. By this method it is possible to greatly reduce the resulting elevation errors in situations of low noise and gentle maneuvers. Higher levels of noise or large maneuvers can lead to sudden loss of track rather than to a moderate degradation of accuracy in the height determination. The causes of this degradation are explored.

An adaptive correlation-based tracker has been developed. It uses discriminant nonlinear filters which offer more robustness to noise, background, and object distortions. Computers simulations show test results for a small target tracking, and good capabilities are demonstrated without post-processing of the correlation plane. The algorithm developed here works where well-known linear filters failed.

Loral Canada completed (May 1995) a Department of National Defense (DND) Chief of Research and Development (CRAD) contract, to study the feasibility of implementing a multi- sensor data fusion (MSDF) system onboard the CP-140 Aurora aircraft. This system is expected to fuse data from: (a) attributed measurement oriented sensors (ESM, IFF, etc.); (b) imaging sensors (FLIR, SAR, etc.); (c) tracking sensors (radar, acoustics, etc.); (d) data from remote platforms (data links); and (e) non-sensor data (intelligence reports, environmental data, visual sightings, encyclopedic data, etc.). Based on purely theoretical considerations a central-level fusion architecture will lead to a higher performance fusion system. However, there are a number of systems and fusion architecture issues involving fusion of such dissimilar data: (1) the currently existing sensors are not designed to provide the type of data required by a fusion system; (2) the different types (attribute, imaging, tracking, etc.) of data may require different degree of processing, before they can be used within a fusion system efficiently; (3) the data quality from different sensors, and more importantly from remote platforms via the data links must be taken into account before fusing; and (4) the non-sensor data may impose specific requirements on the fusion architecture (e.g. variable weight/priority for the data from different sensors). This paper presents the analyses performed for the selection of the fusion architecture for the enhanced sensor suite planned for the CP-140 aircraft in the context of the mission requirements and environmental conditions.

Probabilistic data association algorithms are described for tracking multiple targets with multiple sensor. These algorithms employ multiple frames in the data association processing. These approaches offer improved performance over Joint Probabilistic Data Association tracking. This improved performance is observed, however, at the expense of increased processing load. Three approaches are described that employ multiple frame data association. With these algorithms, design parameters can be selected to adjust performance to suit a specific application.

This paper addresses the multisensor tracking of targets but considers only the special case of targets on a ballistic trajectory. The scenario consists of two radars tracking the same target. One of these radars periodically sends a track to the other radar for fusion with the track generated by the recipient. A track fusion algorithm for tracking ballistic targets is derived. This algorithm is exercised and illustrated by the Sensor Fusion Architecture Model (SFAM) computer program. Since the repeated track fusion of ballistic trajectories results in correlation that must be removed to preserve the optimality in the resultant estimate, an algorithm that requires the preservation of the last update and the error covariance matrix from another Kalman Filter (KF) also is presented. These data then are used to decorrelate the two track inputs originating at the same-source KF.

This paper deals with the design and implementation of MATSurv 1--an experimental Multisensor Air Traffic Surveillance system. The proposed system consists of a Kalman filter based state estimator used in conjunction with a 2D sliding window assignment algorithm. Real data from two FAA radars is used to evaluate the performance of this algorithm. The results indicate that the proposed algorithm provides a superior classification of the measurements into tracks (i.e., the most likely aircraft trajectories) when compared to the aircraft trajectories obtained using the measurement IDs (squawk or IFF code).

The Interacting Multiple Model (IMM) estimator has been shown to be superior, in terms of tracking accuracy, to a well-tuned Kalman filter when applied to tracking maneuvering targets. However, because of the increasing number of filter modules necessary to cover the possible target maneuvers, the IMM estimator also imposes an additional computational burden. Hence, in an effort to design a real-time IMM-based multitarget tracking algorithm that is independent of the number of modules used in the IMM estimator, we propose a `coarse- grained' (dynamic) parallel implementation that is superior, in terms of computational performance, to previous `fine-grained' (static) parallelizations of the IMM estimator. In addition to having the potential of realizing superlinear speedups, the proposed implementation scales to larger multiprocessor systems and is robust. We demonstrate the performance results both analytically and using a measurement database from two FAA air traffic control radars.

A prototype system for tracking tactical ballistic missiles using multiple radars has been developed. The tracking is based on measurement level fusion (`true' multi-radar) tracking. Strobes from passive sensors can also be used. We describe various features of the system with some emphasis on the filtering technique. This is based on the Interacting Multiple Model framework where the states are Free Flight, Drag, Boost, and Auxiliary. Measurement error modeling includes the signal to noise ratio dependence; outliers and miscorrelations are handled in the same way. The launch point is calculated within one minute from the detection of the missile. The impact point, and its uncertainty region, is calculated continually by extrapolating the track state vector using the equations of planetary motion.

The main advantage of a multi-sensor fusion approach is to complement the data of one sensor with that of another sensor in order to obtain better target measurement information and to make a more accuracy estimation. In this paper, one image processing along with neural network algorithm is applied to solve the attribute information. The fundamental idea of this paper is that one decentralized estimation approach for a sensor fusion problems in which a Bayesian mathematical structure denoted 1-step maximum a posteriori estimate algorithm is applied for the data association. In such an algorithm, one also applied a techniques to combine the target attribute data to enhance the tracking results.

It is commonly understood that in active detection system constant-frequency pulses correspond to good Doppler but poor delay resolution capability; and that linearly-swept frequency pulses have the opposite behavior. Many systems are capable of both types of operation, and hence in this paper the fusion of such pulses is examined. It is discovered that in many (but not all) situations the features complement in such a way that tracking performance using a combined CW-FM pulse is improved by an order of magnitude when compared to a scheme using only a full CW or FM pulse. Also investigated are alternating- pulse systems, and while these are suboptimal their performances appear robust.

There are a number of algorithms currently available for tracking highly maneuverable targets using position measurements. A comparison of some of these algorithms using benchmark trajectories is given in a session of the 1994 American Control Conference. Dramatic increases in tracking performance (lower loss of lock rates, larger interdwell intervals, and more accurate state estimates) will likely result from novel uses of additional non-traditional sensor information. In particular, an imaging sensor provides information which can be used to increase tracking performance. In this paper, we use an imaging sensor to detect target maneuvers, which is based on monitoring changes in image features. By accurately and quickly detecting the onset and termination of maneuvers, we are able to reconfigure the tracking filter in order to increase performance. Simulations are provided to show how augmenting a traditional radar only system with an imaging sensor to detect maneuvers can improve tracking performance.

This paper discusses the potential application of Interacting Multiple Model (IMM) filtering to the multi-radar Air Defense System application. This application includes a wide variety of potential target and radar characteristics. The paper begins with a discussion of the three IMM filter models that have been chosen and the choice of Markov transition matrix under the condition of variable update rate filtering. A comparison is given of the track prediction performance of the IMM method with that of a single model filtering system that uses maneuver detection for gain and covariance adjustment. Results show the IMM approach to be uniformly better than a conventional filter that has been designed for the Air Defense System application. However, the relative improvement of the IMM approach is a strong function of the quality of the radar measurement data. Since data association is a key tracking issue, IMM filtering will be adapted for use as part of a Multiple Hypothesis Tracking System. For this purpose, IMM gating and track scoring expressions are discussed and the methods validated through simulation.

Large classes of data association problems in multiple hypothesis tracking applications involving multiple and single sensor systems can be formulated as multidimensional assignment problems. Lagrangian relaxation methods have been shown to solve these problems to the noise level in the problem in real-time, especially for dense scenarios and for multiple scans of data from multiple sensors. This work presents a new class of algorithms that circumvent some of the shortcomings of previous algorithms. The computational complexity of the new algorithms is shown via some numerical examples to be linear in the number of arcs. Numerical results demonstrate the superior solution quality of the relaxation algorithm compared to proven greedy methods. Decomposition is also shown to provide improved execution times for clustered association problems that regularly arise in tracking.

Sensitivity to track initialization error is quantified as a function of clutter density for the nearest neighbor assignment function (NNAF). Two statistical distributions of track initialization error are derived under idealized hypothesis representing excellent and poor performance of the NNAF in clutter. A track initialization error region is obtained by constraining the mean initialization error (under the excellent NNAF performance hypothesis) to have significance level (alpha) (under the poor NNAF performance hypothesis). The initialization sensitivity region is derived for general nonlinear state equations and for measurement equations with additive Gaussian noise. Examples with constant velocity linear models are given. There exists a critical clutter density at which the initialization error region is the empty set. Thus, even perfect track initialization is a poor initialization in clutter whose density exceeds critical density. An explicit expression for the critical clutter density is derived.

When tracking targets with radar, changes in target aspect with respect to the observer can cause the apparent center of radar reflections to wander significantly. The resulting noisy angle errors are called target glint. Glint may severely affect the tracking accuracy, particularly when tracking large targets at short ranges (such as might occur in the final homing phase of a missile engagement). The effect of glint is to produce heavy-tailed, time correlated non-Gaussian disturbances on the observations. It is well known that the performance of the Kalman filter degrades severely in the presence of such disturbances. In this paper we propose a random sample based implementation of a Bayesian recursive filter. This filter is based on the Metropolis-Hastings algorithm and the Gaussian sum approach. The key advantage of the filter is that any nonlinear/non-Gaussian system and/or measurement models can be routinely implemented. Tracking performance of the filter is demonstrated in the presence of glint.

This paper will propose a way to extract target position/range information from the angle-only tracking data with the priori knowledge of the target movement. The target trajectory can be expressed as a function of time, called target function, with n parameters. If m parameters (e.g. target original position, target speed, target acceleration, etc.) are known, or can be estimated to some extent of accuracy, then there remain n-m unknown parameters in the target function. In order to determine these unknown parameters, we should take at least n-m set of tracking data at different times, and construct a system of n-m simultaneous equations. Once all parameters become known by solving this system of equations, the target position and target range can be obtained by substituting the specific time value into the target function. Some typical cases are investigate and the application conditions discussed. Computer simulations are also presented.

Track fusion is one of the algorithm architectures for tracking multiple targets with data from multiple sensors. In track fusion for example, sensor-level tracks can be combined to form global-level tracks that are based on data from all the sensors. These multiple sensor, global- level tracks can then be fed back to the sensor-level trackers to reduce the data association errors. The global tracks, however, are cross-correlated with the sensor-level tracks. A method is needed to take this track-to-track cross-correlation into account. This cross- correlation of the global and sensor tracks must be considered when providing the global tracks to the sensor trackers as well as when providing the sensor tracks to the global tracker. Even without process noise, the global and sensor tracks are cross-correlated because they are based on common data. With feedback, both the global tracks and the tracks from each sensor are based on prior data from not only the sensor itself, but also the other sensors. This paper presents a method for dealing with the cross-correlations of the tracks in track fusion for feeding back the global level tracks. New methods have been recently developed for track fusion without process noise. These new methods address track fusion without feedback of global-level tracks to the lower levels. Application of these new methods are employed in this paper to deal with the complex cross-correlations involved when global tracks are fed back to the sensor-level trackers.