Paul Frank Singer

Improved tracking capability and efficient radar allocation through the fusion of radar and infrared search-and-track observations

The benchmark problem addresses the efficient allocation of an agile-beam radar in the presence of highly maneuverable targets and radar ECM. The multisensor benchmark tracking solution is aided by the presence of a scanning infrared search-and-track (IRST) system. This paper presents methods for applying a tracker with interacting multiple- model (IMM) filtering and multiple-hypothesis tracking (MHT) data asso- ciation to this multiple-sensor tracking and resource allocation problem. It presents a hybrid multisensor tracking architecture in which an IMM- MHT tracker operating on IRST data provides the global IMM-MHT tracker with selected observations. Simulation results quantify the poten- tial improvement from the use of advanced tracking methods and IRST data to enhance agile-beam radar tracker capability.

Multispectral detection of dim slightly extended targets in heavy clutter

The spectral signature of a target is typically unknown apriori because of its dependence upon environmental conditions (e.g., sun angle, atmospheric attenuation and scattering), factors effecting the reflectivity and emissivity of the targets surface (dirt, dust, water, paint, etc) and recent operating history (hot or cold engine, exhaust parts, wheels or tracks, etc.). Because of the high variability of the spectral signature of a target, multispectral detection typically detects spectral anomalies. For example, the canopy of a helicopter hovering in front of tree clutter may glint in the midwave infrared band while the reststrahlen spectral feature of the fuselage paint occurs in the longwave infrared band. Both of these are spectral anomalies relative to the tree clutter. If the target is slightly extended so that it subtends more than one pixel, the spectral anomalies by which the target may be detected will not be spatially collocated. This effectively lowers the ROC (receiver operating characteristic) curve of the detection process. This paper derives the ROC curves for several alternative solutions to this problem. One solution considers all possible spectral n-tuples within a small region. One of these n-tuples would likely contain all of the spectral anomalies of the target. Another solution is to apply a spatial maximum operator to each spectral band prior to the anomaly detector. This also combines all the spectral anomalies form the target into a single n-tuple. These methods have the potential to increase PD but an increase in PFA will also occur. The ROC curves of these solutions to the problem of detecting slightly extended targets are derived and compared to establish relative levels of performance.

Feature-aided tracking (FAT)

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.

Application of IMM/MHT tracking with spectral features to ground targets

This paper considers the problem of tracking dim unresolved ground targets and helicopters in heavy clutter with a ground based sensor. To detect dim targets the threshold must be set low which result in a large number of false alarms. The tracker typically uses the target dynamics to prevent the false tracks. The interesting aspect of this problem is that the targets may be or may become stationary. The tracks of stationary targets are difficult to discriminate from tracks formed by persistent false alarms.

The heavy-tailed distribution of a common CFAR detector

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.

The fusion of parametric and non-parametric hypothesis tests

This paper considers the hypothesis testing problem when two sets of data having significantly different types of prior information are fused. The probability density function of the data in the first set is assumed to be known to within a finite set of parameters so that aparometric test can be used to test the hypothesis. The probability density function of the second set of data, possibly collected with a different sensor, is unknown and the detection hypothesis must be tested with a non- parametric method. The testsperjormed on the twa sets of data will be very different, parametric versus non- parametric, and depend upon significantly different test statistics which are likely to defne two drfferent rejection regions. Other than being measuredfrom the same object, the two sets of data and their corresponding test statistics have lirt/e in common. The absence of a common scale of measurement makes direct comparison meaningless. The parametric test will generally be the superior test when the correctprobabiliry density function of the data is assumed. If the probability densityfunction of the data differs from the probability densityfunction assumed when the test was designed then, if is likely that the power of the non- parametric test will be greater than that of the parametric test. In the absence of the probabilistic information required to fuze the data, the results of the two hypothesis tests will be fuzed using the only common probabilistic measure which is generally available, the statistical level of significance. The critical level is the smallest level of significance at which the hypothesis is rejected given the measured data. The level of significance can be calculated because it is based upon the assumption that the hypothesis is true. The greaier the critical level, the more confidence there is that the decision is correct.

Analysis of the effects of fixed pattern noise on a fully adaptive matched filter

Fully adaptive matched filters typically can suppress clutter to the level of the sensor fixed pattern noise. A fully adaptive filter assumes that the clutter is a wide-sense stationary process which can be modeled by a constant means and unknown covariance function. Fixed pattern noise within a data sequence is unknown and tends to be a non-stationary process. As a result fixed pattern noise is minimally affected by fully adaptive filters. The signal processing philosophy for detecting unresolved targets is to enhance the target signal based on the sensor point spread function. When sensor fixed pattern noise exists, the signal from a point target can be significantly different from the sensor point spread function and can result in a loss in SCR. This SCR loss can make weak targets undetectable. This paper describes the effect of a fully adaptive filter on fixed pattern noise manifested as channel dependent bias and gain errors. Spectral analysis which quantifies the impact of these errors is presented. Experimental results on synthetic data and on real data from an infrared scanning sensor with channel dependent fixed pattern noise are given.

Fully adaptive space-spectral detection of small targets in the absence of a-priori knowledge of the spectral signature of the target

The ability to detect and track dim unresolved targets in heavy clutter can be improved by the inclusion of the spectral dimension. Because of the great variation in targets, operating conditions and environments factors the spectral signature of the target is typically unknown. This paper present a fully adaptive matched filter and tracking paradigm which assumes no a priori information about the spectral signature of the target. It is shown that the full SCR gain can be realized in the absence of the spectral signature of the target. The ROC curve of the detector is used to show that performance loss due to the absence of spectral information is entirely due to an increase in the false alarm probability. This increase in PFA adversely effects tracker performance. The SCR track feature is developed to mitigate these effects. Track features provide an information shunt around the detection threshold nonlinearity that would otherwise block the flow of useful information to the tracker.

Synthetic generation of IRST observations for tracker performance studies

This paper describes an analytic model which generates a synthetic list of detection observations from an IRST. The observation list contains both false detects and target detections. The false detects are generated from a statistical model of the clutter and noise. The user is able to select from a menu of clutter types. This selection determines the values of the statistical parameters. The target type and trajectory are user specified. The target type is selected from a menu and determines the signature of the target. Both the target signature and clutter are propagated through the atmosphere and the sensor. The sensor is modeled as the cascade of transfer functions. The sensor model includes optics, detectors, electronics and noise sources. The signal processing which is part of the sensor model assumes a matched filter is used to increase the S(C + N)R prior to detection. The detection threshold is set to provide the user specified probability of false alarm. Each entry in the observation list includes the observation list includes the observation time, the angular position of the observation, the estimated S(C + N)R of the observation and the number of degrees of freedom which is a measure of clutter severity in the region of the observation. The model is intended to be used as part of a larger simulation for example in a sensor fusion study or to provide tracker test sequences for performance comparison and evaluation.

Analysis of the cascade of track-before-detect and track-after-detect tracking algorithms

Advanced track-after-detect (TAD) trackers are able to operate with detection thresholds as low as 9.5dB with the use of track features. At lower threshold the increased number of false alarms inhibits track confirmation. In order to track weaker targets, the target SNR must be increased prior to detection. Assuming that the SNR has been increased as much as possible through signal processing, further increase in SNR can be obtained by preceding the detection threshold with a track-before-detect algorithms. This paper analyzes the performance of the cascade of a TBD and a TAD tracking algorithm.