Wayne R. Blanding

Offline and Real-Time Methods for ML-PDA Track Validation

We present two procedures for validating track estimates obtained using the maximum-likelihood probabilistic data association (ML-PDA) algorithm. The ML-PDA, developed for very low observable (VLO) target tracking, always provides a track estimate that must then be tested for target existence by comparing the value of the log likelihood ratio (LLR) at the track estimate to a threshold. Using extreme value theory, we show that in the absence of a target the LLR at the track estimate obeys approximately a Gumbel distribution rather than the Gaussian distribution previously ascribed to it in the literature. The offline track validation procedure relies on extensive offline simulations to obtain a set of track validation thresholds that are then used by the tracking system. The real-time procedure uses the data set that produced the track estimate to also determine the track validation threshold. The performance of these two procedures is investigated through simulation of two active sonar tracking scenarios by comparing the false and true track acceptance probabilities. These techniques have potential for use in a broader class of maximum likelihood estimation problems with similar structure

Directed subspace search ML-PDA with application to active sonar tracking

The maximum likelihood probabilistic data association (ML-PDA) tracking algorithm is effective in tracking Very Low Observable targets (i.e., very low signal-to-noise ratio (SNR) targets in a high false alarm environment). However, the computational complexity associated with obtaining the track estimate in many cases has precluded its use in real-time scenarios. Previous ML-PDA implementations used a multi-pass grid (MPG) search to find the track estimate. Two alternate methods for finding the track estimate are presented-a genetic search and a newly developed directed subspace (DSS) search algorithm. Each algorithm is tested using active sonar scenarios in which an autonomous underwater vehicle searches for and tracks a target. Within each scenario, the problem parameters are varied to illustrate the relative performance of each search technique. Both the DSS search and the genetic algorithm are shown to be an order of magnitude more computationally efficient than the MPG search, making possible real-time implementation. In addition, the DSS search is shown to be the most effective technique at tracking a target at the lowest SNR levels-reliable tracking down to 5 dB (postprocessing SNR in a resolution cell) using a 5-frame sliding window is demonstrated, this being 6 dB better than the MPG search.

ML-PDA: Advances and a new multitarget approach

Developed over 15 years ago, the maximum-likelihood-probabilistic data association target tracking algorithm has been demonstrated to be effective in tracking very low observable (VLO) targets where target signal-to-noise ratios (SNRs) require very low detection processing thresholds to reliably give target detections. However, this algorithm has had limitations, which in many cases would preclude use in real-time tracking applications. In this paper, we describe three recent advances in the ML-PDA algorithm which make it suitable for real-time tracking. First we look at two recently reported techniques for finding the ML-PDA track estimate which improves computational efficiency by one order of magnitude. Next we review a method for validating ML-PDA track estimates based on the Neyman-Pearson lemma which gives improved reliability in track validation over previous methods. As our main contribution, we extend ML-PDA from a single-target tracker to a multitarget tracker and compare its performance to that of the probabilistic multihypothesis tracker (PMHT).

Multiple Target Tracking Using Maximum Likelihood Probabilistic Data Association

The maximum likelihood-probabilistic data association (MLPDA) target tracking algorithm is effective in tracking very low observable targets. A key limitation of MLPDA is that it is restricted to tracking a single target. We derive and implement a multiple target version of MLPDA called Joint MLPDA (JMLPDA). While the JMLPDA implementation presented in this paper is focused on a two-target case, this algorithm is extensible to any number of targets. The MLPDA and JMLPDA algorithms are combined to form a multi-target MLPDA tracking algorithm. Performance of the JMLPDA and the multi-target MLPDA algorithms are compared to a probabilistic multi-hypothesis tracker (PMHT) for two crossing targets, focusing on track management/update. Simulation results show that under conditions of heavy clutter, the multi-target MLPDA outperforms PMHT in terms of reduced track errors and longer track life.

Adaptive Phased-Array Tracking in ECM using Negative Information

Target tracking with adaptive phased-array radars in the presence of standoff jamming presents both challenges and opportunities to the track filter designer. A measurement likelihood function is derived for this situation which accounts for the effect of both positive and negative contact information. This likelihood function is approximated a? a weighted sum of Gaussian terms consisting of both positive and negative weights, accounting for the positive and negative contact information. Additionally, recent theoretical results have been reported which have derived an accurate measurement error covariance in the vicinity of the jammer when adaptive beamforming is used by the radar to null the effects of the jammer. We compare the impact of using a likelihood function that accounts for negative contact information and the corrected measurement error covariance by comparing five Kalman filter-based trackers in five different scenarios. We show that only those track filters which use both the negative contact information and the corrected measurement error covariance are effective in maintaining track on a maneuvering target as it passes through the jamming region. This approach can also be generalized to any target tracking problem where the sensor response is anisotropic.

Multisensor Track Management for Targets with Fluctuating SNR

In active sonar tracking applications, targets frequently undergo fading in which the targets detection probability can shift suddenly between high and low values. This characteristic is a function of the undersea environment. Using a multisensor active sonar problem, we examine the performance of track management (confirmation and termination) routines where target detections are based on an underlying hidden Markov model (HMM) with high and low detection states. Rule-based track confirmation tests are compared including M/N rules and rules that differentiate the measurements by receiver source (M/N from at least C sensors), each of which is suboptimal compared with a fixed-length likelihood ratio test. We show that significant performance improvements (to near-optimal) can be obtained using a composite track confirmation test that combines two or three such rules in a logical OR operation. Track termination tests are next compared, and it is shown that a Bayesian sequential test (the Shiryaev test) yields dramatic performance improvements over a K/N track termination rule and the Page test. The model-based results are validated using simulations of a multisensor tracking scenario. The results of this paper are informed by a multisensor sonar application. However, targets may fade in and out of view in other modalities as well, due to aspect-dependent radar cross-section or occlusion. As such, our suggestions for improved HMM-modulated SNR track initiation and termination apply to multisensor radar target tracking as well.

Sequential ML for Multistatic Sonar Tracking

We apply the sequential (as opposed to batch) ML-PDA to several data-sets from the MSTWG (multi-static tracking working group) library: from NURC, ARL/UT and TNO.

Tracking Through Jamming Using Negative Information

Advances in characterizing the angle measurement covariance for phased array monopulse radar systems that use adaptive beamforming to null out a jammer source allow for the use of improved sensor models in tracking algorithms. Using a detection probability likelihood function consisting of a Gaussian sum that incorporates negative contact measurement information, four tracking systems are compared when used to track a maneuvering target passing into and through standoff jammer interference. Each tracker differs in how closely it replicates sensor performance in terms of accuracy of measurement covariance and the use of negative information. Only the tracker that uses both the negative contact information and corrected angle measurement covariance is able to consistently reacquire the target when it exits the jammer interference

ML-PDA track validation thresholds

The maximum likelihood probabilistic data association (ML-PDA) algorithm, developed for very low observable (VLO) target tracking, will always provide a candidate track that must then be either validated or rejected. By comparing the value of the log likelihood ratio (LLR) at the parameter estimate to a threshold value, track validation is accomplished. Using extreme value theory, we show that in the absence of a target the LLR global maximum obeys approximately a Gumbel distribution and not the Gaussian distribution previously ascribed to it in the literature. It is shown that the Gaussian approximation yields inaccurate false track acceptance probabilities. Using a Gumbel distribution, the probability of false track rejection can be obtained for a given threshold value. The probability of true track detection is obtained assuming the LLR global maximum obeys approximately a Gaussian distribution in the presence of a target. A system operating characteristic (SOC) is developed that unifies the detection processing and track algorithm performance into a single performance metric. The performance of this test is demonstrated through simulations

Multi-frame assignment PMHT that accounts for missed detections

Probabilistic multi-hypothesis tracking (PMHT) is an algorithm for tracking multiple targets when measurement-to- target assignments are unknown and must be jointly estimated with the target tracks. Multi-frame assignment PMHT (MF- PMHT) is an algorithm designed to mitigate some performance problems associated with PMHT. In MF-PMHT, the PMHT algorithm is applied to multi-frame sequences in the last L frames of data and considers the set of all possible measurement sequences. While effective in improving tracking performance compared to PMHT, performance of the original MF-PMHT degrades when the target single-frame detection probability is non-unity. This is because missed detections are not considered in the multi-frame sequences. A new MF-PMHT implementation is derived in this paper which explicitly considers missed detections in the multi-frame sequences. Performance of this MF-PMHT is compared to the original MF-PMHT algorithm as well as to a Homothetic PMHT. Simulation results indicate that the new MF- PMHT algorithm performs the same as the original algorithm when there are no missed detections and also performs better than the alternative algorithms considered when there are missed detections.