Steven Schoenecker

ML–PDA and ML–PMHT: Comparing Multistatic Sonar Trackers for VLO Targets Using a New Multitarget Implementation

The maximum-likelihood probabilistic data association (ML-PDA) tracker and the maximum-likelihood probabilistic multihypothesis (ML-PMHT) tracker are tested in their capacity as algorithms for very low observable (VLO) targets (meaning 6-dB postsignal processing or even less) and are then applied to five synthetic benchmark multistatic active sonar scenarios featuring multiple targets, multiple sources, and multiple receivers. Both methods end up performing well in situations where there is a single target or widely spaced targets. However, ML-PMHT has an inherent advantage over ML-PDA in that its likelihood ratio (LR) has a simple multitarget formulation, which allows it to be implemented as a true multitarget tracker. This formulation, presented here for the first time, gives ML-PMHT superior performance for instances where multiple targets are closely spaced with similar motion dynamics.

Maximum Likelihood Probabilistic Multi-Hypothesis Tracker Applied to Multistatic Sonar Data Sets

The Maximum Likelihood Probabilistic Multi-Hypothesis tracker (ML-PMHT) is an algorithm that works well against low-SNR targets in an active multistatic framework with multiple transmitters and multiple receivers. The ML-PMHT likelihood ratio formulation allows for multiple targets as well as multiple returns from any given target in a single scan, which is realistic in a multi-receiver environment where data from different receivers is combined together. Additionally, the likelihood ratio can be optimized very easily and rapidly with the expectation-maximization (EM) algorithm. Here, we apply ML-PMHT to two multistatic data sets: the TNO blind 2008 data set and the Metron 2009 data set. Results are compared with previous work that employed the Maximum Likelihood Probabilistic Data Assocation (ML-PDA) tracker, an algorithm with a different assignment algorithm and as a result a different likelihood ratio formulation.

The ML-PMHT Multistatic Tracker for Sharply Maneuvering Targets

The maximum likelihood probabilistic multi-hypothesis tracker (ML-PMHT) is applied to a benchmark multistatic active sonar scenario with multiple targets, multiple sources, and multiple receivers. We first compare the performance of the tracker on this scenario when it is applied in Cartesian measurement space, a typical implementation for many trackers, against its performance in delay-bearing measurement space, where the measurement uncertainty is more accurately represented. ML-PMHT is a batch tracker, and the motion of a target being tracked must be given a parameterization that describes the motion of the target throughout the batch. In the scenario in which we apply the tracker, the majority of target returns have low amplitudes (i.e., the targets are low-observable), which makes the choice of a batch tracker very appropriate. In prior work, ML-PMHT was implemented with a straight-line parameterization to describe target motion. However, in order to track maneuvering targets, the tracker was implemented in a sliding-batch fashion under the assumption that a maneuvering track could be approximated as a series of short straight lines. Here, we augment the straight-line parameterization by a maneuver-a single course change within the batch-that allows ML-PMHT to follow even sharply maneuvering targets, and we apply it in both Cartesian and delay-bearing measurement space. We also implement this maneuvering-model parameterization with both a fixed batch-length implementation as well as a variable batch-length implementation. Finally, we develop an expression for the Cramer-Rao lower bound (CRLB) for the maneuvering-model parameterization and show that the ML-PMHT tracker with the maneuvering-model parameterization is an efficient estimator.

Maximum likelihood probabilistic data association tracker applied to bistatic sonar data sets

In the early 1990s, the Maximum Likelihood Probabilistic Data Association (ML-PDA) tracker was developed in a passive sonar framework, and subsequent research has shown it to be effective for tracking very low SNR targets. This was done with both active and passive sonar, for targets that have some given type of deterministic motion. Recent work has focused on applying ML-PDA to bistatic sonar data. Here, we apply ML-PDA in a sliding window implementation to three bistatic data sets used by the MSTWG (Multistatic Tracking Working Group): the SEABAR 2007 data set, the TNO Blind 2008 data set, and a new blind data set provided by Metron in 2009.

Extreme-value analysis for ML-PMHT, Part 1: threshold determination

The Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT) can be used as a powerful multisensor, low-observable, multitarget active sonar tracker. It is a non-Bayesian algorithm that uses a generalized likelihood ratio test to differentiate between clutter and targets. Prior to this paper, the detection threshold used for target discrimination was determined either through trial and error or with lengthy Monte Carlo simulations.We present a new method for determining this threshold by assuming that clutter is uniformly distributed in the search space (which is one of the basic assumptions of the ML-PMHT algorithm) and then treating the log-likelihood ratio (LLR) as a random variable transformation. In this manner we can obtain an expression for the value of any random point on the likelihood surface caused by clutter. We then use extreme value theory to obtain an expression for the probability density function (PDF) of the peak point of the LLR surface due to clutter. From this peak PDF, we can then calculate a threshold based on some desired (small) false track acceptance probability.

Maximum likelihood probabilistic data association (ML-PDA) tracker implemented in delay/bearing space applied to multistatic sonar data sets

The Maximum Likelihood Probabilistic Data Association (ML-PDA) tracker is an algorithm that has been shown to work well against low-SNR targets in an active multistatic framework with multiple transmitters and multiple receivers. In this framework, measurements are usually received in time-bearing space. Prior work on ML-PDA implemented the algorithm in Cartesian measurement space - this involved converting the measurements and their associated covariances to (x, y) coordinates. The assumption was made that Gaussian measurement error distributions in time-bearing space could be reasonably approximated by transformed Gaussian error distributions in Cartesian space. However, for data with large measurement azimuthal uncertainties, this becomes a poor assumption. This work compares results from a previous study that applied ML-PDA in a Cartesian implementation to the Metron 2009 simulated dataset against ML-PDA applied to the same dataset but with the algorithm implemented in time-bearing space. In addition to the Metron dataset, a multistatic Monte Carlo simulator is used to create data with properties similar to that in the Metron dataset to statistically quantify the performance difference of ML-PDA operating in Cartesian measurement space against that of ML-PDA operating in time-bearing space.

The Effect of K-Distributed Clutter on Trackability

In the field of target tracking, a tremendous amount of work has been done on designing and implementing algorithms. However, much less work has been performed on analyzing whether, for a given target in a given environment, tracking is possible at all. Our recent work developed a framework to answer just that. But the only clutter amplitude model it could process was Rayleigh. On the other hand, the K-distribution, much heavier-tailed than Rayleigh, has recently been posited to more accurately describe “real” sonar clutter. In this paper, we incorporate K-distributed clutter into the trackability framework, and the differences are significant. We find we answer the question, “When tracking a target, does using amplitude actually help?”

Characteristic Functions of the Product of Two Gaussian Random Variables and the Product of a Gaussian and a Gamma Random Variable

We derive the characteristic function (CF) for two product distributions-first for the product of two Gaussian random variables (RVs), where one has zero mean and unity variance, and the other has arbitrary mean and variance. Next, we develop the characteristic function for the product of a gamma RV and a zero mean, unity variance Gaussian RV. The underlying rationale for this is to develop a model for a “quasi-Gaussian” RV-an RV that is nominally Gaussian, but with mean and variance parameters that are not constant, but instead, are RVs themselves. Due to the central limit theorem, many “real-world” processes are modeled as being Gaussian distributed. However, this implicitly assumes that the processes being modeled are perfectly stationary, which is often a poor assumption. The quasi-Gaussian model could be used as a more conservative description of many of these processes.

ML-PMHT track detection threshold determination for K-distributed clutter

Recentwork developed a novelmethod for determining tracking thresholds for theMaximumLikelihood ProbabilisticMulti- Hypothesis Tracker (ML-PMHT). Under certain “ideal” conditions, probability density functions (PDFs) for the peak points in the ML-PMHT log-likelihood ratio (LLR) due to just clutter measurements could be calculated. Analysis of these clutter-induced peak PDFs allowed for the calculation of tracking thresholds, which previously had to be donewith time-consumingMonte Carlo simulations. However, this work was done for a very specific case: the amplitudes of both target and cluttermeasurements followed Rayleigh distributions. The Rayleigh distribution is a very light-tailed distribution, and it can be overly optimistic in predicting that high-SNR measurements are target-originated. This work examines the case where the clutter amplitudes do not follow a Rayleigh distribution at all, but instead follow a K-distribution, which more accurately describes active acoustic clutter. This will provide a framework for determining accurate tracking thresholds for the ML-PMHT algorithm.

Intelligent active sonar via tuning of transmit waveform and detection threshold

We consider active sonar systems that translate high-level tasks to a set of parameter adaptations and arbitrate among competing demands, thereby incorporating cognitive processing in the system. We propose adopting the goal-driven autonomy (GDA) architecture presented in Klenk et al. [Computational Intelligence, May 2013] to realize intelligent active processing. Using the GDA architecture, the sonar system uses its observations to inform how system parameters are tuned to achieve a set of surveillance goals. In addition, the system is able to reason about its actions, identifying discrepancies between predicted and observed performance and modifying both parameters and goals accordingly. In this work, we focus on a tracking task and consider the transmit waveform and detection threshold as tunable parameters. We describe an active sonar system that tunes these two parameters based on observations of the physical environment and target characteristics, as well as current goals. The intelligent system use...