Maximum Likelihood Probabilistic Data Association Research Articles

Multipath Data Fusion With Recursive ML-PDA and Generative ML-PMHT for VLO Targets in Underwater Environment

We discuss and extend two approaches to target detection and motion parameter estimation in a very low observable (VLO) underwater multipath environment. The maximum likelihood probabilistic data association (ML-PDA) algorithm considers all possible path–measurement hypotheses, whereas the maximum likelihood probabilistic multiple hypothesis tracker (ML-PMHT) assumes independence among the returns’ origins leading to a simpler likelihood formulation. In particular, we present a recursive form of the multipath ML-PDA algorithm for improved computational efficiency and a generative multipath ML-PMHT algorithm that accounts for the prior probability distribution of the number of received measurements. By simulation of an active sonar tracking scenario, we show that while the two algorithms perform similarly for few returns, the added fidelity of the ML-PDA outperforms the ML-PMHT in parameter estimation as returns accumulate over multiple scans and dimensions. However, the computational cost of the ML-PDA discourages its use beyond simple scenarios. This cost, coupled with the comparable detection performance of the two algorithms, suggests that the simpler ML-PMHT is the better choice for practical use. We also show how both the ML-PDA and ML-PMHT can be applied to realistic ocean environments using ocean acoustic modeling software. This article is an extension of previous work on comparing the standard versions of the ML-PDA and ML-PMHT algorithms.

Underwater Target Tracking in Uncertain Multipath Ocean Environments

In order to address the problem of 3-D localization of an underwater target using a 2-D active sonar with unknown oceanographic factors in a multipath environment with heavy clutter, a novel iterative framework based on Maximum Likelihood Probabilistic Data Association (ML-PDA), which considers ocean sound speed profile (SSP) uncertainty and utilizes multiple detections to realize 3-D position estimation with only bearing and time of flight (ToF) measurements, is proposed. ML-PDA is highly effective in low SNR target detection. However, it is limited by its assumption of at most one target-originated detection within a scan. To estimate the 3-D target state with multipath detections under weak observability conditions, we first extend the ML-PDA into a multipath ML-PDA by enumerating the combined association events formed from multiple detection patterns. In contrast to the situation in air target tracking, the water column is nonhomogeneous and the underwater sound speed profile varies, influenced by uncertain ocean factors, e.g., temperature, salinity, and pressure. The resultant acoustic signal travels in a curvilinear path instead of a straight line. In this article, an SSP-dependent ToF measurement model is derived for both the direct path and the surface-reflected path between two remote nodes, so that the SSP uncertainty can be addressed systematically. By adopting an iterative prediction-update methodology, we first propagate the SSP uncertainty into the modified measurement covariance with the help of the unscented sampling technique. Then, we formulate a new joint likelihood ratio (JLLR) function based on the modified measurement covariance within the multidetection ML-PDA framework. A hybrid optimization method with grid search and particle swarm optimization is applied to solve the complex JLLR objective function and to find the optimal target state estimate from a large surveillance region. Finally, a sequential update technique is used to update the SSP state with the estimated target state and sensor measurements. In subsequent iterations, a more accurate JLLR can be rebuilt based on the updated SSP state, which can help find a better parameter estimate eventually. In addition, the Cramér-Rao lower bound, which quantifies the best possible accuracy in the presence of SSP uncertainties, is derived and analyzed. Numerical simulations confirm the underwater target localization performance of the proposed method in the presence of heavy clutter in an unknown ocean environment with a realistic sound propagation model.

Multiple Detection-Aided Low-Observable Track Initialization Using ML-PDA

In low signal-to-noise ratio or heavy clutter environments, target track initialization is a challenging task. The maximum likelihood probabilistic data association (ML-PDA) algorithm has been demonstrated to be effective in dealing with this issue. In practical scenarios, multiple signals from one target via different propagation paths can be detected in a scan. Signals from different propagation paths convey useful information and can improve track initialization performance. However, the conventional ML-PDA algorithm assumes that a target can generate at most one detection per scan. That is, it cannot handle multiple target-originated measurements per scan correctly, nor take full advantage of the additional information contained in those seemingly extraneous returns. In this paper, a multiple-detection ML-PDA (MD-ML-PDA) estimator is proposed to rectify this shortcoming. The proposed estimator exploits the additional information available in all measurements by considering the combinatorial events of association that are formed from MD patterns. It is capable of handling the possibility of multiple target-originated measurements per scan with less-than-unity detection probability for various paths in the presence of clutter. The proposed MD-ML-PDA estimator is applied to a simulated sonar target tracking scenario. The same algorithm can be used on other angle-only tracking problems as well. Results show that MD-ML-PDA can effectively handle multiple target-originated measurements and yield improved track initialization performance over the traditional single detection ML-PDA. The Cramer–Rao lower bound for MD track initialization is also derived.

Passive tracking in heavy clutter with sensor location uncertainty

In order to address the problem of passive tracking from multiple asynchronous angle-only sensors with location uncertainty in heavy clutter, a new iterative maximum-likelihood probabilistic data-association algorithm is proposed in this paper. An iterative prediction–update framework is adopted in the algorithm to simultaneously estimate the target state as well as the sensor state. At the prediction stage, a deterministic sampling approach is used to adjust the measurement covariance with sensor location uncertainty. Then a two-step grid-search technique is proposed to optimize the log-likelihood ratio, combined with a gradient-based search method. At the update stage, the operational sensor states are updated with target state estimates and measurements in corresponding validation gates. The updated sensor states are used to establish a more accurate log-likelihood ratio in the next iteration, which leads to better parameter estimation. In addition, the effects of the sensor location uncertainty on the track acceptance test and the posterior Cram´er–Rao lower bound are also analyzed. Simulation results show that the proposed method provides a computationally efficient way to improve track initialization performance in heavy clutter with sensor location uncertainty. The proposed work has applications in sonar tracking, geolocation, electronic support measures, and infrared search and tracking systems.

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.

Tracking the Tracker from its Passive Sonar ML-PDA Estimates

Target motion analysis (TMA) with wideband passive sonar has received much attention. Maximum likelihood probabilistic data association (ML-PDA) represents an asymptotically efficient estimator for deterministic target motion, and is especially well suited for low-observable targets; the results presented here apply to situations with higher signal-to-noise ratio as well, including of course the situation of a deterministic target observed via “clean” measurements without false alarms or missed detections. Here we study the inverse problem, namely, how to identify the observing platform (following a “two-leg” motion model) from the results of the target estimation process, i.e., the estimated target state and the Fisher information matrix (FIM), quantities we assume an eavesdropper might intercept. We tackle the problem and we present observability properties, with supporting simulation results.

Integrated track initialization and maintenance in heavy clutter using probabilistic data association

Target tracking in high clutter or low signal-to-noise ratio (SNR) environments is an important topic and still a challenging task. Joint Maximum Likelihood Probabilistic Data Association (JML-PDA) is a well-known batch method for initializing the tracks of very low observable (VLO) targets in heavy clutter environments. On the other hand, the Joint Probabilistic Data Association (JPDA) algorithm, which is commonly used for recursive track maintenance, lacks track initialization capability. In this paper, we propose a Combined JML-PDA and JPDA (CJML-PDA) algorithm to automatically initialize and maintain the tracks. This combined approach seamlessly shares information between the initialization and maintenance stages of the tracker. In contrast, in other batch-recursive approaches the initialization and maintenance algorithms operate rather independent of each other. The effectiveness of the proposed algorithm is demonstrated on a heavy clutter scenario and its performance is tested on closely-spaced (but resolved) targets with association ambiguity using angle-only measurements.

Track-Before-Detect Algorithms for Targets with Kinematic Constraints

We propose and assess new algorithms for adaptive detection and tracking based on space-time data. At design stage we take into account possible spillover of target energy to adjacent range cells and assume a target kinematic model. Then, resorting to the generalized likelihood ratio test (GLRT) we derive track-before-detect (TBD) algorithms that can operate in scan-to-scan varying scenarios and, more important, that ensure the constant false track acceptance rate (CFTAR) property with respect to the covariance matrix of the disturbance. Moreover, we also propose CFTAR versions of the maximum likelihood-probabilistic data association (ML-PDA) algorithm capable of working with data from an array of sensors. The preliminary performance assessment, conducted resorting to Monte Carlo simulation, shows that the proposed TBD structures outperform the ML-PDA implementations especially in terms of probability of track detection (and for low signal-to-noise ratio (SNR) values).

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.

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

Bearings-only tracking of maneuvering targets using a batch-recursive estimator

We present a new batch-recursive estimator for tracking maneuvering targets from bearings-only measurements in clutter (i.e., for low signal-to-noise ratio (SNR) targets), Standard recursive estimators like the extended Kalman Iter (EKF) suffer from poor convergence and erratic behavior due to the lack of initial target range information, On the other hand, batch estimators cannot handle target maneuvers. In order to rectify these shortcomings, we combine the batch maximum likelihood-probabilistic data association (ML-PDA) estimator with the recursive interacting multiple model (IMM) estimator with probabilistic data association (PDA) to result in better track initialization as well as track maintenance results in the presence of clutter. It is also demonstrated how the batch-recursive estimator can be used for adaptive decisions for ownship maneuvers based on the target state estimation to enhance the target observability. The tracking algorithm is shown to be effective for targets with 8 dB SNR.