Probabilistic Multi-Hypothesis Tracker Research Articles

SA-HPMHT for Maritime Dim Targets Tracking With Sensor Location Uncertainty

To address the problem of tracking low signal-to-clutter ratio (SCR) maritime targets with sensor location uncertainty, an effective track-before-detect (TBD) method, called the state augmentation histogram probabilistic multihypothesis tracking (SA-HPMHT) algorithm, is proposed in this article. In this algorithm, the initialization of new tracks is realized based on the constant false alarm rate (CFAR) detector with a low threshold and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> -means clustering algorithm. The target and sensor states are then simultaneously estimated in an iterative manner via a synthetic histogram and state augmentation (SA) method. In each iteration, we update the estimated sensor state and yield more accurate measured images, allowing for improved performance of detection and tracking targets. Finally, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}/{N}$ </tex-math></inline-formula> logic technology is invoked to confirm or terminate the tracks. The results of simulation and real dataset verification show that the SA-HPMHT algorithm has a better performance compared with the histogram probabilistic multihypothesis tracking (H-PMHT) algorithm and the sequential Monte Carlo probability hypothesis density (SMC-PHD) algorithm.

Seamless Tracking of Apparent Point and Extended Targets Using Gaussian Process PMHT

In practical target tracking scenarios, targets of different sizes (or extents) may be near or far away from the sensor, which may result in targets appearing as point sources or as extended targets spanning one or more resolution cells, respectively, depending on distance and sensor resolution. In this paper, a new Gaussian Process (GP) measurement model is proposed to explicitly describe the observation about each basis point of GP by an individual dynamic Poisson measurement rate. By employing this model, a novel algorithm to track multiple point targets and extended targets, simultaneously and seamlessly, in the presence of clutter and missed detections is proposed within the Probabilistic Multi-Hypothesis Tracker (PMHT) framework. The proposed algorithm can adapt to spatio-temporally varying target sizes or extents of extended targets and temporally varying target cardinality. In addition, the posterior Cramer-Rao lower bound (PCRLB) for extended targets, which quantifies the accuracies of estimates of multiple extended target states in scenarios with clutter, is derived. Simulations with a scenario consisting of multiple extended targets and point targets are used to verify the effectiveness of the proposed algorithm and to compare its performance with the extended target PCRLB and with those of existing extended target tracking algorithms.

Bayesian approach to multiple extended targets tracking with random hypersurface models

A Bayesian approach to multiple moving extended targets tracking is proposed for estimating the shape approximation of the extended targets in addition to their kinematics. Within this approach, the extended target extensions are modelled with random hypersurface models, and a new variant of probabilistic multi-hypothesis tracking is used for modelling assignments of measurements to extended targets. Moreover, an approximate measurement update that arises directly from the analytical techniques of the variational Bayesian framework is derived to simultaneously estimate the posterior states iteratively including the shape and kinematics of each extended target. The performance of the proposed algorithm is demonstrated with simulated data.

DA-PMHT for Multistatic Passive Radar Multitarget Tracking in Dense Clutter Environment

Multistatic passive radar exploits illuminators of opportunity such as radio or television stations for tracking airborne targets. This paper focuses on broadcast signals in a single frequency network modulated according to the digital audio/video broadcasting (DAB/DVB) standards. The main challenge is that one has to solve the measurement-to-illuminator association ambiguity in addition to the conventional measurement-to-target association ambiguity, which increases data association complexity greatly. In this paper, to solve the additional measurement-to-illuminator data association ambiguity, a novel deterministic annealing probabilistic multi-hypothesis tracker based on the extended Kalman filter is proposed. The proposed algorithm works directly in the original three-dimensional Cartesian space, and can efficiently handle a large number of association hypotheses among the targets, measurements, and illuminators in a natural way, also it is computationally attractive. As the angular measurement is not available or often of extremely poor quality, this paper assumes measurements of bistatic range and range rate and does not process bearing information. The simulation results show that the proposed algorithm works reasonably well in dense clutter environment for multistatic passive radar system.

Reducing Processing Time for Histogram PMHT Algorithm in Video Object Tracking

DOI: 10.26650/electrica.2018.36247 This paper describes a novel approach for reducing the processing time of the histogram probabilistic multi-hypothesis tracker (H-PMHT) algorithm in video applications. Video data of flying vehicles is taken from surface to air, and a temporal difference-based technique is applied to video frames for meeting the intensity demands of H-PMHT algorithm. This technique also enables discrimination between objects and eliminates clutter. Variations between the structures of the standard and the improved version of H-PMHT algorithms are described. In addition, the improved H-PMPT is compared with the standard H-PMHT and another approved tracking algorithm to evaluate the performance and processing time reduction ratings.

Multipath Maximum Likelihood Probabilistic Multihypothesis Tracker for Low Observable Targets

In many practical scenarios with multipath propagation, one target may generate multiple detections in one scan. Proper use of multipath-induced measurements can improve the detection of very low observable (VLO) targets. In this paper, a true multitarget tracker, the joint multipath maximum likelihood probabilistic multihypothesis tracker (JMP-ML-PMHT) is proposed to address this problem. The standard ML-PMHT is extended to incorporate multipath detections and jointly track multiple VLO targets. The Cramer–Rao lower bound with multipath detections is derived. Simulation results with an over-the-horizon-radar scenario show that the JMP-ML-PMHT can detect and track multiple VLO targets by effectively utilizing the information in multipath measurements.

Detecting Low SNR Tracks With OTHR Using a Refraction Model

Over-the-horizon radar is used to detect targets at very long ranges by reflecting of/refracting signals within the ionosphere. Multiple propagation paths exist between the radar and the target, which can result in multiple target-originated measurements in each scan. It is uncertain which path corresponds with each measurement. Due to the necessary low detection threshold for very low signal-to-noise ratio targets, there are also many false alarms. The maximum-likelihood probabilistic multihypothesis tracker, which is a deep track extractor, is generalized to allow multiple propagation paths. A ray-tracing algorithm is used to model the refraction in the ionosphere. Monte Carlo simulation results are presented for three types of targets: a surface target, a constant altitude target, and a constant vertical acceleration target. We also calculate the Cramer–Rao lower bound for these scenarios, and an analysis is done to determine the probability of track detection, $P_{\text{DT}}$ , for specified probabilities of false track $P_{\text{FT}}$ .

A Bootstrapped PMHT with Feature Measurements

The probabilistic multi-hypothesis tracker (PMHT), a tracking algorithm of considerable theoretical elegance based on the expectation-maximization algorithm, will be considered for the problem of multiple target tracking with multiple sensors in clutter. In addition to position observations, continuous measurements associated with the unique, constant—and statistically unknown —feature of each target are incorporated to jointly estimate the states and features of the targets for the sake of tracking and classification, leading to a bootstrapped implementation of the PMHT. In addition, the information matrix for the stacked vector of states for all the targets at all the time steps during the observation time is derived.

H‐PMHT track‐before‐detect processing with DP‐based track initiation and termination

Histogram probabilistic multi-hypothesis tracker (H-PMHT), based on probabilistic multi-hypothesis tracker, is a track-before-detect processing approach to detect dim targets. For the problem that H-PMHT cannot initiate new tracks and terminate tracks of disappeared targets, the authors propose a new dynamic programming (DP)-based H-PMHT algorithm, which can locate new targets by dealing with a few frames of sensor images and confirm disappeared targets according to their energy accumulation values along the existing tracks. With this sort of track initiation and termination mechanism, H-PMHT can be directly applied to realistic environments. Simulation results show that the DP-based H-PMHT algorithm can rapidly locate new targets and initiate tracks with a low false alarm rate, and quickly terminate tracks of disappeared targets with a low false termination probability.

Two Algorithms for Modeling and Tracking of Dynamic Time-Frequency Spectra

This paper considers track-before-detect algorithms that can be applied to modeling and tracking of dynamic time-frequency spectra where the number of spectral components is allowed to vary in time. The algorithms are the adaptive Dirichlet process mixture model-based Rao-Blackwellised particle filter (ADPM-RBPF) and the histogram probabilistic multihypothesis tracker with random matrices (H-PMHT-RM). The ADPM-RBPF uses a time-varying nonparametric Bayesian method based on the Dirichlet process prior to model spectral densities as mixtures of normal distributions with an unknown number of components. This approach estimates the time-varying mean and variance of each spectral mixture component and allows for the inclusion of outliers or clutter measurements. The H-PMHT-RM models each spectrum as a histogram observation of a mixture process. It uses a randomly evolving matrix to estimate the spread of each spectral component and a track management model that enables automated track initiation and termination. The algorithms are compared using simulated and experimental data.

PMHT Approach for Underwater Bearing-Only Multisensor–Multitarget Tracking in Clutter

In this work, we apply the probabilistic multihypothesis tracker (PMHT) for the problem of underwater bearing-only multisensor–multitarget tracking in clutter. The PMHT is a batch tracking algorithm that can efficiently process a large number of measurements from multiple sensors. We investigate both the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) for dealing with the high degree of nonlinearity in the measurement model. Due to multiple sensors, the unobservability of single sensor bearing-only target tracking is avoided. Simulation results show that the PMHT works very well in a highly cluttered environment and its computational load is low.

A Batch Algorithm for Estimating Trajectories of Point Targets Using Expectation Maximization

In this paper, we propose a strategy that is based on expectation maximization for tracking multiple point targets. The algorithm is similar to probabilistic multi-hypothesis tracking (PMHT) but does not relax the point target model assumptions. According to the point target models, a target can generate at most one measurement, and a measurement is generated by at most one target. With this model assumption, we show that the proposed algorithm can be implemented as iterations of Rauch-Tung-Striebel (RTS) smoothing for state estimation, and the loopy belief propagation method for marginal data association probabilities calculation. Using example illustrations with tracks, we compare the proposed algorithm with PMHT and joint probabilistic data association (JPDA) and show that PMHT and JPDA exhibit coalescence when there are closely moving targets whereas the proposed algorithm does not. Furthermore, extensive simulations c comparing the mean optimal subpattern assignment (MOSPA) performance of the algorithm for different scenarios averaged over several Monte Carlo iterations show that the proposed algorithm performs better than JPDA and PMHT. We also compare it to benchmarking algorithm: $N$ -scan pruning based track-oriented multiple hypothesis tracking (TOMHT). The proposed algorithm shows a good tradeoff between computational complexity and the MOSPA performance.

PMHT Approach for Multi-Target Multi-Sensor Sonar Tracking in Clutter.

Multi-sensor sonar tracking has many advantages, such as the potential to reduce the overall measurement uncertainty and the possibility to hide the receiver. However, the use of multi-target multi-sensor sonar tracking is challenging because of the complexity of the underwater environment, especially the low target detection probability and extremely large number of false alarms caused by reverberation. In this work, to solve the problem of multi-target multi-sensor sonar tracking in the presence of clutter, a novel probabilistic multi-hypothesis tracker (PMHT) approach based on the extended Kalman filter (EKF) and unscented Kalman filter (UKF) is proposed. The PMHT can efficiently handle the unknown measurements-to-targets and measurements-to-transmitters data association ambiguity. The EKF and UKF are used to deal with the high degree of nonlinearity in the measurement model. The simulation results show that the proposed algorithm can improve the target tracking performance in a cluttered environment greatly, and its computational load is low.

Histogram probabilistic multi‐hypothesis tracker with colour attributes

The histogram probabilistic multi-hypothesis tracking (H-PMHT) algorithm is a multi-target track-before-detect method that has been demonstrated to be scalable and efficient and shows good performance on video imagery. However, its application has been limited to intensity-only imagery. In practice, colour and information, such as texture, are often available and can be very helpful when targets are close together. This study compares two alternative methods that incorporate colour information in the H-PMHT: an existing method referred to as spectral H-PMHT and a new approach that treats the colour information as attribute data. The methods are compared with intensity-only H-PMHT on simulations and benchmark data from the VS-PETS03 archive.

Efficient Histogram PMHT Via Single Target Chip Processing

The Histogram Probabilistic Multi-Hypothesis Tracker is a multi-target track before detect method with low computational complexity. However, for high resolution sensors with millions of pixels, a naive implementation can be too slow. Single target chip processing is proposed as an approximate implementation scheme that dramatically reduces computation cost without significant performance degradation. Simulated examples are used to quantify the improvements achieved.

Probabilistic multi‐hypothesis tracker for multiple platform path planning

This study considers the problem of automatically coordinating multiple platforms to explore an unknown environment. The goal is a planning algorithm that provides a path for each platform in such a way that the collection of platforms cooperatively sense the environment in a globally efficient manner. The environment is described by a spatially non-homogeneous priority function. The method samples this function to produce a discrete collection of locales that the platforms use as waypoints. The key feature of the method is to treat the assignment of locales to platforms as a target tracking problem and to use the probabilistic multi-hypothesis tracker (PMHT) as a method of performing multi-platform batch data association. This paper introduces the PMHT path planner (PMHT-pp) and compares this algorithm as a method of performing multiple platform batch data association with the Genetic Algorithm to solve the modified multi-travelling salesman problem.

Probabilistic multihypothesis trackerwith an evolving poisson prior

The probabilistic multihypothesis tracker (PMHT) is an efficient multitarget tracking algorithm that performs data association under a conditional independence assumption. A key part of the measurement model is the data-association prior, which can be used as a track quality measure for track management decisions. The original PMHT makes this prior an unknown fixed parameter. The PMHT with hysteresis extended the measurement model by adding a Markov chain hyperparameter to the prior, but this came at the cost of exponential complexity in the number of targets. This complexity comes as a consequence of the normalization of the prior. This article shows that the PMHT data-association model is equivalent to assuming that targets create a Poisson-distributed number of measurements; an alternative PMHT is derived that deals directly with the Poisson model parameters and retains linear complexity in the number of targets.

PMHT with timing uncertainty

This paper considers the problem of tracking a target using measurements where the temporal information is noisy or unreliable. The measurements are modelled as being received with a known stochastic time delay and also with time error parameters that are to be estimated. By treating the true measurement time as missing data and using expectation maximisation, a modified version of the probabilistic multihypothesis tracker (PMHT) is derived for the uncertain-timing problem. This modified PMHT thus associates each measurement to the targets and to time instants. The method is validated using simulations, and the improvement over the standard PMHT is quantified. Further simulations compare the algorithm with existing alternatives dealing with timing uncertainty.

Extreme-value analysis for mlML-PMHT, Part 2: target trackability

The Maximum Likelihood Probabilistic Multi-Hypothesis Tracker (ML-PMHT) can be used as a powerful multisensor, low-observable, multitarget active tracker. It is a non-Bayesian algorithm that uses a generalized likelihood ratio test (GLRT) to differentiate between clutter and targets. We use a new method, initially developed to obtain the probability density function (pdf) of the maximum point in the ML-PMHT log-likelihood ratio (LLR) due to clutter, to now develop a pdf for the maximum value of the ML-PMHT LLR caused by a target. With expressions for the pdfs of the maximum points caused by both clutter (developed in a companion article) and a target, we can, for a given set of tracking parameters (signal-to-noise ratio, search volume, target measurement probability of detection, etc.), develop ML-PMHT tracker operating curves, similar to receiver operating characteristic curves for a detector. Since ML-PMHT can be thought of as an optimal algorithm in the sense that, as long as the target and the environment match the algorithm's assumptions, all the information from all the available measurements can be used, and no approximations are necessary to get the algorithm to function, the analysis presented in this paper offers for the first time part of the answer to the fundamental question: Can a particular target be tracked?

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.