Keith Kastella

Multitarget tracking using the joint multitarget probability density

This work addresses the problem of tracking multiple moving targets by recursively estimating the joint multitarget probability density (JMPD). Estimation of the JMPD is done in a Bayesian framework and provides a method for tracking multiple targets which allows nonlinear target motion and measurement to state coupling as well as nonGaussian target state densities. The JMPD technique simultaneously estimates both the target states and the number of targets in the surveillance region based on the set of measurements made. We give an implementation of the JMPD method based on particle filtering techniques and provide an adaptive sampling scheme which explicitly models the multitarget nature of the problem. We show that this implementation of the JMPD technique provides a natural way to track a collection of targets, is computationally tractable, and performs well under difficult conditions such as target crossing, convoy movement, and low measurement signal-to-noise ratio (SNR).

Sensor management using an active sensing approach

An approach that is common in the machine learning literature, known as active sensing, is applied to provide a method for managing agile sensors in a dynamic environment. We adopt an active sensing approach to scheduling sensors for multiple target tracking applications that combines particle filtering, predictive density estimation, and relative entropy maximization. Specifically, the goal of the system is to learn the number and states of a group of moving targets occupying a surveillance region. At each time step, the system computes a sensing action to take, based on an entropy measure called the Renyi divergence. After the measurement is made, the system updates its probability density on the number and states of the targets. This procedure repeats at each time where a sensor is available for use. The algorithms developed here extend standard active sensing methodology to dynamically evolving objects and continuous state spaces of high dimension. It is shown using simulated measurements on real recorded target trajectories that this method of sensor management yields more than a ten fold gain in sensor efficiency when compared to periodic scanning.

A Bayesian Approach to Multiple Target Detection and Tracking

This paper considers the problem of simultaneously detecting and tracking multiple targets. The problem can be formulated in a Bayesian framework and solved, in principle, by computation of the joint multitarget probability density (JMPD). In practice, exact computation of the JMPD is impossible, and the predominant challenge is to arrive at a computationally tractable approximation. A particle filtering scheme is developed for this purpose in which each particle is a hypothesis on the number of targets present and the states of those targets. The importance density for the particle filter is designed in such a way that the measurements can guide sampling of both the target number and the target states. Simulation results, with measurements generated from real target trajectories, demonstrate the ability of the proposed procedure to simultaneously detect and track ten targets with a reasonable sample size

Foundations and Applications of Sensor Management

This book covers control theory signal processing and relevant applications in a unified manner. It introduces the area, takes stock of advances, and describes open problems and challenges in order to advance the field. The editors and contributors to this book are pioneers in the area of active sensing and sensor management, and represent the diverse communities that are targeted.

Information-based sensor management for multitarget tracking

We present in this paper an information based method for sensor management that is based on tasking a sensor to make the measurement that maximizes the expected gain in information. The method is applied to the problem of tracking multiple targets. The underlying tracking methodology is a multiple target tracking scheme based on recursive estimation of a Joint Multitarget Probability Density (JMPD), which is implemented using particle filtering methods. This Bayesian method for tracking multiple targets allows nonlinear, non-Gaussian target motion and measurement-to-state coupling. The sensor management scheme is predicated on maximizing the expected Renyi Information Divergence between the current JMPD and the JMPD after a measurement has been made. The Renyi Information Divergence, a generalization of the Kullback-Leibler Distance, provides a way to measure the dissimilarity between two densities. We use the Renyi Information Divergence to evaluate the expected information gain for each of the possible measurement decisions, and select the measurement that maximizes the expected information gain for each sample.

A Comparison of Task Driven and Information Driven Sensor Management for Target Tracking

Several authors have proposed sensor scheduling methods that are driven by information theoretic measures. In the information driven approach, the relative merit of different sensing actions is measured by the corresponding expected gain in information. Information driven approaches stand in stark contrast to task driven methods, i.e., methods that select some physical performance criteria and explicitly manage the sensor based on that criteria. This paper investigates the difference between a particular information driven approach, one that maximizes an alpha-Rényi measure of information gain, and task driven methods with a combination of theory and simulation. First, we give a mathematical relation that shows that when the decision error depends only weakly on the target state a certain type of marginalized information gain is a close approximation to the Bayes risk associated with performing a specific task. Second, we perform an empirical comparison between information driven and task driven approaches that maximize information gain or minimize risk, respectively. In particular, we give a task driven method that uses the sensor in a manner that is expected to maximize the probability the target is correctly located after the next measurement. We find as expected that the task driven method outperforms the information driven method when the performance is measured by risk, i.e., probability of localization error. However, the performance difference between the two methods is very small, suggesting that the information gain is a good surrogate for risk for this application.

Efficient methods of non-myopic sensor management for multitarget tracking

This paper develops two efficient methods of long-term sensor management and investigates the benefit in the setting of multitarget tracking. The underlying tracking methodology is based on recursive estimation of a joint multitarget probability density (JMPD), implemented via particle filtering methods. The myopic sensor management scheme is based on maximizing the expected Renyi divergence between the JMPD and the JMPD after a new measurement is made. Since a full non-myopic solution is computationally intractable when looking more than a small number of time steps ahead, two approximate strategies are investigated. First, we develop an information-directed search which focuses Monte Carlo evaluations on action sequences that are most informative. Second, we give an approximate method of solving Bellmans equation which replaces the value-to-go with an easily computed function that approximates the long term value of the action. The performance of these methods is compared in terms of tracking performance and computational requirements.

Tracking multiple targets using a particle filter representation of the joint multitarget probability density

This paper addresses the problem of tracking multiple moving targets by estimating their joint multitarget probability density (JMPD). The JMPD technique is a Bayesian method for tracking multiple targets that allows nonlinear, non-Gaussian target motions and measurement to state coupling. JMPD simultaneously estimates both the target states and the number of targets. In this paper, we give a new grid-free implementation of JMPD based on particle filtering techniques and explore several particle proposal strategies, resampling techniques, and particle diversification methods. We report the effect of these techniques on tracker performance in terms of tracks lost, mean squared error, and computational burden.

Precision tracking of ground targets

The ability of providing an accurate view of a region of interest is standard among existing tracking systems. Extending this capability to work specifically with ground targets presents several interesting challenges. In addition, the goal of our work is to examine the performance at various times in the future. In order to provide this precise representation of the area, we have employed a multiple hypotheses tracking (MHT) algorithm. In this paper, we describe the ground tracking problem and some of the issues that need to be addressed. Furthermore, we give a brief description of the baseline MHT approach and the enhancements to this approach that are required for tracking ground targets. We conclude the paper with some preliminary results.

Multi-target sensor management using alpha-divergence measures

This paper presents a sensor management scheme based on maximizing the expected Renyi Information Divergence at each sample, applied to the problem of tracking multiple targets. The underlying tracking methodology is a multiple target tracking scheme based on recursive estimation of a Joint Multitarget Probability Density (JMPD), which is implemented using particle filtering methods. This Bayesian method for tracking multiple targets allows nonlinear, non-Gaussian target motion and measurement-to-state coupling. Our implementation of JMPD eliminates the need for a regular grid as required for finite element-based schemes, yielding several computational advantages. The sensor management scheme is predicated on maximizing the expected Renyi Information Divergence between the current JMPD and the JMPD after a measurement has been made. The Renyi Information Divergence, a generalization of the Kullback-Leibler Distance, provides a way to measure the dissimilarity between two densities. We evaluate the expected information gain for each of the possible measurement decisions, and select the measurement that maximizes the expected information gain for each sample.