A Bayesian approach to tracking multiple targets using sensor arrays and particle filters (original) (raw)

Bayesian estimation for target tracking, Part III: Monte Carlo filters

Wiley Interdisciplinary Reviews: Computational Statistics, 2012

This is the third part of a three part article series examining methods for Bayesian estimation and tracking. In the first part we presented the general theory of Bayesian estimation where we showed that Bayesian estimation methods can be divided into two very general classes: a class where the observation-conditioned posterior densities are propagated in time through a predictor/corrector method and a second class where the first two moments are propagated in time, with state and observation moment prediction steps followed by state moment update steps that use the latest observations. In the second part, we make the assumption that all densities are Gaussian and, after applying an affine transformation and approximating all nonlinear functions by interpolating polynomials, we recover the sigma point class of Kalman filters. In this third part, we show that approximating a non-Gaussian density by a set of Monte Carlo samples drawn from an importance density leads to particle filter methods, where the posterior density is propagated in time and moment integrals are approximated by sample moments. These methods include the sequential importance sampling bootstrap, optimal, and auxiliary particle filters and more general Monte Carlo particle filters.

MCMC-based particle filtering for tracking a variable number of interacting targets

Pattern Analysis and Machine …, 2005

We describe a particle filter that effectively deals with interacting targets -targets that are influenced by the proximity and/or behavior of other targets. The particle filter includes a Markov random field (MRF) motion prior that helps maintain the identity of targets throughout an interaction, significantly reducing tracker failures. We show that this MRF prior can be easily implemented by including an additional interaction factor in the importance weights of the particle filter. However, the computational requirements of the resulting multi-target filter render it unusable for large numbers of targets. Consequently, we replace the traditional importance sampling step in the particle filter with a novel Markov chain Monte Carlo (MCMC) sampling step to obtain a more efficient MCMC-based multi-target filter.

Particle Markov chain Monte Carlo for Bayesian multi-target tracking

2011

Abstract We propose a new multi-target tracking (MTT) algorithm capable of tracking an unknown number of targets that move close and/or cross each other in a dense environment. The optimal Bayes MTT problem is formulated in the Random Finite Set framework and Particle Markov Chain Monte Carlo (PMCMC) is applied to compute the multi-target posterior distribution.

On MCMC-Based particle methods for Bayesian filtering: Application to multitarget tracking

2009 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2009

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. In this context, one of the most successful and popular approximation techniques is Sequential Monte Carlo (SMC) methods, also known as particle filters. Nevertheless, these methods tend to be inefficient when applied to high dimensional problems. In this paper, we present an overview of Markov chain Monte Carlo (MCMC) methods for sequential simulation from posterior distributions, which represent efficient alternatives to SMC methods. Then, we describe an implementation of this MCMC-Based particle algorithm to perform the sequential inference for multitarget tracking. Numerical simulations illustrate the ability of this algorithm to detect and track multiple targets in a highly cluttered environment.

Multi-target tracking in clutter with sequential Monte Carlo methods

IET Radar, Sonar & Navigation, 2010

For multi-target tracking (MTT) in the presence of clutters, both issues of state estimation and data association are crucial. This study tackles them jointly by Sequential Monte Carlo methods, a.k.a. particle filters. A number of novel particle algorithms are devised. The first one, which we term Monte-Carlo data association (MCDA), is a direct extension of the classical sequential importance resampling (SIR) algorithm. The second one is called maximum predictive particle filter (MPPF), in which the measurement combination with the maximum predictive likelihood is used to update the estimate of the multi-target's posterior. The third, called proportionally weighting particle filter (PWPF), weights all feasible measurement combinations according to their predictive likelihoods, and uses them proportionally in the importance sampling framework. We demonstrate the efficiency and superiority of our methods over conventional approaches through simulations. This paper tackles data association jointly with state estimation via Sequential Monte Carlo (SMC) methods, a.k.a. particle filters (PF) [9-11]. Such particle methods

Monte Carlo Methods for sensor management in target tracking

Surveillance for multi-target detection, identification and tracking is one of the natural problem domains in which particle filtering approaches have been gainfully applied. Sequential importance sampling is used to generate and update estimates of the joint multi-target probability density for the number of targets, their dynamical model, and their state vector. In many cases there are a large number of degrees of freedom in sensor deployment, e.g., choice of waveform or modality. This gives rise to a resource allocation problem that can be formulated as determining an optimal policy for a partially observable Markov decision process (POMDP). In this paper we summarize approaches to solving this problem which involve using particle filtering to estimate both posterior state probabilities and the expected reward for both myopic and multistage policies.

Joint particle filtering of multiple maneuvering targets from unassociated measurements

Journal of Advances in Information Fusion, 2006

The problem of maintaining tracks of multiple maneuvering targets from unassociated measurements is formulated as a problem of estimating the hybrid state of a Markov jump linear system from measurements made by a descriptor system with independent, identically distributed (i.i.d.) stochastic coefficients. This characterization is exploited to derive the exact equation for the Bayesian recursive filter, to develop two novel Sampling Importance Resampling (SIR) type particle filters, and to derive approximate Bayesian filters which use for each target one Gaussian per maneuver mode. The two approximate Bayesian filters are a compact and a trackcoalescence avoiding version of Interacting Multiple Model Joint Probabilistic Data Association (IMMJPDA). The relation of each of the four novel filter algorithms to the literature is well explained. Through Monte Carlo simulations for a two target example, these four filters are compared to each other and to the approach of using one IMMPDA filter per target track. The Monte Carlo simulation results show that each of the four novel filters clearly outperforms the IMMPDA approach. The results also show under which conditions the IMMJPDA type filters perform close to exact Bayesian filtering, and under which conditions not.

A Particle Marginal Metropolis-Hastings Multi-target Tracker

—We propose a Bayesian multi-target batch processing algorithm capable of tracking an unknown number of targets that move close and/or cross each other in a dense clutter environment. The optimal Bayes multi-target tracking problem is formulated in the random finite set framework and a Particle Marginal Metropolis-Hastings (PMMH) technique which is a combination of Metropolis-Hastings (MH) algorithm and sequential Monte Carlo methods is applied to compute the multi-target posterior distribution. The PMMH technique is used to design a high dimensional proposal distributions for the MH algorithm and allows the proposed batch process multi-target tracker to handle a large number of tracks in a computationally feasible manner. Our simulations show that the proposed tracker reliably estimates the number of tracks and their trajectories in scenarios with a large number of closely spaced tracks in a dense clutter environment albeit, more expensive than on-line methods.

Particle Filters for Multiple Target Tracking

Procedia Technology, 2016

Multiple target tracking has immense application in areas such as surveillance, air traffic control, defense and computer vision. The aim of a target tracking algorithm is to estimate the target position precisely from the partial noisy observations available. The real challenges of multiple target tracking are to accomplish the same in the presence of measurement origin uncertainty and clutter. Optimal solutions are available by way of Kalman filters for the special case of linear dynamical systems with Gaussian noise. For a more general scenario, we resort to the suboptimal solutions like Particle filters which implement stochastic filtering through a sequential Monte Carlo approach. Measurement origin uncertainty is resolved by using a suitable data association technique prior to the filtering. This paper explores the possibilities of applying a variant of Ensemble Square Root Filters (EnSRF) in a multiple target tracking scenario and its tracking performance is compared with those of conventional Bootstrap and Auxiliary Bootstrap particle filters. The filtering scheme proposed here incorporates Sample based Joint Probabilistic Data Association (SJPDA) in the EnSRF framework for dealing with measurement origin uncertainty.