Adaptive probability hypothesis density filter for multi-target tracking with unknown measurement noise statistics

Weijun Xu

doi:10.1177/0020294021992800

Abstract

Under the Gaussian noise assumption, the probability hypothesis density (PHD) filter represents a promising tool for tracking a group of moving targets with a time-varying number. However, inaccurate prior statistics of the random noise will degrade the performance of the PHD filter in many practical applications. This paper presents an adaptive Gaussian mixture PHD (AGM-PHD) filter for the multi-target tracking (MTT) problem in the scenario where both the mean and covariance of measurement noise sequences are unknown. The conventional PHD filters are extended to jointly estimate both the multi-target state and the aforementioned measurement noise statistics. In particular, the Normal-inverse-Wishart and Gaussian distributions are first integrated to represent the joint posterior intensity by transforming the measurement model into a new formulation. Then, the updating rule for the hyperparameters of the model is derived in closed form based on variational Bayesian (VB) approximation and Bayesian conjugate prior heuristics. Finally, the dynamic system state and the noise statistics are updated sequentially in an iterative manner. Simulations results with both constant velocity and constant turn model demonstrate that the AGM-PHD filter achieves comparable performance as the ideal PHD filter with true measurement noise statistics.

Highlights

Benefit from the increasing advances in sensing techniques and computer science, multi-target tracking has found its potential applications in various disciplines, such as autonomous robotics, intelligence surveillance, remote sensing and even biomedical research.[1,2,3] The goal of MTT is to estimate the number of targets together with their individual states from a given sequence of measurements, which is contaminated by a number of uncertain sources
To demonstrate the performance of the AGM-probability hypothesis density (PHD) filter for tracking targets with variable parameters of motion model, the targets are assumed to move within the same surveillance region following a nearly constant turn (CT) model[34] with known but varying turn rate
Same as in the first simulation, 200 independent Monte Carlo trials are conducted for all four PHD filters

Summary

Introduction

Benefit from the increasing advances in sensing techniques and computer science, multi-target tracking has found its potential applications in various disciplines, such as autonomous robotics, intelligence surveillance, remote sensing and even biomedical research.[1,2,3] The goal of MTT is to estimate the number of targets together with their individual states from a given sequence of measurements, which is contaminated by a number of uncertain sources. The multi-target state is represented by a Gaussian distribution, while the statistics of the measurement noise is modeled with a Normal-inverse-Wishart distribution. The updated mean and covariance of the target state are estimated by standard update equations of Gaussian filters with the known measurement noise statistics. Time Prediction: Assume that the joint prior intensity of the multi-target state and measurement noise statistics at the time k À 1 is represented by a product of Normal-inverse-Wishart and Gaussian mixtures:. To ensure that the adaptive filter have closed-form solutions, the spontaneous birth are characterized by the intensities comprised of a product of Normal-inverse-Wishart and Gaussian distribution mixtures: And the predicted hyperparameters of the Normalinverse-Wishart distribution are computed in accordance with the equation (21), that is, mjkjkÀ1 = mjkÀ1. Measurement update: Given that the joint predicted intensity at time k is represented by a product of Normal-inverse-Wishart and Gaussian mixtures ykjkÀ1(xk, uk)

JkjkÀ1

D2 0 0

Evaluation with a constant turn model

Conclusion