RES E AR C H Open Access
Sequential measurement-driven
multi-target Bayesian filter
Zong-xiang Liu
*
, Li-juan Li, Wei-xin Xie and Liang-qun Li
Abstract
Bayesian filter is an efficient approach for multi-target tracking in the presence of clutter. Recently, considerable
attention has been focused on probabili ty hyp othesis density (PHD) filter, which is an intensity approximation of
the multi-target Bayesian filter. However, PHD filter is inapplicable to cases in which target detection probability
is low. The use of this filter may result in a delay in data processing be caus e it h and les rece ived measurements
periodically, once every sampling period. To track multiple targets in the case of low detection probability and to
handle received measurements in real time, we propose a sequential measurement-driven Bayesian filter. The
proposed filter jointly propagates the marginal distributions and existence probabilities of each target in the filter
recursion. We also present an impleme ntation of the proposed filter for l inear Gaussian models. Simulation results
demonstrate that the proposed filter can more accurately track multiple targets than the Gaussian mixtur e PHD
filter or cardi nalized PHD filter.
Keywords: Multi-target tracking; Bayesian filter; Probability hypothesis density filter; Marginal distribution;
Existence probability
1 Introduction
Multi-target tracking aims to detect individual targets in
the surveillance region of interest and estimate their
states according to a sequence of noisy and cluttered
measurements collected by sensors. The most efficient
technique for multi-target tracking is the multi-target
Bayesian filter, which propagates joint posterior distribu-
tion of the multi-target state [1, 2]. However, such
propagation is computationally intensive because of the
high dimensionality of the multi-target state space [2, 3].
With the use of the Bayesian framework to propa gate
the posterior intensity of multiple targets recursively, the
probability hypothesis density (PHD) filter provides a
numerically tractable solution to this problem [2, 3].
Two numerical solutions, namely sequential Monte
Carlo (SMC) [4–9] and Gaussian mixtures (GM) [10–17],
have been developed for the PHD filter. Extensions of
the PHD filter have also been proposed to improve its
performance. PHD filters with observation-driven birth
intensity were independently proposed in [16, 18, 19] to
eliminate the need for exact knowledge of birth
intensity. Methods for maintaining track continuity were
proposed in [4, 20] for the SMC-PHD filter and in [21]
for the GM-PHD filter. To improve the accuracy and
stability of the target number estimate, the cardinalized
PHD (CPHD) filter, which jointly propagates moment
and cardinality, was proposed in [22]. Methods for esti-
mating an unknown clutter rate, which is an important
parameter of the PHD and CPHD filters , were proposed
in [23] and [24]. In [12], the GM-PHD filter was ex-
tended to linear jump Markov multi-target models for
use in tracking maneuvering targets.
Although the PHD filter has several advantages, it be-
comes inefficient in cases with low target detection
probability. This inefficiency occurs because the PHD
filter has a weak memory and is easily influenced by new
incoming measureme nts [ 2, 17, 22]. Owing to its weak
memory, the PHD filter fails to provide state estimates
of existing targets if these targets are missing from new
incoming measurements [2]. Moreover, the PHD filter
may result in data processing delay. This delay occurs
because the PHD filter handles new incoming measure-
ments periodically, once every sampling period. In this
manner, new measurements have to be gathered for a
sampling period before being processed. Therefore, a
* Correspondence: liuzx@szu.edu.cn
ATR Key Laboratory, College of Information and Engineering, Shenzhen
University, P.O. Box 2–603, 518060 Shenzhen, China
© 2015 Liu et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium,
provided the original work is properly credited.
Liu et al. EURASIP Journal on Advances in Signal Processing (2015) 2015:43
DOI 10.1186/s13634-015-0228-8