Research Of Marginal Distribution Bayesian Filter In Multi-target Tracking

The Bayes filter based on Finite Sets Statistics(FISST) is an efficient approach for tracking multi-targets. Probability hypothesis density(PHD) filter is an approximation implementation of it. Differing from traditional tracking methods, they represents multi-target state and measurement as two random finite sets, therefore avoids the data association which is necessary in traditional tracking methods to assign the measurements to individual targets. For which, they can track unknown and time-varying number of targets. However, the two methods cannot distinguish multiple distinct targets when they are closely spaced. The main purpose of this paper is to solve this problem.Firstly, the multi-target Bayes filter and the PHD filter are introduced. The theoretically optimal approach to multisensor-multitarget detection, tracking, and identification is multi-target Bayesian filter, which propagates joint posterior distribution. However, it is so computationally challenging due to the integrals of high dimensions. The PHD filter propagates the first-order moment of multi-target posterior density and avoids the combinatorial problem that arises from data association. However, they cannot distinguish multiple distinct targets when they are closely spaced. In this case, the state estimate given by the PHD filter is that of the target group, not that for either of the two targets. To solve this problem, we derive and propose a marginal distribution Bayesian(MDB) filter. The proposed filter sufficiently considers the independences of individual targets. Instead of maintaining the joint posterior density of the multi-target state, the filter propagates the marginal distributions of each target. Based on novel filter recursion, a marginal distribution Bayesian filter accommodating linear and Gaussian models is also developed. The simulation results demonstrate that the proposed filter is better at distinguishing distinct targets and tracking multiple targets than the Gaussian mixture PHD filter.To solve the problem of nonlinear and Gaussian systems for tracking multi-targets, we propose two extensions of the closed-form recursion of the MDB filter using the linearization technique of nonlinear function and the unscented transform technique to accommodate nonlinear multi-target models. The first is the extended Kalman marginal distribution Bayesian(EK-MDB) filter, and the second is the unscented Kalman marginal distribution Bayesian(UK-MDB) filter. The simulation results show that both the EK-MDB and UK-MDB filters track multiple targets well in the presence of clutter as well as target appearance and disappearance, and that the computational complexity of the EK-MDB filter is less than that of the UK-MDB filter.