Efficient joint probabilistic data association filter based on Kullback–Leibler divergence for multi‐target tracking

Abstract

To deal with the track coalescence problem of the joint probabilistic data association (JPDA) filter, a novel approach based on the Kullback-Leibler divergence (KLD) is developed in this study. In JPDA, the posterior probability density function (PDF) is approximated by a single Gaussian PDF at each time step. The authors propose a novel method of optimising the posterior PDF to obtain a single Gaussian PDF that minimises the KLD from the posterior PDF. However, the KLD is intractable because the posterior PDF is a Gaussian mixture model. Hence, an approximation of the KLD is introduced as the cost function to simplify the problem. The cost function is a linear combination of multiple objective functions which are not conflicting. Therefore, the minimisation of the cost function is easier to operate, because all objective functions can be optimised simultaneously. In addition, an iterative method is adopted for minimising the cost function. In the iteration process, the tracking accuracy is improved with the monotonic decrease of the cost function. Theoretical analysis and example show the feasibility of the proposed approach. Simulation results demonstrate the advantages of the new approach over others when tracking closely spaced targets with contaminated sensor measurements.