Cauchy-Schwarz Divergence-Based Set Joint Probabilistic Data Association Filter for Tracking Multiple Objects in Cluttered Environment

Conditioned on measurement data from sensors, the joint probabilistic data association (JPDA) filter is a popular methodology for tracking multiple objects in clutter. The JPDA filter, however, suffers from the severe track coalescence effect, i.e., tracks following objects in close proximity tend to coalesce. To improve the tracking accuracy, we propose a novel Cauchy-Schwarz set JPDA (CSSJPDA) filter by optimizing the posterior Gaussian mixture density with an iterative successive component-based optimization (ISCO) algorithm in the Cauchy-Schwarz sense. The posterior Gaussian mixture density is marginalized by Gaussian densities to estimate object states at each time step. To improve the marginalization accuracy, the posterior density is optimized in the random finite set (RFS) family. We derive a closed-form expression of the Cauchy-Schwarz divergence between the posterior density and its Gaussian approximation and use it as a cost function for density optimization. To improve the optimization efficiency, we propose the ISCO algorithm to minimize the cost function successively along one Gaussian component at a time and prove its monotone convergence. Two indicative examples are used to illustrate the effectiveness of the CSSJPDA filter. With the iteration, the cost function decreases and the Gaussian approximation becomes more accurate. Simulation results demonstrate that the CSSJPDA filter provides a good tradeoff between the tracking accuracy and the computational efficiency compared to the existing methods. Numerical experiments with a real-world dataset further verify the performances of the proposed method.