Constrained Multi-Sensor Control Using a Multi-Target MSE Bound and a δ-GLMB Filter

The existing multi-sensor control algorithms for multi-target tracking (MTT) within the random finite set (RFS) framework are all based on the distributed processing architecture, so the rule of generalized covariance intersection (GCI) has to be used to obtain the multi-sensor posterior density. However, there has still been no reliable basis for setting the normalized fusion weight of each sensor in GCI until now. Therefore, to avoid the GCI rule, the paper proposes a new constrained multi-sensor control algorithm based on the centralized processing architecture. A multi-target mean-square error (MSE) bound defined in our paper is served as cost function and the multi-sensor control commands are just the solutions that minimize the bound. In order to derive the bound by using the generalized information inequality to RFS observation, the error between state set and its estimation is measured by the second-order optimal sub-pattern assignment metric while the multi-target Bayes recursion is performed by using a δ-generalized labeled multi-Bernoulli filter. An additional benefit of our method is that the proposed bound can provide an online indication of the achievable limit for MTT precision after the sensor control. Two suboptimal algorithms, which are mixed penalty function (MPF) method and complex method, are used to reduce the computation cost of solving the constrained optimization problem. Simulation results show that for the constrained multi-sensor control system with different observation performance, our method significantly outperforms the GCI-based Cauchy-Schwarz divergence method in MTT precision. Besides, when the number of sensors is relatively large, the computation time of the MPF and complex methods is much shorter than that of the exhaustive search method at the expense of completely acceptable loss of tracking accuracy.