From Target Tracking to Targeting Track -- Part II: Regularized Polynomial Trajectory Optimization

Target tracking entails the estimation of the evolution of the target state over time, namely the target trajectory. Different from the classical state space model, our series of studies, including this paper, model the collection of the target state as a stochastic process (SP) that is further decomposed into a deterministic part which represents the trend of the trajectory and a residual SP representing the residual fitting error. Subsequently, the tracking problem is formulated as a learning problem regarding the trajectory SP for which a key part is to estimate a trajectory FoT (T-FoT) best fitting the measurements in time series. For this purpose, we consider the polynomial T-FoT and address the regularized polynomial T-FoT optimization employing two distinct regularization strategies seeking trade-off between the accuracy and simplicity. One limits the order of the polynomial and then the best choice is determined by grid searching in a narrow, bounded range while the other adopts $\ell_0$ norm regularization for which the hybrid Newton solver is employed. Simulation results obtained in both single and multiple maneuvering target scenarios demonstrate the effectiveness of our approaches.

Arithmetic Average Density Fusion -- Part IV: Distributed Heterogeneous Fusion of RFS and LRFS Filters via Variational Approximation

This paper, the fourth part of a series of papers on the arithmetic average (AA) density fusion approach and its application for target tracking, addresses the intricate challenge of distributed heterogeneous multisensor multitarget tracking, where each inter-connected sensor operates a probability hypothesis density (PHD) filter, a multiple Bernoulli (MB) filter or a labeled MB (LMB) filter and they cooperate with each other via information fusion. Earlier papers in this series have proven that the proper AA fusion of these filters is all exactly built on averaging their respective unlabeled/labeled PHDs. Based on this finding, two PHD-AA fusion approaches are proposed via variational minimization of the upper bound of the Kullback-Leibler divergence between the local and multi-filter averaged PHDs subject to cardinality consensus based on the Gaussian mixture implementation, enabling heterogeneous filter cooperation. One focuses solely on fitting the weights of the local Gaussian components (L-GCs), while the other simultaneously fits all the parameters of the L-GCs at each sensor, both seeking average consensus on the unlabeled PHD, irrespective of the specific posterior form of the local filters. For the distributed peer-to-peer communication, both the classic consensus and flooding paradigms have been investigated. Simulations have demonstrated the effectiveness and flexibility of the proposed approaches in both homogeneous and heterogeneous scenarios.