Arithmetic Average Density Fusion - Part V: Fisher Information Weighted Fusion of Multi-rate Filters

This paper, as the fifth part of a series of papers on the arithmetic average (AA) density fusion approach and its application for target tracking, addresses the challenging problem of fusing multi-rate Bayesian filters operating at different sampling rates. We adopt a flexible time alignment strategy that aligns asynchronously calculated local densities to the fusion time using a stochastic differential equation (SDE). A novel weighted AA fusion strategy is proposed that assigns fusion weights to time-aligned local densities in proportion to the Fisher information (FI) of local sensors, which is derived in the continuous time (CT) domain via matrix block recursion and the Schur complement Lemma based on the SDE. Both tracking scenarios with and without clutter and misdetection are considered, respectively, with specific attention paid to the linear Gaussian system for which the exact FI exists. Furthermore, we derive the CT Cramér-Rao lower bound (CT-BCRLB) that gives a tight/achievable lower bound for any time, equal to the discrete time (DT) BCRLB at the sampling time but much higher at the non-sampling time. This fills the gap left by existing DT BCRLBs, which fail to provide a tight lower bound at non-sampling times. By simulation, the FI weights are demonstrated in the context of both the AA and geometric average fusion, outperforming existing weighting strategies in their respective classes.