Robust Divide-and-Conquer Multiple Importance Kalman Filtering via Fuzzy Measure for Multipassive-Sensor Target Tracking

Abstract

Multipassive-sensor target tracking systems (MPSTTs) enable noncontact and covert acquisition of the target status, with bearings processing being a prerequisite for accurately predicting the target behavior over large spatial ranges. However, MPSTTs are prone to fuzziness owing to coordinate coupled and Gaussian truncation errors. To address these challenges, we propose a high-precision robust tracker that uses divide-and-conquer multiple-importance Kalman filtering (DCMIKF) via a fuzzy measure. Specifically, we designed coupling maneuver models and attached their model-truth probabilities as a fuzzy set. The measurements-to-target data association was then formulated as a fuzzy maxima searching problem with soft spatiotemporal causal constraints. The proposed approach enables the integration of all available information to derive the fuzzy measure, dividing the hybrid state estimation into variable-structure model estimation and model-conditioned filtering. Simultaneously, DCMIKF combines importance prediction with constrained convex measurement updating using KF and fuses the outputs via fuzzy model probability. Besides, it offers a purely mathematical approach for quantifying the average fuzziness yielded from the fuzzy set, thereby smoothing the mismatches between multilikelihoods, proposal distribution, and target posterior. Simulated and measured results conformed well; compared with the regression Gaussian process motion tracker, DCMIKF overcame the prior hypotheses in machine learning, reducing the problematic cubic complexity in the number of time steps to the linear time complexity; compared to the interacting multiple model minimax particle filter, DCMIKF significantly improves filtering accuracy and tracking robustness.