Robust Multimodal Fusion of Kalman and GM Filters via Graph Centrality

In the presence of outliers or non-Gaussian noise in linear estimator design, lightweight Kalman filters (KFs) suffer from severe vulnerability, whereas robust Gaussian mixture filters (GMFs) incur much higher computational costs. To reconcile the robustness of the estimation with resource constraints, this letter investigates a distributed heterogeneous fusion architecture integrating GMFs with KFs. For this multimodal KF-GMF fusion case, we prove the robustness superiority of the arithmetic average (AA) fusion in comparison to the geometric average (GA) fusion. Furthermore, to resolve the mode conflict caused by anomalous outliers in the KF nodes, a graph-centrality-based anomaly isolation mechanism is proposed. By mapping the statistical consistency of fused Gaussian components into a weighted topological graph, this mechanism utilizes a node strength criterion to identify and eliminate disturbance-induced, topologically isolated modes/components with theoretical guarantees. Simulations demonstrate that the proposed KF-GMF AA fusion approach significantly outperforms the GA fusion in terms of tracking accuracy and convergence.