Robust State Estimation via Dual-threshold NIS-based Kalman-FIR Switching

Abstract

This study proposes a robust state estimation framework for discrete-time linear time-invariant systems using a statistically grounded switching mechanism between the Kalman filter (KF) and the optimal finite impulse response (OFIR) filter. While the KF provides minimum-variance estimates under nominal Gaussian assumptions, its performance degrades under model mismatch and unknown disturbance conditions. In contrast, the OFIR filter offers inherent robustness due to its finite-memory structure, although its performance is influenced by the horizon length. Existing switching or hybrid estimators often suffer from chattering due to single-threshold logic, increased computational complexity from parallel filter structures, and the lack of a theoretically grounded mechanism ensuring state continuity during mode transitions. To address these limitations, a normalized-innovation-squared (NIS)-based dual-threshold hysteresis hysteresis switching strategy is introduced. The proposed scheme employs chi-squared quantile-based thresholds to suppress chattering and ensure stable mode transitions. In addition, a covariance synchronization procedure based on the OFIR-finite horizon Kalman filter (FH-KF) equivalence is established, guaranteeing bounded estimation error during mode transitions without heuristic tuning. The proposed framework is validated using numerical simulations on three benchmark systems, including a 2D target tracking model, a linearized F-404 turbofan engine, and a DC motor system in various disturbance scenarios. Simulation results demonstrate that the proposed method achieves KF-level estimation accuracy under nominal conditions while significantly reducing estimation error during disturbance intervals. The dual-threshold hysteresis structure also effectively reduces unnecessary mode transitions compared with conventional single-threshold approaches, demonstrating the effectiveness and general applicability of the proposed framework.