A Stable Adaptive Kalman Filter with Decay‐Factor Recursive Covariance Estimation

ABSTRACT

Existing adaptive Kalman filters for unknown and time‐varying noise statistics often exhibit numerical instability arising from the coupling between state and noise estimation. To overcome these issues, this paper proposes a Stable Adaptive Kalman Filter with Decay‐Factor Recursive Covariance Estimation (SAKF‐DFRCE). The proposed framework presents a non‐augmented, decoupled estimation strategy by constructing noise‐sensitive measurement difference sequences. This allows for the estimation of process and measurement noise covariance matrices via a linear least‐squares formulation, independent of the state estimation loop. A recursive update mechanism incorporating a dynamic decay factor facilitates robust adaptation to non‐stationary noise typical of maneuvering targets. Theoretical analysis establishes the strong consistency of the noise estimators and the asymptotic stability of the filter. The proposed SAKF‐DFRCE achieves estimation accuracy comparable to the theoretical benchmark of a standard Kalman filter while exhibiting reduced computational runtime compared to existing adaptive methods, making it suitable for high‐reliability, resource‐constrained aerospace applications. Monte Carlo simulations, including nonlinear radar tracking scenarios, validate the effectiveness of the proposed method.