Limited Memory-Based Random-Weighted Kalman Filter

The Kalman filter is an important technique for system state estimation. It requires the exact knowledge of system noise statistics to achieve optimal state estimation. However, in practice, this knowledge is often unknown or inaccurate due to uncertainties and disturbances involved in the dynamic environment, leading to degraded or even divergent filtering solutions. To address this issue, this paper presents a new method by combining the random weighting concept with the limited memory technique to accurately estimate system noise statistics. To avoid the influence of excessive historical information on state estimation, random weighting theories are established based on the limited memory technique to estimate both process noise and measurement noise statistics within a limited memory. Subsequently, the estimated system noise statistics are fed back into the Kalman filtering process for system state estimation. The proposed method improves the Kalman filtering accuracy by adaptively adjusting the weights of system noise statistics within a limited memory to suppress the interference of system noise on system state estimation. Simulations and experiments as well as comparison analysis were conducted, demonstrating that the proposed method can overcome the disadvantage of the traditional limited memory filter, leading to im-proved accuracy for system state estimation.