Adaptive unscented Kalman filter based on maximum posterior and random weighting

The unscented Kalman filter (UKF) is an effective technique of state estimation for nonlinear dynamic systems. However, its performance depends on prior knowledge on system noise. If the characteristics of system noise are unknown or inaccurate, the filtering solution may be biased or even divergent. This paper presents a new maximum posterior and random weighting based adaptive UKF (MRAUKF) by combining the concepts of maximum posterior and random weighting to overcome this limitation. The proposed MRAUKF computes noise statistics based on the maximum posterior principle, and subsequently adopts the random weighting concept to optimize the obtained maximum posterior estimations by online adjusting the weights on residuals. The maximum posterior and random weighting estimations of noise statistics are established to online estimate and adjust system noise statistics, leading to the improved filtering robustness. Simulation and experimental results demonstrate that the proposed MRAUKF outperforms the classical UKF and adaptive robust UKF in the presence of uncertain system noise statistics.