An extended Kalman filtering algorithm based on minimum robust weighted square error

Abstract Traditional Kalman filtering is based on the minimum mean square error (MMSE) criterion and has been widely applied in state estimation. However, its performance can be considerably degraded in the presence of abnormal measurements, due to the sensitivity of MMSE to outliers. To address this problem, we design a robust weighted square error and integrate it into the Kalman filtering framework, resulting in the minimum robust weighted square error-based extended Kalman filtering (MRWSE-EKF) algorithm. This unified framework subsumes several existing robust Kalman filtering approaches as special cases. A generalized robust loss function is taken as an example to illustrate the guidelines for parameter settings. Simulation results demonstrate that the proposed algorithm effectively suppresses the influence of abnormal measurements and significantly improves state estimation accuracy in the presence of outliers. The parameter comparison results also reveal how different parameter settings affect filtering performance, providing practical guidelines for parameter selection.