An improved real-time adaptive Kalman filter with recursive noise covariance updating rules

Kalman filter (KF) is used extensively for state estimation. Among its requirements are the process and observation noise covariances which are unknown or partially known in real life applications. Biased initializations of the covariances result in performance degradation of KF or divergence. Therefore, an extensive research is carried on to improve its performance however, relying on a moving window, heavy computations, and the availability of the exact model are the fundamental problems in most of the proposed techniques. In this paper, we are using the idea of the recursive estimation of KF to propose two recursive updating rules for the process and observation covariances respectively designed based on the covariance matching principles. Each rule is a tuned scaled version of the previous covariance in addition to a tuned correction term derived based on the most recent available data. The proposed adaptive Kalman filter AKF avoided the aforementioned problems and proved itself to have an improved performance over the conventional KF. The results show that the AKF estimates are more accurate, have less noise and more stable against biased covariance initializations.