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

The 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. Uncertain and biased values of the covariances result in KF performance degradation or divergence. Unlike previous methods, we are using the idea of the recursive estimation of the KF to develop two recursive updating rules for the process and observation covariances, respectively designed based on the covariance matching principles. Each rule has a tuning parameter that enhances its flexibility for noise adaptation. The proposed adaptive Kalman filter (AKF) proves itself to have an improved performance over the conventional KF and, in the worst case, it converges to the KF. The results show that the AKF estimates are more accurate, have less noise, and are more stable against biased covariances.