Analysis of the “Extended Kalman Filter – Adaptive Digital Filter” System Operation in Filtering of Non-Stationary Signals

Processing of various origin non-stationary signals in control systems for robotic devices is an urgent problem. The use of the extended Kalman filter (EKF) for working with non-stationary signals, including signal filtering, is limited by the precise settings of the filter — the observed system model and the covariance matrices of the EKF algorithm, which requires the adaptability of the filter algorithm under conditions of an input rapidly changing noised non-stationary signal. In this regard, the paper proposes to use the system “extended Kalman filter — adaptive digital filter” (EKF-ADF system) for filtering of non-stationary signals, which is the EKF augmented with an adaptive digital filter with the NLMS (normalized least mean squares) adaptation algorithm in order to compensate for the error in the operation of the EKF when non-stationary signal filtering is performing. The study of the operation of the EKF-ADF system as a filter for non-stationary signals shows that under conditions of a significant noise applied on a non-stationary signal, the algorithm of the EKF-ADF system, in comparison with the EKF algorithm, which has settings similar to the EKF settings in the EKF-ADF system, possesses the highest values of the “signal-to-noise ratio” evaluation of filtering results. The EKF-ADF system can be used as a state observer of robotic devices, which is capable of operating under conditions of non-stationary processes.