On the design of an adaptive Kalman filter for on-line processing of sensor signals

This paper presents algorithms for on-line estimation of the optimal parameters of the Kalman filter applied to sensor signals when the structure of the signal model is known exactly, but all the parameters of the signal and noise are unknown. A first order spectrum of a pure signal and white Gaussian measurement noise have been assumed. The proposed adaptive algorithms have been examined for various spectra of the pure signal and for various signal to noise ratios. The effect of the length of an adaptation step and a sampling frequency on the mean square errors of the pure signal estimation has also been tested. The presented results might be helpful for designers who synthesize optimal linear digital filters for sensor signals in the case of unknown parameters of the signal and noise. Although that particular algorithm has been applied for stationary signals, its modifications can also be used successfully for time varying sensor signals when the signal and noise parameters vary very slowly in comparison to the length of adaptation step. The method for the best choice of the adaptation step and the sampling frequency for filtering nonstationary signals has been proposed.