On the Application of an Adaptive Kalman Filter for Sensor Signals

This paper presents the algorithm for on-line estimation of the optimal gain of the Kalman filter applied to sensor´s signals when the structure of the signal model is known exactly, but the signal to noise ratio is unknown. A first order spectrum of a pure signal and white Gaussian measurement noise have been assumed. The proposed adaptation algorithm has been examined for various spectra of the signal and for various signal to noise ratios. The effect of the length of an adaptation step on the convergence properties of the algorithm and on errors of the pure signal estimation has also been tested. The presented considerations might be helpful for designers who synthesize optimal linear digital filters of sensors signals in the case of unknown signal to noise ratio. Although that particular algorithm has been applied for stationary signals, it can be also used successfully for time variant sensor´s signals when the signal to noise ratio varies very slowly in comparison to the length of adaptation step.