Online adaptive Kalman filtering algorithms for sensor signals with coloured noise

Two algorithms are presented for online estimation of the optimal gain of the Kalman filter applied to sensor signals when the signal-to-noise ratio is unknown. First-order spectra of a pure signal and coloured measurement noise are assumed. The proposed adaptive Kalman filtering algorithms have been tested for errors of the pure signal estimation. Although the tests have been performed for stationary signals, the algorithms can also be used successfully for time-varying sensor signals when the signal-to-noise ratio varies in comparison to the length of the adaptation step