Real-time state estimator without noise covariance matrices knowledge – fast minimum norm filtering algorithm

The digital filtering technology has been widely applied in a majority of signal processing applications. For the linear systems with state-space model, Kalman filter provides optimal state estimates in the sense of minimum-mean-squared errors and maximum-likelihood estimation. However, only with accurate system parameters and noise statistical properties, the estimation obtained by standard Kalman filter is the optimal state estimate. Most of time, the exact noise statistical properties could not be obtained as a priori information or even wrong statistical properties may be captured by the offline method. This may lead to a poor performance (even divergence) of Kalman filtering algorithm. In this study, a novel real-time filter, named as fast minimum norm filtering algorithm, has been proposed to deal with the case when the covariance matrices of the process and measurement noises were unknown in the linear time-invariant systems with state-space model. Tests have been performed on numerical examples to illustrate that the fast minimum norm filtering algorithm could be used to obtain acceptable precision state estimation in comparison with the standard Kalman filter for the discrete-time linear time-invariant systems.