Performance analysis of linear estimators with unknown changes in sensors characteristics

Minimum variance state estimation for linear time-invariant systems with Gaussian state and measurement noise is achieved by the Kalman filter. This estimator is known to be robust to model uncertainties, however, it relies upon the knowledge of the measurement covariance. This is a serious limitation when measurement noise covariance changes unpredictably because of external events, such as changes of lighting conditions, presence of smoke/fog, external magnetic fields, etc. In this paper, we consider and analyze a three stage estimation algorithm comprising of: 1) Covariance estimation, estimating the accuracy of each sensor; 2) Measurement gating, rejecting measurements until a new accuracy estimate is provided; and 3) the Kalman filter, estimating the state and its error covariance. The main results of this paper are estimation error characterization of the proposed three stage filter when the measurement noise covariance undergoes sudden and unknown changes. We consider both the single and multi-sensor scenarios and provide a complete analysis for scalar systems along with key insights and preliminary results for the vector setting.