Measurement difference autocovariance method for noise covariance matrices estimation

The paper deals with the estimation of the noise covariance matrices of a linear time-varying system described by the state-space model. In particular, the stress is laid on the correlation methods and a novel method, the measurement difference autocovariance method, is proposed. The proposed method is based on the statistical analysis of differenced linearly transformed and shifted measurements resulting in a system of linear matrix equations. Compared to other correlation methods, the proposed method provides unbiased estimates even for a finite number of measurements. The theoretical results are discussed and illustrated in numerical examples.