Design of measurement difference autocovariance method for estimation of process and measurement noise covariances

Abstract

The paper deals with the estimation of the process and measurement noise covariance matrices of a system described by the linear time-varying state–space model. In particular, the stress is laid on the correlation methods and a novel method, the measurement difference autocovariance method, is designed. The proposed method is based on the statistical analysis of an augmented measurement prediction error leading to a system of linear matrix equations for the elements of the noise covariance matrices. 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 a numerical example.