Estimation of Noise Means and Covariance Matrices for Linear Time-Varying Models

The paper deals with the estimation of the means and covariance matrices of the noises of a linear time-varying system described by the state-space model. The proposed measurement difference method is based on a statistical analysis of differenced, linearly transformed, and shifted augmented measurement vector resulting in a system of linear matrix equations for consistent estimation of both; noise means and noise covariance matrices. The theoretical results are discussed and illustrated in a numerical example.