A new SVD modification of the discrete-time filtering algorithm with finite-step autocorrelated measurement noise

The paper considers the discrete-time filtering problem in the class of the linear stochastic system models with finite-step autocorrelated measurement noise. A new SVD modification of the discrete-time filtering algorithm is proposed. It was proved that the new SVD algorithm is algebraically equivalent to the conventional one but has improved computational properties. The algorithm is implemented in MATLAB. The results of numerical experiments confirmed the working capacity and numerical efficiency of the new SVD algorithm when compared with the standard Kalman filter and the extended Kalman-type algorithm. In the case where the noise covariance matrix in the state equation is close to zero, the extended Kalman-type algorithm diverges and quickly loses its functionality due to a huge increase in estimation errors. At the same time, the proposed SVD modification remains workable and allows for calculating estimates of the state vector with high accuracy. The results obtained can be used to solve practical problems related to the processing and analysis of measurement data in areas such as target tracking, communication networks, signal and image processing.