Adaptive estimation of the dispersion noise matrix at linear measurements based on non-periodic accurate observations

Abstract

The lack of modern methods for ensuring the stability of Kalman filtering under the priori uncertainty condition of the dispersion matrix measurement interference is the absence of strict criteria for choosing adaptation coefficients when calculating the posterior covariance matrix or the inability to adaptively evaluate in real time from the minimum covariance of the update sequence due to the need for its preliminary calculation. The article is devoted to the development of a new approach to adapting the Kalman filter, using the ability to obtain accurate measurements for a wide class of objects that irregularly enter their monitoring system (reference point, reference points, radio frequency identifiers, etc.). It is shown that for the distinguished case, the problem of adaptive estimation of the dispersion noise matrix of a linear meter in the Kalman filter can be solved analytically by using matrix methods of linear algebra. A numerical example illustrating the effectiveness of the procedure for estimating the state vector of a moving object based on the proposed algorithm in comparison with the traditional approach is presented. The simplicity and accuracy of the proposed algorithm provide the possibility of its effective application for the widest class of information-measuring systems. Keywords adaptive estimation; dispersion matrix of measurement noise; Kalman filter; non-periodic accurate observations