Stochastic estimation using the Kalman filter as a state observer for dynamic systems

The practical application of the Kalman filter in many technical applications leads to the divergence of the evaluation process. The existing methods of reducing estimation error and increasing the stability of the filtering procedure are focused only on assessing the state of specific systems. The analysis of the possibility of their generalized use is hampered by the nonlinear evolution of the a posteriori covariance matrix, which directly affects the convergence of the estimation error. To solve the problem of increasing the accuracy and stability of the filtration process, the article considers a stochastic estimation algorithm using the estimation vector at the output of the Kalman filter as an observer of the state vector of a dynamic system. Such use leads to an adaptive change in the intensity of measurement interference in the new filtering circuit, which reduces the frequency and amplitude of vibrations of the elements of the a posteriori covariance matrix and significantly increases the accuracy of the current estimate. The results of numerical modeling are presented, illustrating the effectiveness of the proposed approach. The proposed stochastic filtering method can be applied to a broad class of problems, including measurement processing, navigation, seismology, space research, and other areas.

stochastic estimation, Kalman filter, observer of the state vector, a posteriori covariance matrix, estimation error