Methods to Improve the Accuracy of State Estimation in Nonlinear Kalman Filter in Case of a Priori Uncertainty

The paper is devoted to the problem of estimating the state of a complex system with nonlinear dynamic behavior using nonlinear filtering. Modern numerical methods of nonlinear filtering for estimating the unknown state vector of a stochastic differential system of Itô type with discrete measurements are studied. The relevance of the work is due to the necessity to improve the accuracy of state vector estimation in dynamic systems under conditions of a priori uncertainty of information about the system functions and measurement. In this paper, a nonlinear system with formant Wiener noise is considered. As the chosen method of nonlinear filtering the sigma-point Kalman filter is used, which has sufficient accuracy of state vector estimation at low computational complexity. The paper discusses ways to improve the accuracy of nonlinear system vector estimation using sigma-point Kalman filter. Mathematical description of the sigma-point Kalman filter operation is given, and the methods of improving the quality of operation under conditions of a priori unknown functions of the system and measurement by estimating the values of covariance matrices of random processes are proposed. The paper presents the results of modeling of the sigma-point Kalman filter for both linear and nonlinear measurement functions. The obtained values of RMS error under conditions of a priori uncertainty of system and measurement functions under approximation of covariance matrices have the same order as in the case of a priori known functions. The paper presents the results of nonlinear filtering simulation at different values of the sampling period. In conclusion, recommendations for the choice of parameters of the sigma-point Kalman filter when working under conditions of a priori uncertainty of system and measurement functions are given.