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<p>In many engineering applications, the use of the Kalman filter results in state vector estimation divergence. Existing methods for reducing the errors of state vector estimation and improving the stability of filtering algorithms focus only on estimating the state of specific dynamic systems. A&#xa0;feasibility study of the generalized use of these algorithms is complicated by the nonlinear evolution of the posterior covariance matrix, which directly affects the estimation error convergence. In order to improve the filtering accuracy and stability, this article proposes a&#xa0;stochastic estimation algorithm in which the output estimation vector of the Kalman filter is used as a&#xa0;stochastic state vector observer for the dynamic system. Such use of the considered algorithm leads to an adaptive change in the measurement noise intensity in the new filtering cycle. This change in the measurement noise intensity reduces the frequency and amplitude of oscillations in the posterior covariance matrix elements and significantly improves the accuracy of continuous estimation. The authors present the results of numerically simulating stochastic estimation with the Kalman filter; the effectiveness of the proposed algorithm is proved on the example of navigation parameter estimation for an unmanned aerial vehicle. The proposed stochastic estimation algorithm can be applied to a&#xa0;broad class of problems, for example, in navigation, seismology, space research, etc.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Sergey V. Sokolov,
  • Vadim A. Pogorelov,
  • Irina V. Reshetnikova

摘要

In many engineering applications, the use of the Kalman filter results in state vector estimation divergence. Existing methods for reducing the errors of state vector estimation and improving the stability of filtering algorithms focus only on estimating the state of specific dynamic systems. A feasibility study of the generalized use of these algorithms is complicated by the nonlinear evolution of the posterior covariance matrix, which directly affects the estimation error convergence. In order to improve the filtering accuracy and stability, this article proposes a stochastic estimation algorithm in which the output estimation vector of the Kalman filter is used as a stochastic state vector observer for the dynamic system. Such use of the considered algorithm leads to an adaptive change in the measurement noise intensity in the new filtering cycle. This change in the measurement noise intensity reduces the frequency and amplitude of oscillations in the posterior covariance matrix elements and significantly improves the accuracy of continuous estimation. The authors present the results of numerically simulating stochastic estimation with the Kalman filter; the effectiveness of the proposed algorithm is proved on the example of navigation parameter estimation for an unmanned aerial vehicle. The proposed stochastic estimation algorithm can be applied to a broad class of problems, for example, in navigation, seismology, space research, etc.