Robust Stochastic Estimation Based on a Modified Kalman Filter

The practical application of schemes for estimating the state of nonlinear stochastic systems built on the basis of the Kalman filter is limited by the need for an accurate a priori description of the dynamics of the observed object and the measurement process, as well as the probabilistic characteristics of object noise and measurement interference. The absence of this information leads to instability in the assessment process. Despite the numerous modifications of the Kalman filtering scheme, the problem of increasing the filtering accuracy in the absence of information about the probabilistic characteristics of object noise and measurement interference has not yet had a satisfactory solution. In this regard, the article discusses a new approach to constructing a robust Kalman filtering scheme. The proposed robust filtering method is based on the synthesis of the filter gain from the condition of minimizing a nonlinear functional determined by the most unfavorable class of measurement noise distributions. In addition to robust properties, the resulting filter has a significantly smaller dimension compared to the Kalman filter, which coincides with the dimension of the object, which sharply reduces the computational costs of its implementation. The results of a numerical experiment illustrating the effectiveness of the considered approach are presented.