The divergence criterion and the adaptation algorithm of the recurrent algorithm of the state vector estimation
Recurrent estimation algorithms (Kalman filter) is widespread in solving a wide range of problems of control, identification and filtering. These algorithms have several advantages over other algorithms for solving these problems. The main of these advantages is an optimal estimate of the state vector (minimization of the mean square error of estimation) and the recurrence property when a "new" estimate of the state vector is obtained from an “old” estimate (evaluation at the previous step) and processing a "new" measurement. This scheme has received the predictor-corrector name. The recurrence property significantly reduces the computational cost to build estimates of the state vector and (in most cases) allows implementing the estimation process in real-time. However, when these algorithms are used in practice, the problem of divergence arises when the "true" error of estimation of the state vector is significantly higher than the "design" values calculated through the estimated correlations of the estimation algorithm, i.e. the estimation algorithm does not works optimally. To overcome the divergence, the estimation algorithm must detect the violation of the optimal mode and to correct the computational scheme of the algorithm. In this paper we construct a simple divergence criterion of the recurrent algorithm estimation well implemented in practice, which accurately detects the time when the algorithm loses the optimality property, i.e. the beginning of a sharp increase in the root mean square error of estimation. This criterion is based on testing statistical hypotheses of properties of the updating process that represents the difference between the current measurement and the predicted value of this measurement. When such a moment occurs, the proposed adaptation algorithm which modifies the variance-covariance matrix of the prediction error intervenes so as to giveback the optimality property to the estimation algorithm. The implementation of the computing experiment showeda high efficiency of the constructed criterion and the proposed adaptation algorithm, even with large errors in the matrix model of the dynamic system.