Robust Estimation of State Parameters of Discrete Nonlinear Stochastic Systems

Abstract

The paper deals with a class of discrete nonlinear stochastic systems that are subject to the disturbing effect of noise with unknown distribution densities belonging to the class of distributions with bounded mean squares and observed under noise conditions with unknown distribution densities belonging to the same class. For these discrete stochastic systems, the problem of synthesis of a stable (robust) recurrent estimate of the state vector of the system is posed and solved. To solve this problem, a new robust estimation criterion is introduced, from the optimization condition of which a recurrent form of a robust estimate of the state vector of the studied class of discrete nonlinear stochastic systems is obtained. The advantages of this robust estimation algorithm are both its optimality in the sense of the proposed robust estimation criterion and its dimension, coinciding with the dimension of the state vector of the object being evaluated, in contrast to existing filtering algorithms, the dimension of which significantly exceeds the dimension of the object state vector due to estimates of the a posteriori covariance matrix, probabilistic characteristics of interference, etc. This circumstance makes it possible to significantly reduce computational costs in the implementation of this algorithm, which is especially important for on-board information-measuring and control systems of moving objects. The results of a numerical experiment are presented, illustrating the effectiveness of the practical use of the proposed approach.