Optimized Robust Filter for Uncertain Discrete Time System and Its Application to Flight Test

Abstract

An optimized robust filtering algorithm for uncertain discrete-time systems is presented. To get a series of computational equations, the uncertain part generated by the uncertain systematic matrix in the expression of the error-covariance matrix of time update state estimation is optimized and the least upper bound of the uncertain part is given. By means of these results, the equivalent systematic matrix is obtained and a robust time update algorithm is built up. On the other hand, un-certain parts generated by the uncertain observation matrix in the expression of the error-covariance matrix of measurement update state estimation are optimized, and the largest lower bound of the un-certain part is given. Thus both the time update and measurement update algorithms are developed. By means of the matrix inversion formula, the expression structures of both time update and measurement update algorithms are all simplified. Moreover, the convergence condition of a robust filter is developed to make the results easy to application. The results of flight data processing show that the method presented in this paper is efficient.