A filtering-based recursive extended least squares algorithm and its convergence for finite impulse response moving average systems

This article considers the parameter identification problems of stochastic systems which described by the finite impulse response moving average model. Since the system is disturbed by colored noise, we introduce the data filtering technique from a view point of improving the parameter estimation accuracy. The data filtering technique is to use a filter to filter the input and output data of the system disturbed by colored noise so as to improve the identification accuracy. By using the data filtering technique, this article proposes a filtering-based recursive extended least squares (F-RELS) algorithm. The convergence analysis indicates that the parameter estimates can converge to their true values. Compared with the recursive extended least squares algorithm, the proposed F-RELS algorithm can obtain more accurate parameter estimation. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.