An Adaptive Algorithm for Fast Identification of IIR Systems

This paper considers the problem of adaptive identification of IIR systems when the system output is corrupted by noise. The standard recursive least squares algorithm is known to produce biased parameter estimates in this case. A new type of fast recursive identification algorithm is proposed which is built upon approximate inverse power iteration. The proposed adaptive algorithm can recursively compute the total least squares solution for unbiased adaptive identification of IIR systems. It is shown that the proposed adaptive algorithm has global convergence. The significant features of the proposed adaptive algorithm include efficient computation of the fast gain vector, adaptation of the inversepower iteration, and rank-one update of the augmented covariance matrix. The proposed adaptive algorithm is superior to the standard recursive least squares algorithm and other recursive total least squares algorithms in such aspects as its ability for unbiased parameter estimation, its lower computational complexity, and its good long-term numerical stability. Computer simulation results that corroborate the theoretical findings are presented.