Maximum likelihood least squares identification for systems with autoregressive moving average noise

Maximum likelihood methods are important for system modeling and parameter estimation. This paper derives a recursive maximum likelihood least squares identification algorithm for systems with autoregressive moving average noises, based on the maximum likelihood principle. In this derivation, we prove that the maximum of the likelihood function is equivalent to minimizing the least squares cost function. The proposed algorithm is different from the corresponding generalized extended least squares algorithm. The simulation test shows that the proposed algorithm has a higher estimation accuracy than the recursive generalized extended least squares algorithm.