Consistency of the extended gradient identification algorithm for multi-input multi-output systems with moving average noises

The consistency of identification algorithms for systems with colored noises is a main topic in system identification. This paper focuses on the extended stochastic gradient ESG identification algorithm for the multivariable linear systems with moving average noises. By integrating the noise regression terms and the noise model parameters into the information matrix and the parameter vector, and based on the gradient search principle, the ESG algorithm is presented. The unknown noise terms in the information matrix are replaced with their estimates. The convergence analysis shows that the parameter estimation error converges to zero under a persistent excitation condition. Two simulation examples are given to illustrate the effectiveness of the algorithm.