Hierarchical stochastic gradient parameter estimation algorithms for multivariable systems with colored noises

This paper develops a hierarchical extended stochastic gradient identification algorithms for MIMO ARMAX-like systems to deal with colored noises based on the hierarchical identification principle. The convergence performance of such algorithms is studied in detail; in particular, conditions for parameter estimation errors to converge to zero are established, which include persistent excitation of the extended information vectors and strict positive realness of the noise models. Finally, the proposed algorithms are tested on an example to show their advantages and effectiveness.