Hierarchical least squares based iterative estimation algorithm for multivariable Box–Jenkins-like systems using the auxiliary model

This paper presents a hierarchical least squares iterative algorithm to estimate the parameters of multivariable Box–Jenkins-like systems by combining the hierarchical identification principle and the auxiliary model identification idea. The key is to decompose a multivariable systems into two subsystems by using the hierarchical identification principle. As there exist the unmeasurable noise-free outputs and noise terms in the information vector, the solution is using the auxiliary model identification idea to replace the unmeasurable variables with the outputs of the auxiliary model and the estimated residuals. A numerical example is given to show the performance of the proposed algorithm.