Hierarchical Least Squares and Hierarchical Multi‐Innovation Least Squares Identification for Multivariable ARX Systems Based on the Coupled Identification Model

For a multivariable ARX system of inputs and outputs, the corresponding subsystem recursive least squares identification algorithm requires large computational burdens as it does not consider the input information vector coupling across subsystems. In this paper, we derive the coupled identification model for the whole multivariable ARX system. Based on this coupled identification model, this paper presents a hierarchical least squares (HLS) identification algorithm and a hierarchical multi‐innovation least squares identification algorithm for multivariable ARX systems. The HLS algorithm requires 66.6% fewer computational cost than the subsystem recursive least squares algorithm.