HLS parameter estimation for multi-input multi-output systems

In order to reduce computational burden of identification methods for multivariable systems, a hierarchical least squares (HLS) algorithm is developed. The basic idea is to use the hierarchical identification principle to decompose the identification model of the multivariable system into several submodels with smaller dimensions and fewer variables, and then to identify the parameter vector of each submodel. The analysis indicates that the parameter estimation error given by the proposed algorithm converges to zero under the persistent excitation. Also, the algorithm has much less computational efforts than the recursive least squares algorithm and is easy to implement on computer. Finally, we test the proposed algorithm by an example.