Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems

Abstract This paper considers the parameter estimation problems of two-input single-output Hammerstein finite impulse response systems. A hierarchical least squares algorithm is proposed for improving the computational efficiency through combining the hierarchical identification principle and the identification model decomposition, and a multi-innovation least squares algorithm is proposed for enhancing the parameter estimation accuracy based on the multi-innovation identification theory. The key is to derive two sub-identification models, each of which contains a set of merged parameter vectors. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the over-parametrization identification method, and can be easily extended to multi-input multi-output systems. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.