L₂-optimal identification of MIMO errors-in-variables models from the v-gap geometrical interpretation

Abstract

An L ₂-optimal identification method is extended to cope with MIMO errors-in-variables (EIV) model estimation based on a geometrical interpretation for the v-gap metric. The L ₂-optimal approximate models are composed of system and noise models and characterised by a normalised right graph symbol (NRGS) and its complementary inner factor (CIF), respectively. This metric can be evaluated as the supreme of sine values of the maximal principal angles between NRGS frequency responses of two concerned models. In order to make full use of the angular cosine formula for complex vectors to reduce computational loads, a CIF of the NRGS of the perturbed model is introduced and thus, the system parameter optimisation can be efficiently solved by sequential quadratic programming methods. With the estimated system model, the associated noise model can be built by right multiplication of an inner matrix. Finally, a simulation example demonstrates the effectiveness of the proposed identification method.

Keywords:

• L ₂-optimal identification
• MIMO errors-in-variables
• v-gap geometrical interpretation
• sequential quadratic programming (SQP)

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. 61178081), the Scientific Research Foundation of the Ministry of Education of China for Young Scholars (Grant No. 11YJC790048), the Science and Technology Development Foundation of Tianjin Higher Education, China (Grant No. 20110834) and the Scientific Research Foundation of Tianjin University of Technology and Education, China (No. KJYB11-2).