A New Weighted Average Method For Weighting Matrices In Subspace Identification

Subspace identification methods (called SIM) proposed since1990s have attracted more attention in many fields such as industrial control, signal processing and system identification, while over in the last decade, a relatively complete theoretical system has been gradually formed from the subspace identification methods including in algorithm design, algorithm application and performance analysis, meanwhile which plays an important role in industrial control and multivariate input and output system.In the preface of this article, the background of the subspace identification proposed is introduced, the advantage of the subspace identification methods is presented also. Then three representative subspace identification methods such as N4SID, MOESP and CVA are addressed briefly, and the main contribution of this paper mentioned.In the first section, a system model about combined deterministic-stochastic identificat-ion and some assumption conditions are presented, accordingly the input and output Hankel matrices, other relevant matrices and the idea behind subspace identification algorithm are represented.In the second section, firstly some preliminary knowledge is proposed including in Moor-Penrose (called MP) pseudo inverse, the definition of projections, some relevant statistical tools and geometric tools in a statistical framework, these are basic work of this article. Secondly some theorems about subspace identification and state space basis with related theory are addressed, which provide a theoretical basis for the designed algorithms of this papers.In the third section, it is key part of this paper also. A combined matrices input-output equation is proposed firstly, this is research object of system identified model, three subspace identification methods such as N4SID, MOESP and CVA are analyzed briefly, and to reveal as each method when implemented has self-shortcoming, at last the detailed constructing process of a weighted average method to given weighting matrices is presented in system subspace identification, in order to reduce the complexity of process implemented, the block Hankel matrix involved is decomposed by using QR tool, finally the specific implementation steps of the new algorithm are listed, the given weighting matrices to use the weighted average method are treated, the weighting matrices will generated more choice ways. The simulation examples are given in the last section, this part presents the comparison of numerical experiments among N4SID, MOESP and two kinds of different weighted average methods MOESN4WAc, MOESN4WAd, it is proved that the final results are effective and satisfactory.