Estimation error analysis of system matrices in some subspace identification methods

Explicit formulation of dominant parts of the estimation errors of system matrices in PO-MOESP method and a robust N4SID like method are derived based on a proposing lemma on a gap between two singular subspaces. By considering the gap instead of the perturbations of the singular vectors, it is shown that the estimate in PO-MOESP method is unbiased while the estimate in the robust N4SID like method has an asymptotic bias when the past horizon p is finite.

[1]  M. Jansson.  Asymptotic Variance Analysis of Subspace Identification Methods , 2000 .

[2]  Tosio Kato.  Perturbation theory for linear operators , 1966 .

[3]  Dietmar Bauer,et al.  Asymptotic properties of subspace estimators , 2005, Autom..

[4]  Kenji Ikeda.  On the precision of the plant estimates in some subspace identification methods , 2014 .

[5]  W. Scherrer,et al.  LOCAL OPTIMALITY OF MINIMUM PHASE BALANCED TRUNCATION , 2002 .

[6]  Michel Verhaegen,et al.  Filtering and System Identification: Frontmatter , 2007 .

[7]  Lennart Ljung,et al.  Some facts about the choice of the weighting matrices in Larimore type of subspace algorithms , 2002, Autom..

[8]  K. Ikeda.  Error analysis of state approaches in subspace identification methods , 2014, 2014 Proceedings of the SICE Annual Conference (SICE).

[9]  Patrick Dewilde,et al.  Subspace model identification Part 1. The output-error state-space model identification class of algorithms , 1992 .

[10]  M. Deistler,et al.  The Analysis of the Asymptotic Variance of Subspace Algorithms , 1997 .

[11]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

[12]  Bart De Moor,et al.  A unifying theorem for three subspace system identification algorithms , 1995, Autom..

[13]  Dietmar Bauer,et al.  Analysis of the asymptotic properties of the MOESP type of subspace algorithms , 2000, Autom..

[14]  Bart De Moor,et al.  N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems , 1994, Autom..

[15]  Alessandro Chiuso,et al.  On the ill-conditioning of subspace identification with inputs , 2004, Autom..

[16]  Dietmar Bauer,et al.  Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs , 1999, Autom..

[17]  A. Chiuso,et al.  The asymptotic variance of subspace estimates , 2004 .

[18]  Kenji Ikeda.  Asymptotic Properties of MOESP-Type Methods , 2013, ALCOSP.

[19]  Michel Verhaegen,et al.  Identification of the deterministic part of MIMO state space models given in innovations form from input-output data , 1994, Autom..

[20]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  M. Verhaegen.  Subspace model identification Part 2. Analysis of the elementary output-error state-space model identification algorithm , 1992 .

[22]  Gene H. Golub,et al.  Matrix computations , 1983 .