Subspace angles between ARMA models

Abstract We define a notion of subspace angles between two linear, autoregressive moving average, single-input–single-output models by considering the principal angles between subspaces that are derived from these models. We show how a recently defined metric for these models, which is based on their cepstra, relates to the subspace angles between the models.

[1]  Richard J. Martin.  A metric for ARMA processes , 2000, IEEE Trans. Signal Process..

[2]  H. Hotelling.  Relations Between Two Sets of Variates , 1936 .

[3]  Michèle Basseville,et al.  Subspace-based fault detection algorithms for vibration monitoring , 2000, Autom..

[4]  Thomas Kailath,et al.  A view of three decades of linear filtering theory , 1974, IEEE Trans. Inf. Theory.

[5]  C. Jordan.  Essai sur la géométrie à $n$ dimensions , 1875 .

[6]  B. Moor,et al.  Subspace angles and distances between ARMA models , 2000 .

[7]  Stephen A. Dyer,et al.  Digital signal processing , 2018, 8th International Multitopic Conference, 2004. Proceedings of INMIC 2004..

[8]  Seamus D. Garvey,et al.  Parameter subset selection in damage location , 1997 .

[9]  B. De Moor,et al.  Subspace angles between linear stochastic models , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[10]  James Clary,et al.  Stochastic theory of minimal realization , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[11]  R. J. Martin,et al.  Autoregression and cepstrum-domain filtering , 1999, Signal Process..

[12]  John E. Mottershead,et al.  Combining Subset Selection and Parameter Constraints in Model Updating , 1998 .

[13]  G. Golub,et al.  The canonical correlations of matrix pairs and their numerical computation , 1992 .

[14]  R. Gittins,et al.  Canonical Analysis: A Review with Applications in Ecology , 1985 .

[15]  P. Graefe.  Linear stochastic systems , 1966 .