SUBSPACEIDENTIFICATION ALGORITHMS FOR THE STOCHASTIC PROBLEM 1
Peter Van Overschee Bart De Moor 2
3
ESAT , Department of Electrical Engineering , Katholieke Universiteit Leuven Kardinaal Mercierlaan 94 , 3001 Leuven (Heverlee) , Belgium tel: 32/16/220931 fax: 32/16/221855 email:
[email protected] ,
[email protected]
Abstract In this paper, we derive a new algorithm to consistently identify stochastic state space models from given output data without forming the covariance matrix and using only semi-innite block Hankel matrices. The algorithm is based on the concept of principal angles and directions. We describe how they can be calculated with only QR and QSVD decompositions. We also provide an interpretation of the principal directions as states of a non-steady state Kalman lter.
1. Introduction Let yk 2
