A note on LQ decomposition in stochastic subspace identification

Abstract

In this paper, we consider the role of LQ decomposition in the realization-based subspace identification method for discrete-time stochastic systems as a continuation of our earlier work [6] in deterministic setting. Under the assumption that the past horizon of the data matrix is infinite, we reveal a nice block lower triangular structure of a certain L-factor related to the stochastic component in the LQ decomposition. Adapting this theoretical result to finite input-output data, we derive an approximate method of identifying all the system parameters, including the steady state Kalman gain and the covariance of the innovation process, from L-factors of a single LQ decomposition of the data matrix. © 2010 Springer-Verlag Berlin Heidelberg.