A LINEAR-REGRESSION APPROACH TO STATE-SPACE SUBSPACE SYSTEM-IDENTIFICATION

Recently, state-space subspace system identification (4SID) has been s uggested as an alternative to the more traditional prediction error sy stem identification. The aim of this paper is to analyze the connectio ns between these two different approaches to system identification. Th e conclusion is that 4SID can be viewed as a linear regression multist ep-ahead prediction error method with certain rank constraints. This a llows us to describe 4SID methods within the standard framework of sys tem identification and linear regression estimation. For example, this observation is used to compare different cost-functions which occur r ather implicitly in the ordinary framework of 4SID. From the cost-func tions, estimates of the extended observability matrix are derived and related to previous work. Based on the estimates of the observability matrix, the asymptotic properties of two pole estimators, namely the s hift invariance method and a weighted subspace fitting method, are ana lyzed. Expressions for the asymptotic variances of the pole estimation error are given. From these expressions, difficulties in choosing use r-specified parameters are pointed out. Furthermore, it is found that a row-weighting in the subspace estimation step does not affect the po le estimation error asymptotically.