Analysis of state space system identification methods based on instrumental variables and subspace fitting (original) (raw)

Subspace-based State Space System IDenti cation (4SID) methods have recently been proposed as an alternative to more traditional techniques for multivariable system identi cation. The advantages are that the user has simple and few design variables, and that the methods have robust numerical properties and relatively low computational complexities. Though subspace techniques have been demonstrated to perform well in a number of cases, the performance of these methods is neither fully understood nor analyzed. Our principal objective is to undertake a statistical investigation of subspace based system identi cation techniques. The studied methods consist of two steps. The subspace spanned by the extended observability matrix is rst estimated. The asymptotic properties of this subspace estimate are derived herein. In the second step, the structure of the extended observability matrix is used to nd a system model estimate. Two possible methods are considered. The simplest one only uses a certain shift-invariance property, while in the other method a parametric representation of the null-space of the observability matrix is exploited. Explicit expressions for the asymptotic estimation error variances of the corresponding pole estimates are given.