ABSTRACT
This chapter presents the basic theory of a family of system identification procedures known generically as “subspace methods.” The aim of the subspace methods is to estimate the matrices of an state-space (SS) model given a series of input and output measurements. Subspace methods are a set of algorithms based on systems theory, linear algebra, and statistics, which estimate the parameters in an SS model. The basic idea of these methods consists of estimating the sequence of system states, without further information on the model dynamics. The chapter presents the assumptions required to set up the foundation of the subspace methods. It describes the procedures specifically adapted or designed for subspace methods. The chapter provides a fast and stable algorithm to estimate time series models written in their equivalent SS form. The algorithm is based on the subspace methods. The chapter presents examples to illustrate the performance of the subspace methods with univariate models and to identify a multivariate model.
