Structure and order estimation of multivariable stochastic processes

The author presents a procedure for estimating the structure of a state-space representation for a multivariable stationary stochastic process from measured output data. It is assumed that the observed vector time series is a realization of a process with rational spectrum or the output of a stable, invariant, linear system driven by white noise. While the main objective is the determination of the order and structure invariants, the procedure also furnishes estimates of the parameters of part of a canonical representation which can then be completed by standard algorithms and used as a model for the process or as initial conditions for an efficient identification scheme. The author proposes an algorithm which selects a maximal set of linearly independent rows of the Hankel matrix built upon the estimated covariance sequence. Simulation results are presented which confirm the effectiveness of the proposed procedure