Structure determination and parameter identification for multivariable stochastic linear systems

This paper will consider the problem of using output data to identify a constant, multivariable, stochastic linear system which has unknown dimension, system matrices, and noise covariances. In order to obtain consistent parameter estimates, we use the innovations representation for the output process, in which the system matrices are chosen in a certain (invariant) canonical form. A systematic procedure is described for estimating the system structure and parameters of the innovations representation. Simulation results are presented to illustrate the identification method. A large-sample error analysis of the identification method is also given.