An efficient implementation of maximum likelihood identification of LTI state-space models by local gradient search

We present a numerically efficient implementation of the nonlinear least squares and maximum likelihood identification of multivariable linear time-invariant (LTI) state-space models. This implementation is based on a local parameterization of the system and a gradient search in the resulting parameter space. The output error identification problem is discussed, and its extension to maximum likelihood identification is explained. We show that the maximum likelihood framework yields parameter errors that converge to the Cramer-Rao bound. Furthermore, the implementation is shown to be fast and able to handle large sample size problems.