Continuous-time canonical state-space model identification via Poisson moment functionals

In this paper, a method is presented for estimating continuous-time state-space models for linear time-invariant multivariable systems. The proposed method does not require the observation of all state variables which is seldom the case in practice. The Poisson moment functional approach is used to handle the time-derivative problem. It is shown that the simple least-squares algorithm always gives asymptotically biased estimates in the presence of noise. An instrumental variable algorithm based on Poisson moment functionals of system signals is then developed for reducing the bias of the parameter estimates. The least-squares and instrumental variable algorithms are evaluated by means of a numerical example through Monte Carlo simulations.