Linear multivariable identification using observable state space parameterizations

The selection of a suitable parameterization for the plant model, a crucial step in the identification of multivariable systems, has direct impact on the numerical properties of the parameter estimation algorithm. We employ a parameterization, particularly suitable for system identification, which has the following properties: observability, match-point controllability, and matchability. Using it, the number of model parameters is kept to a minimum, no undesired pole-zero cancellations can appear, and the use of nonlinear estimation is not necessary. We relate this parameterization to classical autoregressive model structures, and propose an algorithm for parameter estimation. By means of Monte Carlo simulations it is found that the algorithm is promising: fewer data points and lower signal-to-noise ratio are required to obtain results that are similar or better than those obtained by traditional methods.