Comparison of Prediction-Error-Modelling Criteria

Single and multi-step prediction-error-methods based on the maximum likelihood and least squares criteria are compared. The prediction-error methods studied are based on predictions using the Kalman filter and Kalman predictors for a linear discrete-time stochastic state space model, which is a realization of a continuous-discrete multivariate stochastic transfer function model. The proposed prediction error-methods are demonstrated for a SISO system parameterized by the transfer functions with time delays of a continuous-discrete-time linear stochastic system. The simulations for this case suggest to use the one-step-ahead prediction-error maximum-likelihood (or maximum a posteriori) estimator. It gives consistent estimates of all parameters and the parameter estimates are almost identical to the estimates obtained for long prediction horizons but with consumption of significantly less computational resources. The identification method is suitable for predictive control.