Iterative Identification For CARMA Models And Output Error Models

Based on the Project "Study of Modeling and Identification of a Class of Nonlinear Systems (The National Nature Science Foundation of China)", this thesis studies identification methods for the CARMA models and output error models with significant theroy and potential values in applications. The results are as follows:1. Based on the iterative least squares principle, two identification algorithms, a least-squares-iterative and an iterative gradient based are developed for CARMA models. Compared with the recursive least squares algorithms and the recursive stochastic gradient algorithm, these two iterative algorithms use all measured input-output data at each iteration, and thus have high accurate parameter estimation and faster convergence rates. The basic idea of the iterative methods is to adopt the iterative estimation theory and hierarchical identification principle, the parameter estimates rely on the noise estimates, and the noise estimates are computed by the preceding parameter estimates. This performs a hierarchical computation processes.2. Based on the iterative least squares principle, two identification algorithms, a least-squares-iterative and an iterative gradient based are developed for output error models. Compared with the auxiliary model based recursive least squares algorithm and auxiliary model based stochastic gradient algorithm, these two iterative algorithms use all measured input-output data at each iteration, and thus have higher accurate parameter estimation and faster convergence rates.3. Extending the iterative algorithms for output error models to the Hammerstein nonlinear output error models consisting of memoryless nonlinear blocks plus a linear dynamical block described by output error models, we give a least-squares-iterative algorithm by fixing the first coefficient of the nonlinear function to unity.4. Apply the iterative algorithms proposed to a kind of non-uniformly sampled-data systems. The state-space model is estabilished and then according to the transform relation between the transfer function and the state-space model, we derive the transfer function of non-uniformly sampled-data systems and give an iterative identification algorithm.The simulation results indicate that all proposed algorithms can produce higher accurate parameter estimation than existing recursive identification algorithms.