Two-Stage Least Squares Identification For Stochastic Systems With Colored Noises

The thesis is based on the Project "Study of Modelling and Identification of a Class of Nonlinear Systems"(National Nature Science Foundation of China) and presents the title "Iden-tification for Stochastic Systems with Colored Noises".It is not only significant in theory,but also potentially values in applications.The author researches and reads lots of related references in the literature and study "Two-Stage Least Squares Identification for Stochastic Systems with Colored Noises".The main contributions are as follows.1.In order to improve the parameter estimation accuracy,the thesis uses the interactive esti-mation theory in the hierarchical identification to present a least-squares-iterative algorithm for the controlled ARAR models(CARAR models),namely,dynamical adjusting models. The basic idea is to replace the unmeasurable noise terms in the information vector/matrix with their estimation values which are computed iteratively by using the preceding parameter estimates.Comparing with the popular recursive generalized least squares algorithms, the proposed iterative algorithms make sufficient use of all data at each iteration and thus can produce more accurate parameter estimates and have faster convergence rate.Simulation results are gives.2.For stochastic systems decribed by the dynamical adjusting models,the thesis presents a new-type least-squares-iterative algorithm of identifying the system parameter vector and noise parameter vector,respectively.The basic idea is to derive the least squares estimation of these two parameter vectors by minimizing the criterion function with the information matrix containing unknown noise terms,which are replaced with their corresponding iterative estimation residuals computed by using the preceding parameter estimates.They perform a hierarchical computational process.Comparing with the recursive generalized least squares algorithms with data filtered by using the estimated noise models,the proposed iterative algorithms are also suitable for on-line identification and make enough use of all data at each iteration and thus highly accurate parameter estimates can be obtained.3.Based on the two iterative least squares principle above,two least-squares-iterative algorithms are developed for CARMA models,namely,controlled autoregression and moving average models and input error models.These two iterative algorithms can improve the parameter estimation accuracy.For CARARMA models,two least-squares-iterative algorithms are developed by using the interactive estimation theory in the hierarchical identification to present two least-squares-iterative algorithms.The simulation results indicate that the proposed algorithm can produce high accurate parameter estimation.4.Many nonlinear systems can be modelled by a Hammerstein model or Wiener models. The thesis developed two least-squares-iterative identification algorithms to identify Ham- merstein nonlinear systems with linear dynamical blocks described by CARAR models. Simulation example confirms the theoretical results.All in all,the thesis mainly studies two-stage identification methods based on the interactive estimation theory in the hierarchical identification principle for linar or nonlinear model with colored noises.Comparing with existing recursive identification,the proposed algorithms have obvious advantages.Finally,many simulation examples are included.