Least Squares Parameter Estimation For Multivariable Equation-Error Models

In industrial control, multivariable systems can be found almost everywhere, so the re-searches of multivariable systems identification methods appear more realistic academic signif-icance. And multivariable equation-error model is an important kind of multivariable systems.Based on the least squares identification method, this thesis researches the parameter estima-tion of multivariable equation-error models. By consulting a number of relevant literature andconducting the deep research, the achivements can be obtained as follows:1. Combining least-square principle with iterative identification technology, least squares basediterative algorithms are proposed based on multivariable equation-error models with col-ored noises. Equation-error models exist unknown noise terms in the information vector,and iterative identification can be used for identification system with unknown items in theinformation vector. By means of the interactive estimation theory in hierarchical identifi-cation principle, iterative estimated residuals depend on the unknown noise terms, whichare computed through the preceding parameter estimates. Comparing with recursive leastsquare algorithms, the proposed algorithms make full use of all the measured data informa-tion in the system at each iteration process and obtain more accurate parameter estimation.2. Based on the data filtering and the least-square principle, filtering based least squares algo-rithms are derived for multivariable equation-error models with colored noises. The basicidea is to choose the appropriate filter according to the specific models to filter input-outputdata, and obtain two identification models from the model, a system model containing sys-tem parameter and a noise model containing noise parameter, then use recursive leastsquares algorithms respectively, and estimate the system model and noise model parame-ters, with the uncertain colored noises and white noises in the information vector replacedby their estimates. Comparing with general recursive least squares algorithms, the pro-posed algorithms can not only identify system parameters, but also can get noise modelparameter estimations. The system is divided into two models with white noise interfer-ence respectively, the dimensions of their covariance matrices become smaller than generalrecursive least squares algorithms, thus can get higher computing effciency and producemore accurate parameter estimation.In conclusion, this thesis deduces least squares based iterative algorithms and filteringbased least squares algorithms based on multivariable equation-error models in theory, and the simulation results indicate and analyze the proposed algorithm are effectiveness and superiority.Finally a simple conclusion and prospect summarizes the characteristics of two algorithms, alsopoints out that there exist some insuffcient in the thesis and the further work needs to be morein-depth research.