Recursive Computation Of The Criteiron Functions For Identiifcation Methods

Identifcation method is an important mean to solve the problem of system identif-cation, while the criterion function is a vital basis for the parameter estimation. Usingdiferent manners to optimize the criterion function, diferent parameter estimation al-gorithms could be obtained. This criterion function is the square sum of the diferencesbetween the system outputs and the model outputs. As a model can only describes themain characters of the system, we all wish the error between the model and the system aslittle as possible. The criterion function can characterize this error clearly. By updatingthe values of the criterion functions, the accuracy of the parameter estimation can bemeasured. This dissertation focuses on “Recursive Computation of the Criterion Func-tions for Identifcation Methods” and the proposed methods have important theoreticalsignifcances and academic value. The main results are described as follows.1. For the least squares algorithm of the scalar system, this dissertation studies the re-cursive calculations of the criterion functions of the recursive least squares algorithmand the fnite-data-window least squares algorithm. Giving a compare of the compu-tation load between the one-time calculational formula and the recursive algorithm forthe criterion function. According to simulation examples, the results of the criterionfunction obtained from the two kinds of computational formulas are compared. And,expanding that derived recursive computational formulas to the weighted recursiveleast squares algorithm, the forgetting factor least squares algorithm and the leastsquares parameter estimation algorithm for pseudo-linear regression models.2. The thesis derives the recursive computational formula of the cost function for recur-sive least squares algorithm with a forgetting factor for the multivariable regressionsystem. It is easy to fnd that the recursive formula of the criterion function has lesscomputation load. The derived recursive computational formula of the cost functioncan be extend to the multivariable recursive least squares algorithm, the multivariablefnite-data-window least squares algorithm with a forgetting factor and so on.3. To the multi-innovation least squares algorithm and the interval-varying multi-innova-tion least squares algorithm, the recursive computational formulas of the criterionfunctions of which can be derived. Meanwhile, the simulation results indicate thatthe proposed recursive algorithms are efective.In conclusion, the thesis makes a deep research on the recursive computationof the criterion functions for the type of the least squares parameter estimation al- gorithms. The exampled simulation results indicate that the value of the criterionfunction can well measure the accuracy of the corresponding algorithm, that meansthe proposed recursive algorithms are efective. However, for the other identifca-tion algorithms (i.e. the stochastic gradient identifcation algorithm and the iterationalgorithm), the identifcation algorithms for the nonlinear system, the simplifed com-putation for criterion functions of which need further study.