Maximum Likelihood Least Squares Estimation For Equation-Error Type Models

With the development of system identification theory,maximum likelihood identificationalgorithm has been widely developed in recent years,especially in the area of Spacecraft,robots,power,chemical and SO on Therefore,the iilaxiiiluiil likelihood identification algorithm of thesystem model has important theoretical and practical value The thesis is based on''TheNational Nature Science Foundation of China"．and the maximum likelihood identificationalgorithm systems are presented based on equation-error models The existing literatures isjust identified the maximum likelihood method of a simple ARMAX system,This is becausethe noise is a moving average process(that is,the noise transfer function is a polynomial model)As the noise term of the dynamic adjustment system model and the controlled autoregressiveautoregressive Moving average system model are both a rational fraction transfer function．Thisis just one of the difficulties in the identification problems in the papers After reviewing therelevant ljteratu re the jnnovatjon research result in the thesis as follOWS:l According to the dynamic adjustment system,firstly,the system identification model was derived secondly,the criteria function of the model was written based on the iilaxiiiluiil likelihood identification algorithm Then the Davidon Fletcher Powell(DFP)identifi—cation algorithm of the dynamic adjustment model was proposed The simulation results2 Based on the principles of iterative identification,An Newton Raphson algorithm with filtering and an recursive iilaxiiiluiil likelihood estimation algorithm are obtained for the dynamic adjustment system The simulation results indicate that the Newton Raphson algorithm with filtering and the recursive iilaxiiiluiil likelihood identification algorithm of the dynamic adjustment models are effective,Also,the recognition accuracy of recursive iilaxiiiluiil likelihood identification algorithm is better than the recursive generalized least squares identification algorithm3 For the controlled autoregressive autoregressive Moving average system model,the DFP identification algorithm,the Newton Raphson algorithm and the recursive maximum likeli- hood estimation algorithm are derived As the autoregressive autoregressive moving average system model is the most general form of the equation error class model system There- fore．identification Mgorithms fOr the derivation of the models is more general than othersFinally,the simulation results verify the feasibility of the proposed algorithmsIn suiiliilary,in the paper several identification algorithms are researched and derivedbased on the equation error class models,and the corresponding examples are simulated bythe Matlab software,The simulation results illustrate that these identification algorithms cancan effectively identify the parameters of the equation error class models Finally,the papersuininarizes and prospects the results,also,make a brief on the difficulties of the subject andthe direction to be in-depth study For example,the iilaxiiiluiil likelihood estimation algorithmsare applied in practical areas...