The Method Of Parameter Estimation Based On Synthetically Diagnosing Of Multicollinearity

Generally, the multicollinearity problem not only exists in Global Position System (GPS) data processing, surveying adjustment, observation deformation analysis and Geodesy inversion, etc, but also its ill effects are very serious. How to analyze the essence, overcome the ill effects of multicollinearity and obtain more accurate and stable estimation of the unknown parameters are very important in many fields, such as GPS surveying data processing, and have been determined as an important studying field in contemporary surveying error theory and engineering data processing.At present, there are the methods of multicollinearity disposal, biased estimator and TIKHONOV regularization method, but both of them can't make use of the results of multicollinearity diagnosis and measurement. So the methods obviously lack effectiveness and pertinence.The dissertation which bases on systematically reviews the multicollinearity research history and research current situation, directly connect the results of multicollinearity diagnosis and measurement with the management of the multicollinearity problem; put forward some new parameter estimate methods, so that it can more pertinently weaken and overcome the ill effects of multicollinearity, better deal with the problem of multicollinearity. The main achievements which we get are as follows:(1) Combining condition index and variance decomposition proportion of multicollinearity diagnosis with signal-to-noise ratio of measuring multicollinearity, putting forward a new multicollinearity diagnosis method, (namely) synthetical diagnosis method, through this method, reasonably classifying the unknown parameters; toward the different use with the different methods; show clearly the correct work direction of more pertinently weakening and overcoming the ill effects of multicollinearity.(2) Basing on the multicollinearity synthetical diagnosis, put forward some new biased estimators, that is partial shrunken LS estimator, which based on synthetically diagnosing of multicollinearity. Its properties are discussed and three special forms-partial ridge estimator, partial principal components estimator and partial combined ridge with shrunken estimator are given. The determination of biased parameter in the partial ridge estimator is discussed too.(3) Basing on the multicollinearity synthetical diagnosis, put forward the regularization method of multicollinearity synthetical diagnosis; give elective methods of regularizer and definite formula of smoothing parameter.Largely numerical tests indicate that the methods of biased estimator and TIKHONOV regularization of multicollinearity synthetical diagnosis, aim at greatly weakening and overcoming the ill effects of multicollinearity, more effective than former methods.