Measurement Adjustment System Diagnosis And Treatment Of Morbid

Generally, the ill-conditioning problem not only exists in global positioning 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 effect of ill conditioning 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 by the International Association of Geodesy (1AG).The dissertation begins with review of the main history of ill conditioning research. And then it emphatically discusses and investigates some problems concerning the mechanism analysis, the diagnostics, measurement and the processing of the ill-conditioning adjustment system. To weaken and overcome the ill effects, some methods and algorithms are suggested and illustrated.The concept of multicollinearity is put forward with variant and data column, respectively. The relation between ill conditioning and multicollinearity is discussed. The mechanism analysis of the ill-conditioning adjustment system is studied through classifying. And then the ill effects are discussed in the view of computation and statistics, respectively.A new diagnostics technique so-called stability analysis method is proposed. The Characteristics Analysis, the Condition Number and the Condition Indexes & Variance Decomposition Proportions Methods are discussed, respectively. How the parameterization and transformation influence on the ill conditioning adjustment system is studied then.A new biased estimator so-called Ridge Type-Generalized Inverse (RG1) estimator is constructed after summing-up the historical and present condition of biased estimation theory in surveying data processing. The prosperities of RG1 estimator are studied especially by Pitman's criteria. The other biased estimator so-called Partial Root Root (PRR) estimator is generated. The major characteristics of PRR estimator lie in that it is a partial shrunken estimator. Theory analysis and numerical simulation demonstrate that the two estimators can effectively improve the LS estimator.As we know, there exist some defects in solving normal equation system. In order to overcome the shortcomings, the singular-value decomposition method and its applications in direct solving theill-conditioning observation equation are studied. Based on the singular-value decomposition method, several schemes to readjust the singular value of design matrix are proponed through perturbation analysis, and a simulated example is studied for illustrating these schemes can overcome the ill effect when there exist ill conditioning among the columns of the design matrix. The problem of selecting the biased parameter is studied in every scheme.