Biased Estimate A Number Of Issues

As we know, the ill-conditioning problem is present in data processing of geodesy networks adjustment, GPS (Global Positioning System) fast orientation, geodesy inversion and distortional inspecting networks. Moreover, its damage is serious. If the ill-conditioning is really existence in adjustment model, we must take measures to remove or weaken its influence in order to gain good precisions of parameters estimator and adjustment production. In order to get this, some useful explorations on how to analysis and solve the problem of the ill-conditioning have been made and several biased estimators have been put forward. In fact, analyzing the essence, overcoming the effect of ill-conditioning and obtaining more accurate and stable parameters estimator is an new task in GPS surveying data processing, which have been determined as an important studying field in contemporary surveying error theory and engineering data processing by the International Association of Geodesy (IAG).In order to reduce the deficiencies of ridge estimator, Stein shrunken estimator and principal component estimator, two new biased estimators, so-called combining ridge and shrunken estimator, and, combining ridge and principal component estimator, are constructed respectively. Their good properties in the mean squared error and the numerical value stability are investigated, the determination of biased parameter of the estimators are discussed, and some important conclusions are obtained, respectively. Theory analysis and the computational results demonstrate that the two estimators potential estimator in surveying adjustment.The comparisons between the two most important biased estimators, ordinary ridge estimator and principal components estimator, and LS estimator are conducted by using the criterion of mean squared error; and the conditions to show the superiority of each of these two estimators over the LS estimator have been obtained. Then, the tests have been suggested to verify whether or not these conditions hold in given situations by using the statistical method. Finally, the computational results demonstrate that the problem of selection between biased estimator and least squares estimator can be solved effectively by using the hypothesis testing approach.In order to combat the influences of both outlier and ill-conditioning on geodetic adjustments, a new robust-biased estimation method is proposed by combining quasi-accurate detection (QUAD) of gross error and biased estimation. Several selection schemes of the biased parameters included in the biased estimators based on QUAD are given in detail. A numerical example illustrates that the new robust-biased estimation method not only can resist the bad influence of outlier and effectively overcome the difficulty caused by ill-conditioning simultaneously, but also is far more accurate than LS estimation, biased estimation, robust estimation and generalized shrunken type-robust estimation.The influence analysis is studied in the ordinary ridge estimator. The cross influence and theaction of masking, boosting, reducing, enhancing, etc, among the surveying data are discussed under the Cook distance. The essence relationship among the observation data is shown out and a new approach to outlier identification is found.At last the paper summarizes the research productions and the next development direction.