Unbiased Estimate Of Theoretical Research And Its Application To Gps Data Processing

Although ill-conditioning problems extensively exist in various fields of surveying, they are mainly studied theoretically currently, which means they are not practical problem-oriented but theory-based. Aiming at applications of ill-conditioning problems in practice, this thesis concentrates on the process of fast positioning using GPS, of which the observation time is short and no big variations of positions of satellites can be observed, which result in ill-conditioning in the coefficient matrix of normal equation and unsatisfactory solutions by the Least Squares Estimation. As the ill-conditioning of the coefficient matrix can be reduced to complex co-linearity, it is not economical nor timely to reduce the complex co-linearity by elongating observation period. In order to solve the problem, we propose a method that applies the biased estimation in processing GPS phase observations. Based on the advantage that the biased estimation can overcome the strong correlation in normal matrix, the method tries to produce accurate float solutions of the ambiguity with less observation epochs, and thus improves the efficiency of ambiguity searching and shortens observation time. This thesis attempts to apply the biased estimation in the solution of the fast positioning of GPS. The main work is as follows.The baseline solution of double-difference of GPS observations if studied at length, in which advantages and disadvantages of various ambiguity searching as well as the concrete model of cycle-clip detection, are discussed, and the double-difference model is built up that suits short baseline solution for which the basic procedure and models are presented. Applicable software for baseline solution is made and the comparison with its commercial GPS counterparts shows that the software can be used in practice.A new robust biased estimation method, named the Robust Ridge-Type combined Major Component Estimation is proposed, which is based on the combination of the Ridge-Type Major component Estimation and the Robust M-Estimation model. The estimated values of adjustment parameters using the new method, as well as their a posteriori accuracy and the error functions, are derived. Results of computations show that the new method can not only reduce the ill-conditioning in the efficient matrix of normal equation, but also resist the interference of outliers within observations effectively, which makes the solutions of parameters both accurate and reliable.Aiming at the difficulty of the determination of ridge parameters in the biased estimation a new method for the determination of ridge parameters is put forward based on the Ridge Trace Method.Results of practical examples show that the new method is effective and excellent.Partial Ridge Estimation, which applies to the GPS fast positioning model,shares the difficulty of the determination of ridge parameters.Several methods of ridge parameters determination under the Partial Ridge Estimation Model are formulated, and their performance is also analysed.The ill-conditioning as well as its generation in the base-line solution model of double-difference of GPS observations is analyzed systematically based on the combination of biased estimation and GPS data processing, the formulation of the Ridge Estimation, the Partial Estimation, the generalized Ridge Estimation and the Major Component Estimation with respect to baseline data of double-difference of GPS observations of discussed and the applicability is also analyzed.