Research Of The Ill-conditioned Problem In Single Frequency GPS Positioning With Carrier-phase Measurements

This thesis focuses on problems encountered in the GPS baseline fast resolution, including the ill-conditioned problem in the normal equation and methods of using priori information.The wide application of GPS has motivated the research of GPS positioning. One of the most important means of GPS positioning is realized by GPS baseline fast resolution, which can get relative high precise position results in short time. But there are some problems in the baseline fast resolution, one of which is that the normal equation of the model is ill-conditioned as the observation time is not long enough. The ill-conditioned problem will obviously reduce the precision. Therefore, this paper researches on methods of overcoming the ill-posed problems to improve the positioning results with single frequency obvservations.This paper mainly focuses on following aspects:1. Present the research status of ill-conditioned problem in solving equations. Analyze reasons and characteristics of the ill-conditioned problem in the GPS carrier phase equation set. Introduce the methods to resolve this problem and summarize main approaches.2. Introduce the ridge estimate theory and algorithm. Methods of choosing ridge parameter are presented, some of which are used to resolve the carrier phase equation of GPS baseline and the results are analyzed. After that, we try to find the best ridge parameter which can make the estimate value more closely to the real value. The analysis of the best ridge parameter and the computation results are presented.3. The modified ridge estimation is introduced to overcome the ill-conditioned problem. As the modified ridge estimation need priori information, the ambiguity computed from CA code is brought in as the information. Then, some methods are used to choose the ridge parameter, containing the Course method and the Variance Components Estimation. At last, contrastive analysis of their results is presented.4. Considering the priori information can overcome the problem of ill-conditioned equation very well, we bring in the known height information which is common in GPS usage to help solve the carrier phase equation. Two methods of using the known height information are introduced, one of which is to resolve the baseline in topocentric coordinate system and the other one is adding a constraining equation to the carrier phase equation set. The computation results are analyzed.