Research On Morbid Problems Of GPS Baseline Solution

Classical least squares (LS) is the most widely used method in GPS data processing. While affected by many factors, the phenomenon of lack of observation information and over-parameterized model selection often appears, in this condition, the deviation of LS estimation with unknown parameters becomes larger which leads to the morbid state of the linear equation group and brings serious impact on calculation and statistics. It’s urgent to study the generating mechanism and diagnostic methods of morbid state linear equation group in the Surveying adjustment system. The problem of morbid state in the GPS surveying adjustment system is studied in this article, the main content include the following aspects:(1) The problem of morbid state in the surveying adjustment system is analyzed according to the perturbation theory of normal equation, and then the relation between morbid state and mean square error, multi-collinearity is respectively described, after summing up the courses of morbid state in surveying adjustment system, the advantages and disadvantages of various types of methods that diagnose and measure morbid state are studied.(2) The essence and difficulties of the biased estimate method and the direct solution method of morbid model are analyzed. The determination of ridge parameters with the means of ridge trace and L-curve in biased estimation is deep analyzed, and on this basis, an improved method of ridge trace is proposed, according to some examples, the reliable ridge parameter can be obtained with this improved method, which can be a reference for other scholars. Then the applicability of truncated singular value decomposition (TSVD) and corrected singular value method is analyzed according to the types of singular values.(3) The GPS data are firstly processed with LS estimation method to calculate the coefficient matrix of normal equation and the observed values, then the biased estimation method and the directly solution method of morbid model are applied to the GPS data processing according to the problems of the morbid state, finally, the results of data processing with different methods are compared and analyzed.The results indicate that the methods of ridge estimation and partial ridge estimation in biased estimation theory as well as the TSVD in the direct solution method of morbid model can obtain more accurate parameters and more reliable adjustment outcomes compared with LS estimate method when solving the problems of morbid state in GPS measurement. The quality of the processing of the measurement data will improved with these methods. The results provide a theoretical basis for the problem of morbid state in surveying adjustment system and make a foundation for the deeper study.