Research On Analysis Theory And Application For Ⅱ Ill-Conditioned System

The ill-conditioned problem is one of the main factors affecting the quality of the parameters estimation, its harm is extremely serious, so analyzing the reason that the ill-conditioned produced and searching for mitigating measure is the problem which must be faced in the data processing work. In the geodetic survey, there are â…  or â…¡ two kinds ill-conditioned problems, but the â…¡ one plays the main role, especially with the application of the GPS localization and the navigation, the radarscope photograph survey and other advanced mapping technology, the ill-conditioned have already become one of the major influence factors to improve the space position's precision, so it is important to analysis and process â…¡ ill-conditioned.By analyzing and summarizing the existing research, this paper discusses â…¡ ill-conditioned in the geodetic survey.Analyzed the structures of observation spaces by use of G-S orthogonalizing method andthe measure theory on the distance or angle in H space. Deducted the measure methods of observation vector's relation by the numbers. Pointed out the difference and relation among different measurement methods, did research on the relations of the observation subspaces thoroughly. Put forward the geometry expressing and numerical calculating methods of observation space structures. Unveiled the spatial character and the essential of â…¡ ill-conditioned.Suggest the improving method of measuring information of observation by analyzing the structures of observation. By use of this method, we may measure the effect of observation vector to parameters estimate effectively, so this method is propitious to analyze the relation between observation validity and â…¡ ill-conditioned.The diagnosis method of â…¡ ill-conditioned was put forward in this paper. For the influence of individual observation to the ill-conditioned, the diagnosis method was put forward based on the projection matrix, for all observations the diagnosis method of â…¡ ill-conditioned was suggested based on volume U that observation vectors formed. In view of the positioning accuracy measurement index of GDOP in the GPS, analyzed its diagnosis significance of â…¡ ill-conditioned, and indicate the ill-condition essence in the GPS, and provide the important basis for taking the effective action to enhance positioning accuracy.