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《Acta Geodaetica Et Cartographic Sinica》 2005-03
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Investigation on Solutions of Ill-conditioned Problems in Rapid Positioning Using Single Frequency GPS Receivers

WANG Zhen-jie~1, OU Ji-kun~2, LIU Lin-tao~2(1. School of Architectural Engineering, Shandong University of Technology,Zibo 255049, China; 2. Institute of Geodesy and Geophysics, Chinese Academy of Sciences,Wuhan 430077, China)  
A new approach is proposed for ill-conditioned problems in rapid positioning using single frequency GPS receivers. First, an appropriate regularizer R is chosen to weaken the ill-condition of the normal equation based on TIKHONOV regularization method, according to the characteristics of the normal equation formed by DD (double difference) phase observations of the single frequency GPS receivers. The float ambiguity solutions calculated by the new approach are much closer to the correct integer ambiguities than those calculated by LSE; in the meantime, corresponding MSEM (Mean Square Error Matrix) is obtained. Then, combined with LAMBDA method, the new approach can fix the integer ambiguities correctly and quickly using MSEM instead of the covariance matrix to determine the ambiguity search space. At last, the baseline vector is resolved. The effect of the new approach is illustrated by one numerical example. The comparisons are made between the new approach and LSE, RE (Ridge Estimate) and TSVM (Truncated Singular Value Method) combining with LAMBDA method to fix the integer ambiguities, respectively. The results show that: the success rate of fixing the integer ambiguities is high and the fixed ambiguities are reliable using the new approach; the new approach shortens the observation span and thus boosts the efficiency in rapid positioning.
【Fund】: 国家自然科学基金资助项目(40474009);; 中国科学院百人计划资助项目(2003)
【CateGory Index】: P228.4
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