单频GPS快速定位中病态问题的解法研究

研究只利用少数历元GPS载波相位观测值进行快速定位时的新解法.在分析病态法矩阵结构特性的基础上,基于TIKHONOV正则化原理,提出一种选择正则化矩阵R的新方法,减弱法方程的病态性.与其他方法相比,新方法得到与模糊度准确值更接近的浮动解及其相应的均方误差矩阵.结合LAMBDA方法,用均方误差矩阵代替协方差阵确定模糊度的搜索范围,可准确快速地确定模糊度,最后得到基线向量的解.结合算例,将新解法与最小二乘估计、岭估计和截断奇异值法分别结合LAMBDA方法解算模糊度的结果进行比较分析,展示新解法的效果.

Investigation on Solutions of Ill-conditioned Problems in Rapid Positioning Using Single Frequency GPS Receivers

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.