基于TIKHONOV正则化的白化滤波快速解算模糊度方法

An improved whitening filter algorithm for GPS rapid ambiguity resolution based on TIKHONOV regularization principle

提出了只利用少数历元的GPS单频相位数据快速定位的新方法,主要从两方面考虑:一方面基于TIKHONOV正则化原理,通过构造合理正则化矩阵来减弱法方程的病态性,得到较准确的模糊度浮动解及其相应的均方误差阵;另一方面采用改进的白化滤波方法固定模糊度.与一般白化滤波方法不同,本文对均方误差阵进行白化处理解算模糊度,然后对检验通不过的模糊度采用LAMBDA中的条件最小二乘方法进行搜索,可以有效提高模糊度解算成功率.

A new efficient approach for rapid differential GPS positioning using only few-epoch single frequency GPS data was proposed. It was considered from two sides. On the one hand, the ill condition of the normal equation was weakened by proper selection of a reasonable regularizer based on TIKHONOV regularization principle and much precision float ambiguities were obtained. On the other hand, the correct integer ambiguities were fixed using improved whitening filter method. Different with the normal whitening filter technique, the improved one proposed utilizes Mean Square Error Matrix （MSEM） instead of the covariance matrix to determine the ambiguity search space. After that, the correct ambiguities must be searched using conditional least square method employed in the famous LAMBDA method if the fixed ambiguities cannot pass hypothesis test. Therefore, this improved whitening filter method can obviously raise success rate of integer ambiguities.