一种改进型的GPS单频整周模糊度快速解算方法

针对高精度的快速定位中观测矩阵存在病态性问题，研究了单频GPS整周模糊度快速解算方法。依据Tikhonov正则化原理和奇异值分解(SVD)的扰动性质，设计了SVD分解的改进算法，避免了因较小奇异值发生较大抖动而使正则化矩阵出现不稳定的情况；在分析法矩阵病态性特点的基础上，设计了正则化矩阵的构造方法，并从理论上证明了其优越性。实验结果表明，与传统方法和Tikhonov正则化-LAMBDA法相比，新算法能更有效地改善法矩阵的病态性，只利用3～5个历元即能实现模糊度浮点解的快速解算及其固定，且结果可靠，浮点值更加接近真实值。

An Improved Method for Rapid Ambiguity Calculation Using Single Frequency GPS Receiver

Aimed at ill-condition observation matrix in precise rapid positioning, a new algorithm for ambiguity resolution using single frequency GPS receiver was studied. According to the principle of Tikhonov regularized algorithm and the perturbation theory of singular value decomposition, an improved algorithm for singular value decomposition (SVD) was designed, and then the non-stabilization on regularized matrix caused by little singular values was avoided. The improved regularized matrix was educed, the construction method was established on the basis of analyzing the characteristics of ill-condition matrix, and it was proved theoretically. The experiment results indicate that the improved algorithm is more effective to improve ill-condition observation matrix, comparing with conventional LAMBDA algorithm and Tikhonov regularized-LAMBDA algorithm; the more precise floating-point and fixing-point solutions can be acquired quickly and credible.