小波分析在单频GPS快速精密定位中的应用研究

Application study on wavelet analysis in single frequency GPS rapid precise positioning

单频GPS快速定位方程是严重病态的,应用最小二乘原理得到的模糊度浮点解大大偏离其准确值,应用LAMBDA方法难以正确地固定模糊度。本文将GPS载波相位双差观测量在不同的小波空间和尺度空间进行分解和重构,去除高频测量噪声,可减小测量噪声对GPS快速定位中病态方程解的影响,提高模糊度浮点解的精度,缩小模糊度搜索空间。实验表明,对于GPS短基线,仅利用1min左右的单频载波观测数据,经过基于haar、db4、coif4和sym4小波的5尺度小波变换后,可获得较准确的模糊度浮点解,应用LAMBDA法可正确地固定模糊度,达到厘米级定位精度。

The equations of single frequency GPS rapid positioning are seriously ill-conditioned, which causes float solutions of ambiguities have large deflection compared with accurate solutions using least-squares principle and the integer ambiguities cannot be correctly fixed using LAMBDA method. GPS double-differenced carrier observables were decomposed in different wavelet function and different scaling function based on wavelet transform, and the high-frequency noise was removed. Then the de-noised double-differenced observables were used to estimate unknown parameters to reduce the effect of measurement noise on the solution of ill-conditioned equations in GPS rapid positioning. So the precision of float solutions of ambiguities was improved and the searching space of ambigui- ties was reduced. The experiment results showed that the integer ambiguities can be correctly fixed using LAMBDA method only using about 1 min single frequency phase observables by five scaling wavelet transform based on haar, db4, coif4 and sym4 wavelet bases, and centimeter-level of positioning accuracy could be achieved.