卫星轨道误差对定位精度影响的摄动分析方法

Study on Perturbation Analysis Method of the Influence of Satellite Orbit Error on Positioning Accuracy

卫星导航系统定位精度受伪距测量误差、大气时延误差、卫星原子钟钟差及卫星轨道误差等多方面因素综合影响。传统通常采用基于精度因子与用户等效伪距误差的方法对定位误差进行评估,但在其精度表征公式推导过程中需对测量方程组系数矩阵H及用户等效伪距误差分布做若干假设,因此它实际上是一个近似评估公式。此外,各类误差源中的卫星轨道误差属于三维误差,需经过坐标转换,并利用经验参数模型才能换算至用户等效伪距误差。为此,提出采用矩阵摄动数学理论研究卫星轨道误差对定位方程组解的影响,利用谱范数条件数对方程组形态进行刻画。仿真结果表明,方法能够直接反映卫星轨道误差对定位精度的影响,无需进行轨道坐标及用户等效伪距误差换算,能够更加直接和准确地评估卫星轨道误差对定位解精度的影响。

GNSS positioning accuracy is affected by pseudo-range measuring error, atmospheric time-delay error, satellite atomic clock error and satellite orbit error, et al. Traditionally, the DOP and UERE parameters are used to estimate positioning error. However, several assumptions are needed in the derivation process of precision representation formula, thus it is actually an approximate estimating formula. In addition, the satellite orbit error of various error sources belongs to three-dimensional error, which requires coordinate transformation and experience parameter model to switch to UERE. Therefore, the paper proposes using matrix perturbation mathematical theory to study the influence of satellite orbit error on positioning accuracy; and describes equation form by conditional number using spectral norm. The simulation result demonstrates that this method can reflect the influence directly without transformation of orbit coordinate and UERE error so that it is more direct and precise to assess the influence of satellite orbit error on positioning accuracy.