基于样条迭代随机建模的高精度星间相对定位方法

A High-Precision Inter-satellite Relative Positioning Method Based on Spline Stochastic Modelling

利用GPS确定星间相对位置,在无法得到精确的卫星相对运动动力学模型时,事后处理一般采用最小二乘方法,但实际应用时该方法采用的随机模型没有考虑实测GPS数据的异方差、时间和空间相关特性.为提高相对定位精度,本文提出了一种利用样条函数模型进行迭代随机建模的相对位置确定方法,即先根据相对位置参数的连续特性,建立基于样条表示的函数模型;然后根据历元差分原理消除原始双差GPS观测量的时间相关性;再利用MINQUE方法求解去相关GPS观测量的方差-协方差分量,最后利用LAMBDA方法固定整周模糊度并确定相对位置.实验仿真得到两个结论:(1)函数模型的样条表示不仅有利于消除动态条件下测量量的时间相关性,而且能起到节省参数、平滑噪声的作用,因此可大大提高相对定位的精度;(2)在样条函数模型的基础上,采用MINQUE方法迭代随机建模,能进一步提高相对定位精度.

when GPS is used to determinate the inter-satellite relative position and the precise dynamic model of inter-satellite relative movement cannot be obtained, the least square method is usually used in the post data processing, but in practice, the stochastic model used by LS method do not take into account the characteristic of heteroscedastic, space- and time-correlated of real GPS measurements. In order to solve this problem and improve the positioning precision, this paper proposes a new relative positioning method, which first founds the spline function model based on the continuity of the relative position, then eliminate the time correlation of GPS double-difference measurements based on epoch-difference theory, then uses MINQUE to solve variance-covariance components of de-correlated GPS measurements iteratively, finally uses LAMBDA to fix the integer ambiguities and determinates the relative position. The experiment simulation gets two conclusions： （1）spline function model can not only benefit eliminating time correlation of GPS measurements in dynamic condition, but also improve the relative positioning precision greatly because of its functions of saving the number of tmknown parameters and smoothing noise; （2） the iterative stochastic modeling using MINQUE method can improve relative positioning precision more based on spline function model.