从编队卫星的高精度星间相对定位需求出发,基于未来全球导航卫星系统(GNSS)多频信号测量体制的发展,综合利用观测数据与待估参数的几何关系以及待估参数随历元连续变化的约束,根据函数逼近理论,提出基于多频GNSS观测的编队星间相对定位样条表示模型,给出多频数据相对于双频数据、样条表示模型相对于传统逐点模型在改善星间相对位置解算精度方面的理论基础与仿真实例。在复杂误差仿真条件下,通过三频观测数据与样条表示模型的结合,对星间相对位置的估计精度可达到毫米量级。在整周模糊度都正确固定的情况下,利用三频数据比双频数据的精度提高了10%以上,样条表示模型比逐点模型的精度提高了80%以上。
A relative positioning spline representation model based on multi-frequency global navigation satellite system (GNSS) is proposed to meet the demand of precise inter-satellite relative positioning for formation flying satellites and the employment of multi-frequency signal measurement scheme of future GNSS. This model is based on the function approximation and parameter-saving modeling theory. The geometric relationship between the observation data and the estimated parameters is utilized and combined with the constraints of the continuous variation of the estimated parameters with epochs. The theoretical basis and simulation results of the relative positioning precision improvement are presented. The advantages of multi-frequency data over dual-frequency data and those of the spline representation model over the traditional point-wise model are shown. Under the condition of complex error simulation, the relative position of the inter-satellite estimates reaches the accuracy of millimeter level by applying the triple-frequency observation data and the spline representation model. Once the ambiguity resolutions are fixed to the correct value, using triple-frequency data can improve the accuracy up to 10% higher than the dual-frequency data, and using the spline representation model can improve the accuracy up to 80% higher than the point-wise model.
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