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导航卫星速度和加速度的计算方法及精度分析

李显1,吴美平2,张开东曹聚亮1,黄杨明4   

  • 收稿日期:2012-06-11 修回日期:2012-08-29 出版日期:2012-12-25 发布日期:2013-04-17
  • 通讯作者: 李显

Navigation Satellites Velocity and Acceleration Computation: Methods and Accuracy Analysis

  • Received:2012-06-11 Revised:2012-08-29 Online:2012-12-25 Published:2013-04-17

摘要:

导航卫星自身的速度和加速度的计算是利用GNSS解算用户速度和加速度的前提和关键,其计算精度也直接影响解算结果。系统分析和总结了基于广播星历和精密星历的导航卫星速度和加速度的计算方法,包括:(1)基于广播星历的公式法;(2)基于导航卫星位置序列的数值差分法;(3)基于导航卫星位置序列的解析差分法。首先在基于广播星历的公式法中,推导了Kepler根数型、GEO型、位置-速度型等三类广播星历计算卫星速度和加速度的解析计算公式,通过比较表明:(1)广播星历解析公式总体计算精度较低;(2)位置-速度型广播星历的加速度计算精度高,而Kepler型广播星历的速度计算精度高;(3)高轨道卫星的速度、加速度计算精度优于中轨卫星。进一步分析了基于精密星历的数值差分法和解析差分法的卫星速度和加速度的计算方法,两种方法的比较研究表明,解析差分法虽然在计算效率上具有优势,但利用短期位置序列建立的解析模型难以表达卫星的真实轨道特征,导致计算的卫星速度较数值差分法低,但两者的加速度计算精度相当。最后通过来自于连续运行参考系统(Continues Operational Reference System, CORS)站点上的实测数据对上述各方法的计算精度进行了评估和比较,表明数值差分法具有最高的速度和加速度计算精度,在高精度应用中应尽量采用。

关键词: 关键词:速度, 加速度, 精度分析, 数值差分, 解析差分, 广播星历, GNSS

Abstract:

The velocities and accelerations computation of the navigation satellites is the prerequisite of the velocities and accelerations determination of the receivers. This paper made a systemic analysis of the different methods to calculate the velocities and accelerations of the navigation satellites, including (1) the closed analytical method based on broadcast ephemeris; (2) the numerical differencing method based on position series of the satellite; (3) the analytical differencing method based on position series of the satellite. Firstly, the analytical expressions were deduced based on broadcast ephemeris, three types of broadcast ephemeris, including Kepler elements, GEO, and position-velocity type are discussed. The results can be drawn from precision comparison as follows: (1) The accuracy of velocity and acceleration derived from broadcast ephemeris is relative low, and can not match the high precision applications, such as airborne gravimetric measurement; (2) The acceleration accuracy is higher derived from position-velocity broadcast ephemeris while the Kepler type has higher velocity accuracy; (3) the orbit height is one of the factors of the computation precision. Then, the analytical differencing and numerical differencing based on precision ephemeris to derive velocities and acceleration were analyzed and compared, the results shows that although the analytical method has advantages on efficient, the velocities computation precision is lower for the orbit analytical model built from short term position series is inaccurate, however, the acceleration computation precision compared to the numerical differencing method. In high precision applications, numerical differencing methods should be used for its highest velocity and acceleration computation accuracy. Finally, a static experiment is conducted which data from two CORS (Continues Operational Reference System) stations to evaluate and compare the computation accuracy among the methods mentioned above.

Key words: Key words:velocity, acceleration, accuracy analysis, numerical differencing, analytical differencing, broadcast ephemeris, GNSS

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