基于GPS矢量观测信息的姿态确定算法

摘要

The vectorized algorithms for GPS based attitude determination can be equivalent to a two-level optimal estimation problem. In the first level estimation the GPS carrier phase measurements can be converted to the vector observations in a sense of least squares. The second level estimation is the Wahba's problem which describes how the attitude matrix can be derived from the vector observations. In contrast to the traditional algorithms resolving the Wahba's problem through the quaternion approach,e.g. the QUEST method, this paper presents an iteration method to resolve the Wahba's problem through the small-angle approach. The two-level optimal estimation turns out to be globally optimal under the so-called balanced constellation condition or the balanced baseline condition. The experiment results show that the iteration method can produce the solution of the same accuracy as the solution derived from the QUEST algorithm. The improved TRIAD algorithm is also presented and evaluated in the experiments.%用于GPS姿态确定的矢量化算法可等价于两级最优问题.第一级把GPS载波相位观测量转换为矢量观测量.第二级是Wahba问题,即从矢量观测量获得最佳姿态解.Wahba问题可用四元数法求解,如QUEST方法.本文采用基于小角度的迭代法求解Wahba问题.在均衡星座或均衡基线条件下,两级最优解亦是全局最优解.实验结果表明迭代解的精度与QUEST解相同.实验中也应用了改进的TRIAD算法以比较两级最优解.