星图分布对星敏感器最小二乘姿态精度的影响

星敏感器的姿态确定是其导航最基本、最关键的环节。为了分析星图分布对最小二乘姿态测量精度的影响，描述了星敏感器的姿态角定义，研究了最小二乘法求解星敏感器姿态的过程，并从数学角度推导了存在一定观测误差的情况下，最小二乘方法产生较差姿态测量精度的部分主要原因，即系数矩阵的条件数变化。最后以星图模拟的方式在不同条件下模拟了三组典型的星图分布，对其进行姿态测量和结果统计。统计结果表明:姿态测量精度除了受条件数描述的导航星间相对位置的影响外，还与导航星组在星图中的不同位置以及不同的星敏感器参数模型有关。

Impact analysis of star distribution on least square attitude measuring precision in star sensor

As the highest measurement precision attitude sensor, attitude determination is the most basic and critical section in navigation. To analyze the impact of star distribution on least square attitude measuring precision, the definition of the attitude angle was described, the problem-solving process by least square method was researched, and the condition number of the coefficient matrix, that leads to poor precision under a certain observational error, was derived from the view of mathematical. Lastly, three sets of typical star distribution under different conditions were simulated, calculate the results and conduct the statistics, the simulation results indicate that measurement precision is influenced by different locations of the star group in image and different device parameter models for star sensor, besides the relative position of the star group described by condition number.