卫星自主导航中卡尔曼滤波算法改进与计算机仿真

Kalman Filtering Algorithm Improvement and Computer Simulation in Autonomous Navigation for Satellite

该文以基于组合大视场星敏感器的卫星自主导航方法为例,建立了在地球非球形下的状态方程,建立了组合大视场星敏感器的观测方程及卫星轨道摄动等数学模型,在状态最优估计周围对模型进行了线性化,滤波过程中将传统的广义卡尔曼滤波的一步预测算法修改为一步初步预测和一步初步预测的校正的滤波算法,在每步的推进计算中对均方矩阵的元素进行了平均值处理,避免舍入误差的积累造成其失去对称性、甚至负定性的可能;通过计算机仿真及结果分析,说明了改进的广义卡尔曼滤波算法对减小采样周期所带来的轨道误差有很好的效果,并使卫星位置和速度的均方差估计趋于稳定,在一定程度上能很好地克服离散误差对轨道估计精度的影响。

This paper makes a sample at autonomous navigation for satellite with a large field group of star sensors, gives a state equation at aspect of non-sphericity earth, gives an observation equation with a large field group of star sensors, gives an arith model of satellite orbit perturbation, makes model linearization around optimization estimation, improves traditional algorithm of wide Kalman filtering, first step principium forecast and it's emendation replaces first step principium forecast during filtering, counterpoises element of the difference of average square in push calculation step so as to avoid non-symmetry or reversion. Computer simulation result shows improved algorithm of wide Kalman filtering can bring a good effect in decreasing orbit error as a result of sampling cycle, and make position and velocity error of satellite stabilized, and diminish infection of discrete error to the precision of orbit estimation in some way.