基于截断误差的改进脉冲星导航观测方程

针对X射线脉冲星导航中，传统的扩展卡尔曼滤波（EKF）算法因为线性化需要从而忽略观测模型高阶项导致较大截断误差的问题，提出一种适用于脉冲星导航的改进线性观测方程。首先，详细分析了观测方程简化过程中会造成截断误差的周年视差效应及引力延迟效应的物理意义，介绍了2个高阶项的数学模型，并对2项进行了详细的数值分析。其次，利用泰勒展开等方式，将2个高阶项进行线性化处理，建立一种改进的线性观测方程。最后，利用地球卫星轨道数据，将2个线性观测方程分别应用到脉冲星导航的EKF解算中验证改进线性观测方程的有效性。结果表明，在考虑高阶项影响的条件下，改进的线性观测方程均能保证250 m和2 m/s以内的位置和速度估计误差而且对高阶项变化表现出一定的鲁棒性，但传统的简化线性观测方程却会导致发散。

Improved pulsar navigation measurement equation based on truncation errors

Considering that the traditional extended Kalman filter (EKF) algorithm has to neglect the higher order terms of the measurement model because of linearization, which causes the problem of large truncation errors in X-ray pulsar navigation, an improved linear measurement equation suitable for pulsar navigation is proposed. First, the paper analyzes the physical meaning of annual parallax effect and Shapiro effect which cause the truncation error in the process of simplifying the measurement equation. The two higher order terms' mathematical models are established and numerical analysis is conducted. Then, using the method of Taylor expansion, the two higher order terms are linearized to establish an improved linear measurement equation. Finally, using the earth satellite orbit data, the two measurement equations are respectively applied to the EKF algorithm of the pulsar navigation to verify the validity of the improved measurement equation. The results show that the improved linear measurement equation can guarantee the position and velocity estimation error within 250 m and 2 m/s under the consideration of the higher order terms, and that the improved linear measurement equation has some robustness to the higher order term changes. However, the traditional simplified measurement equation can cause divergence.