基于高阶容积卡尔曼滤波的极区惯性/重力梯度组合导航方法

INS/GGI Navigation in Arctic Area Based on High Degree Cubature Kalman Filter

针对现有的导航手段在极区应用都存在一定的缺陷这一问题,提出了一种基于惯性/重力梯度的组合导航方法。建立了组合导航系统模型,首先,考虑到传统惯导解算方法在极区存在经线收敛的问题,给出了一种基于格网坐标系的惯导解算模型;基于重力梯度仪的误差特性,建立了系统的量测模型。为提高算法的估计精度和稳定性,并解决惯性/重力梯度组合导航系统雅克比矩阵求解复杂等问题,采用高阶容积卡尔曼滤波算法,结合重力梯度图,设计了组合导航滤波器。其中,为保证四元数的归一化,采用修正的罗德里格斯参数表示姿态误差。最后进行了蒙特卡洛数学仿真,仿真结果证明了该方法可以准确地估计出飞行器的位置和速度等信息,且估计精度高于扩展卡尔曼滤波;此外,通过仿真结果分析了重力梯度仪精度、地形、飞行器高度等影响组合导航精度的关键要素。

Due to the particularity of the polar environment,existing navigation means have some defects in arctic application. To solve this problem,navigation algorithm based on Inertial Navigation System( INS)/Gravity Gradient Instrument( GGI) is proposed. In order to establish integrated navigation system model,an inertial navigation solution model in grid reference frame is firstly proposed to solve the convergence of the longitude at pole,and the measure model which is based on error characteristic of GGI is given. In order to improve the precision and stability of the algorithm and avoid solving the complex Jacobian matrix,high degree cubature kalman filter( HCKF) is adopted to build integrated navigation filter with gravity gradient map. Modified Rodrigues parameters are used to stand for attitude error and ensure the normalization of quaternion. At last,the Monte-Carol simulation is conducted,and the simulation results show the method can estimate the position and velocity accurately. Besides, HCKF has higher accuracy than EKF. In addition,the precision impact analysis caused by GGI’s accuracy,terrain,vehicle altitude and GGI’s update frequency is accomplished through the simulation results.