基于对偶四元数的捷联惯导算法在发射点惯性系下的应用研究

Strapdown Inertial Navigation Algorithm Based on Dual Quaternion in Launch Point Inertial Coordinate System

针对导弹类载体在做复杂的高动态机动时,采用传统的捷联惯导算法容易产生圆锥误差与划船误差,从而导致解算精度降低的问题,在发射点惯性系下设计了基于对偶四元数的捷联惯导算法。在建立发射点惯性系下的捷联惯导解算模型的基础上,详细推导了基于对偶四元数的捷联惯导解算算法,通过对比分析其中的速度更新过程与传统算法的差异,说明该算法可以有效提高速度和位置解算精度。在设计的多条机动飞行轨迹下,以三子样更新为例,对对偶四元数算法和传统算法的性能进行了仿真对比分析。仿真结果表明,对偶四元数导航算法可以有效提高速度和位置解算精度,且姿态机动情况越复杂、持续时间越长,改善效果越显著。

For the missile carrier with complex high dynamic maneuvering,the traditional solution method of strapdown inertial navigation system(SINS)tends to produce the coning error and the sculling error,and leads to reduction of the accuracy of the solution.A SINS algorithm in launch point inertial coordinate system(LIC)is designed based on the dual quaternion.Based on the basic SINS model under LIC,the SINS algorithm based on the dual quaternion is deduced in detail.The difference of velocity update process between the proposed algorithm and the traditional algorithm is analyzed to illustrate that the proposed algorithm can effectively improve the accuracy of velocity and position.Under the designed multiple maneuvering flight trajectories,the performances of the proposed algorithm and the traditional algorithm are simulated and compared by taking the three subsamples updating as an example.The simulation results show that the proposed algorithm can effectively improve the accuracy of velocity and position calculation.And the more complex the attitude maneuvering is,the longer the duration is,the more significant the improvement effect is.