Milne-Hamming线性多步法在求解姿态四元数微分方程中的应用

姿态微分方程的求解是SINS(Strap-down Inertial Navigation System)导航解算中一项重要的内容,对算法的稳定性、精度和计算量有较高的要求。引入了一种求解姿态四元数微分方程的新方法——Milne-Hamming线性多步预测校正方法,详细推导了应用此方法求解姿态四元数微分方程的过程。应用仿真数据和实测数据对此算法和四阶龙格-库塔算法进行了对比验证,结果表明Milne-Hamming线性多步预测校正方法是一种求解姿态四元数微分方程的有效方法,其稳定度明显优于四阶龙格-库塔算法并且计算量小。

Application of Milne-Hamming Linear Multi-step Forecasting-Correcting Algorithm to Solve Attitude Quaternion Differential Equation

Solving attitude differential equation is an important content in the SINS navigation computation,which has more demands to algorithm's stability,accuracy and computational cost.A new algorithm Milne-Hamming linear multi-step forecasting-correcting algorithm was introduced in this paper.The processes of solving attitude quaternion differential equation were derived in detail.This paper verified the algorithm via the simulative and real data compared with the Fourth-Order Runge-Kutta method.The results show that Milne-Hamming linear multi-step forecasting-correcting algorithm was an effective method to solve attitude quaternion differential equation.It was obvious that the stability of the proposed method was superior to the Fourth-Order Runge-Kutta and the computational cost was low.