一种基于Adams-PECE捷联惯导数值更新算法

A SINS numerical updating algorithm based on Adams-PECE

捷联惯导k子样算法的速度更新需要对Rodrigues旋转公式近似,积分区间为k个采样间隔。为避免速度更新中Rodrigues旋转公式近似,缩小积分区间,提出一种基于Adams-PECE捷联惯导数值更新算法。由Adams预测公式估计当前速度与位置,采用预测参数参与姿态矩阵和当前加速度计算;由Adams校正公式计算当前速度与位置,并更新姿态矩阵。所提算法无需计算划桨和旋转误差,积分区间为一个采样间隔。基于捷联惯导真值数据,所提算法的逼近精度比k子样算法高10倍以上;随着测量误差的增加,所提算法在天向通道和偏航通道上偏差小于k子样算法,偏航通道最大差为4.89×10^(-4)度,高程最大差为20.60 m,在其他通道上与k子样算法偏差相近,表明所提算法比k子样算法具有更好的适用性。

The speed updating of the k-sample method(KSM)for strapdown inertial navigation system(SINS)requires the approximation of Rodrigues’rotation formula,and the integral interval is k sampling intervals.In order to avoid the approximation of Rodrigues’rotation formula and reduce the integral interval in speed updating,a SINS numerical updating algorithm based on Adams-PECE is proposed.The current velocity and position are estimated by Adams-Bashforth formula,and the prediction parameters are used to calculate the attitude matrix and the current acceleration.The current velocity and position are calculated by Adams-Moulton formula,and the attitude matrix is updated.The proposed algorithm does not need to calculate sculling errors and rotation errors,and the integral interval is one sampling interval.Based on the SINS true data,the approximation accuracy of the proposed algorithm is more than 10 times higher than that of KSM.With the increase of measurement errors,the deviation of the proposed algorithm is smaller than that of KSM in vertical channel and yaw channel.The maximum deviation in yaw is 4.89×10^(-4) degree and the maximum deviation in altitude is 20.60 m.The deviation of the proposed algorithm is similar to that of the KSM in other channels which has better applicability than KSM.