基于矩阵分解的惯导安装误差矩阵解耦方法

针对捷联惯性导航系统级标定中安装误差矩阵存在3组耦合关系问题,提出一种基于矩阵分解的解耦方法。该方法将安装误差矩阵分解为对称误差矩阵和斜对称误差矩阵后,推导其对惯性导航姿态方程和速度方程的影响,揭露系统级标定中安装误差矩阵存在耦合的原因——陀螺仪表组和加速度计仪表组的斜对称误差对误差方程的影响是耦合的,进而提出适当选取体坐标系使得陀螺仪表组的斜对称误差矩阵为0的解耦方法。该解耦方法是一种均值分配方法,与传统解耦方法相比能减少系统运算中的二阶舍项误差。仿真实例说明了该解耦方法是有效的。

SINS installation error matrix decoupling method based on matrix decomposition

For the strapdown inertial navigation system’s system level calibration installation error matrix contains three groups of coupling relationship problems, a decoupling method based on matrix decomposition is proposed. The installation error matrix is decomposed into symmetric matrices and skew symmetric matrices at first. Then the influence is deduced to the strapdown inertial navigation system’s attitude equation and the rate equation. Under this deduced conclusions, the reason why there are coupling installation error matrices in the calibration of the system level is revealed, that is, influence of skew symmetric error and gyro instrument group skew symmetric error of the accelerometer instrument cluster on the system level calibration is coupled. And then a decoupling method that appropriately selects the reference frame to set the gyro instrument skew symmetric matrix to zero is proposed. The decoupling method is a kind of average allocation method. Compared with the traditional decoupling method, this method can reduce the second order truncation error of system operation. Simulation example shows that the decoupling method is effective.