基于Rodrigues参数和量测非线性的SINS/GPS动基座对准

In-motion alignment for SINS/GPS based on Rodrigues parameter and nonlinear measurement

对GPS辅助下,捷联惯导系统动基座对准问题进行了研究。利用姿态阵分解,将动态对准问题转换为一个常值姿态的估计,采用Rodrigues参数进行姿态描述,建立了系统方程线性,量测方程具有二阶非线性的对准模型,进而推导了基于二阶非线性量测完整泰勒级数展开的滤波算法。同时,对Rodrigues参数描述姿态时的奇异点问题进行了详细地讨论,设计了能自动判别并规避奇异点的滤波对准方案。以车辆典型机动轨迹为对象进行了蒙特卡洛仿真,结果表明,所设计算法能够在5 s内实现奇异点的判别及处理,且当GPS速度误差为0.1 m/s,位置误差为3 m,更新率为1 s时,惯性级捷联惯导系统在120 s时间内,可以达到水平姿态误差角均方根小于10″,方位误差角均方根小于4′的对准精度。

The alignment of strapdown inertial navigation system/GPS on moving base is studied. Based on the direct cosine matrix decomposition and Rodrigues parameter description, an alignment model with linear system equation and second-order nonlinear measurement equation is established. Furthermore, an optimal estimation algorithm using exact Taylor series expansions of second-order nonlinear measurement is deduced. Meanwhile, the singular problem of Rodrigues parameter description is discussed and a singular point avoidance schema is proposed. Finally, Monte Carlo simulation for the representative trajectory of the land vehicle is performed, and the results indicate that the singular point can be recognized and avoided within 5 s. In addition, the root mean square errors of level attitudes are less than 102 and the root mean square error of yaw is less than 4′ after 120 s alignment for inertial-grade IMU, in case the errors of velocity and position are within 0.1 m/s and 3 m.