捷联惯导准静基座大失准角线性初始对准方法研究

SINS Linear Initial Alignment under Quasi-Static Conditions with Large Misalignment

研究了利用线性卡尔曼滤波实现准静基座捷联惯导大失准角初始对准的问题。根据李群理论,如果系统模型具有仿射性,则其对应的线性误差模型是独立于状态估计值的,同时可以从该线性模型精确反推出李群上的非线性状态误差。分析指出,准静基座条件下捷联惯导姿态微分方程满足仿射性条件,其对应的姿态误差方程是独立于姿态估计值的。但是,如果将速度考虑进状态,则整体的状态模型不再满足仿射条件,无论是基于SO(3)+R^(3)还是SE(3)姿态描述,所对应的状态误差方程都不能做到独立于状态估计值。基于上述分析,直接对SO(3)+R^(3)状态描述下的速度误差方程进行改造,用重力矢量直接替换比力项,从而构造出独立于状态估计值的状态转移矩阵。仿真实验结果表明,利用所构造的线性状态空间模型,即使在大失准角条件下也能快速收敛到极限对准精度;车载晃动实验结果表明,利用所构造的线性状态空间模型,在大失准角条件下同样能够快速地跟上小失准角条件下的线性卡尔曼滤波对准结果。

This paper is devoted to investigating the quasi-static base strapdown inertial navigation system(SINS)large misalignment angle initial alignment making use of linear Kalman filtering.According to the Lie theory,if a model is a group affine model,its linear error model is independent of the state estimate,and the nonlinear state error on the group manifold can be exactly recovered from the linear error.It is pointed out that under quasi-static conditions,the SINS attitude differential equation satisfies the group affine condition and the corresponding linear attitude error equation is independent of the state estimate.However,when the velocity is incorporated into the state,the model is no longer a group affine model.Whether based on SO(3)+R^(3) or SE(3)description,the resulting linear error models are both dependent on the state estimate.Based on the above analysis,through formulating the state as SO(3)+R^(3),the velocity error equation is modified through substituting the specific force based factor with gravity.The resulting state transition matrix is now independent of the state estimate.The simulation test results show that making use of the modified linear state space model,the initial alignment can achieve the utmost precision under static condition even with very large misalignment angle.The results of car-mounted swaying experiment show that making use of the modified model,the initial alignment results with large misalignment angle can fast reach the ones by the Kalman filtering based initial alignment with small misalignment angle.