摇摆基座上基于信息的捷联惯导粗对准研究

A Clever Way of SINS Coarse Alignment despite Rocking Ship

舰船的摇摆使陀螺无法测出地球自转角速度,无法根据陀螺和加速度计的输出直接计算出姿态阵。针对这一问题,提出了基于重力加速度的粗对准算法。该算法中,姿态阵分散成4个矩阵求取,所利用的信息为:摇摆基座姿态变化信息;重力加速度相对惯性空间随地球旋转引起的方向变化信息;地球自转信息;地理信息。算法的巧妙之处是应用惯性凝固假设,建立了基座惯性坐标系ib0,使舰体相对ib0坐标系的姿态阵初值成为单位阵,从而使姿态更新解算成为可能。仿真结果表明,在舰船横摇、纵摇、艏摇幅值分别为10°、7°和5°,周期分别为6 s、5 s和7 s,横荡、纵荡、垂荡幅值分别为0.02 m、0.03 m和0.3 m,周期分别为7 s、6 s和8 s的环境下,由50个样本确定的东、北、天向失准角的均值分别为2.01′-、1.38′和-0.20,°相对的标准差为0.26′、0.21′和1.3,°在此基础上完全可以实现精对准。

Ship rocking causes well-known hard-to-overcome difficulties in SINS （Strapdown Inertial Navigation System） coarse alignment. We aim to overcome these difficulties with a clever way, which can be mathematically very simply expressed by the matrix equation Cb^n=Ce^nCi^eCi^i b0,Cb^b 0, given as eq. （1） in the paper. The expanded forms of matrix Ce^n（built of the geography message） and Ci^e （built of the earth rotation message） are given in eq. （2）. Eq. （14） is the formula for calculating matrix Ci^i b0. Matrix Cb^b 0 is calculated by the attitude updating algorithm which is well known in the field of inertial navigation. In the full paper we explain in detail how, with eq. （1）, we can achieve satisfactory coarse alignment despite ship rocking. Here we omit this explanation. In the Monte Carlo simulation scenarios, the moored ship is rolling, pitching and yawing with the amplitudes of 10°, 7° and 5° with the periods of 6 s, 5 s and 7 s respectively; meanwhile the ship is surging,swaying and heaving with the amplitudes of 0.02 m, 0.03 m and 0. 3 m with the periods of 7 s, 6 s and 8 s respectively. 50 samples are treated. The mean values of the misalignment angles along the east, the north and the upside are 2.01＇, -1.38＇, -0.20°, and the standard deviations are 0. 26＇, 0. 21＇, and 1. 3° respectively. The coarse alignment guarantees the accurate alignment that follows.