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Rapid coarse alignment for marching vehicle based on GPS and odometer
TA Gaoming , SONG Lailiang , RAN Longjun
School of Instrumentation Science and Opto-electronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-01-15; Accepted: 2016-04-01; Published online: 2016-05-04 14:06
Corresponding author. E-mail:songlailiang@buaa.edu.cn
Abstract: Aimed at vehicle-mounted strap-down inertial navigation system (SINS), a rapid coarse alignment method for marching vehicle is proposed. The matrix between navigation frame and body frame is decomposed into three parts. The problem to solve the matrix between navigation frame and body frame is attributed to solving the matrix between initial body frame and inertial frame, which can be obtained by the non-colinear vectors constructed with the vehicle's velocity from GPS in navigation frame and that from odometer in body frame. The only requirement of this alignment method for marching vehicle is a turning movement in the alignment stage. Compared with the existing alignment methods, this method does not use the measurement information of accelerometers. The simulation results show that the coarse alignment can be fulfilled in 1 minute, and the alignment error is less than 0.3° with low accuracy gyros whose zero bias is 0.1(°)/h.
Key words: coarse alignment     GPS     odometer     non-colinear vectors     turning movement

1 坐标系定义

1) 地球坐标系(e系)：Oxe轴在赤道平面内且指向中央子午线，Oze轴沿地球自转轴方向，3轴构成右手坐标系；e系与地球固连，相对惯性空间的旋转角速度为地球的自转角速度ωie

2) 初始时刻地球坐标系(e0系)：在初始对准开始时刻(即t=t0=0 时)Oxe0轴在赤道平面内且指向当地经线，Oze0轴沿地球自转轴方向，3轴构成右手坐标系；e0系也与地球固连，相对惯性空间的旋转角速度为地球的自转角速度ωie

3) 初始时刻惯性坐标系(i0系)：在对准开始时刻i0系的坐标轴与e0系对应的坐标轴重合，且i0 系相对惯性空间静止，即e0系相对i0系沿Ozi0轴以角速度ωi0e旋转。

4) 导航坐标系(n系)：选取“东-北-天”坐标系为导航坐标系。

5) 初始时刻导航坐标系(n0系)：把开始对准时刻的导航坐标系定义为n0系，它相对于地球表面不动。

6) 载体坐标系(b系)：定义“右-前-上”坐标系为载体坐标系。

7) 初始时刻载体惯性坐标系(ib0系)：在对准开始时刻ib0系与b系重合，且ib0系相对惯性空间静止。

2 对准算法

 (1)

2.1 求解矩阵Ci0n(t)

 (2)

 (3)

 (4)

2.2 求解矩阵Cbib0(t)

 (5)

 (6)

 (7)
2.3 求解常值矩阵Cib0i0

 (8)
 (9)

 (10)

 (11)

 (12)

 (13)

3 误差分析 3.1 误差分析方法1

 (14)

 (15)

δCbib0(t)引起的误差[24]

 (16)

 (17)

 (18)

 (19)

 (20)

 (21)

 (22)
3.2 误差分析方法2

 (23)

t2 时刻为对准结束时刻t ，将式(23)代入式(1)可得

 (24)

 (25)

 (26)

 (27)

 (28)

 (29)

 (30)

 (31)

4 仿真实验与分析 4.1 仿真条件设置

 传感器误差 常值偏移 随机误差 陀螺仪误差/((°)·h-1) 0.1 0.01 东向速度GPS误差/(m·s-1) 0.1 0.01 北向速度GPS误差/(m·s-1) 0.1 0.01 天向速度GPS误差/(m·s-1) 0.1 0.01 里程计误差/(m·s-1) 0.05 0.005

4.2 仿真结果与分析

 图 1 俯仰角误差、横滚角误差及偏航角误差曲线 Fig. 1 Alignment errors for pitch angle，roll angle and yaw angle

 姿态角 误差均值/(°) 误差标准差/(°) 俯仰角 0.225 8 0.025 2 横滚角 -0.247 2 0.001 6 航向角 -0.234 6 0.012 6

2种误差分析方法中都假定了俯仰角和横滚角为0°，同时再考虑计算误差和舍入误差等的影响，必然使得由误差方程计算得到的误差与通过仿真得到的误差之间存在微小的差异。

5 结 论

1) 该行进间对准方法能在1min之内完成粗对准，采用0.1(°)/h的低精度陀螺，对准误差小于0.3°。

2) 姿态角误差主要受GSP提供的速度的常值误差的影响，且载车的运行速度越快，姿态角误差越小。

3) 与现有的对准方法相比，该方法没有用到加速度计的测量信息，这使得该方法只能在行进间完成对准；与现有的行进间对准方法相比，该方法对载车的机动方式没有过多的限制，且可以快速完成粗对准。

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#### 文章信息

TA Gaoming, SONG Lailiang, RAN Longjun

Rapid coarse alignment for marching vehicle based on GPS and odometer

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(1): 121-127
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0053