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The simplest multi-position analytic alignment for SINS
TAN Caiming, WANG Yu, SU Yan, ZHU Xinhua
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Abstract: The strapdown inertial navigation system (SINS) need to be installed on a servo platform and rotated through 90 ° or 180 ° about the up axis for traditional multi-position analytic alignment method. Thus it will bring inconvenience, and the precision of the servo platform will directly affect the precision of the multi-position analytic alignment method. To address the issue, a simplest multi-position analytic alignment method was proposed. The multi-position analytic alignment can be done by any two positions, or to say, the constant biases of the inertial measurement unit (IMU) can be ordinarily obtained through the information in any two positions. The computation procedure of this method was given and simulations proved the validity of this method. The simplest multi-position analytic alignment with any two positions can be used as a simple initial alignment method or a field calibration method. Moreover, it is proposed that the constant bias of the accelerometer or the constant drift of the gyroscope in a certain axis can be well estimated when the IMU stays in some particular attitudes. The conclusion can be used for further improvement of the multi-position alignment method.
Key words: multi-position alignment     analytic alignment     constant bias     initial alignment     strapdown inertial navigation system (SINS)

1 任意两位置解析对准 1.1 理论分析

IMU是捷联惯导系统的主要组成部分.它由互相重合的三轴陀螺和三轴加速度计组成,记三轴陀螺的输出为w=[wx,wy,wz]T,三轴加速度计的输出为f=[fx,fy,fz]T.若基座完全静止,IMU受且仅受地球自转和重力作用.地球自转角速度大小为wie,重力加速度值为g,IMU所在地球纬度为L.设三轴陀螺的输出误差∇w=[∇wx,∇wy,∇wz]T,三轴加速度计的输出误差为∇f=[∇fx,∇fy,∇fz]T.将当地东北天地理坐标系作为导航坐标系(简记为n系),IMU载体坐标系简记为b系,n系到b系的坐标变换矩阵记为Cnb,则有下式成立[6, 13]:

 图 1 两球面相交成圆周的截面图 Fig. 1 Cross-section of a circumference formed by two intersected spherical surfaces

 图 2 圆周的平移和翻转 Fig. 2 Translational and rotational motion of circumference

1.2 实例仿真

 图 3 三轴加速度计常值偏置取值范围 Fig. 3 Value range of constant biases of three-axis accelerometers
 图 4 三轴陀螺常值漂移取值范围 Fig. 4 Value range of constant drifts of the three-axis gyroscopes

 图 5 取不同α和β的值时对应的J1值 Fig. 5 J1 value given different values of α and β
 图 6 取不同α和β的值时对应的J2值 Fig. 6 J2 value given different values of α and β

J1J2都趋于零的点在图 5图 6所示的中间区域,进一步缩小搜索范围并减小搜索步长进行二次搜索,直到搜索得到满足所需求解精度的唯一解,计算出的加速度计常值偏置和陀螺常值漂移和题设一致.

2 特殊姿态下的偏置估计

 图 7 Δz随∇x及∇y的变化对应的取值范围 Fig. 7 Value range of ∇z changing with different values of Δx and ∇y

3 结论

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#### 文章信息

TAN Caiming, WANG Yu, SU Yan, ZHU Xinhua

The simplest multi-position analytic alignment for SINS

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(9): 1645-1650.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0033