Influence of Horizontal Disturbing Gravity on Position Error in Inertial Navigation Systems
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摘要: 研究了不同运动状态下扰动重力水平分量（HDG）对高精度惯导系统（inertial navigation system，INS）的位置误差影响。首先推导了HDG对INS误差影响的状态空间方程，进而推导出3种运动条件下INS位置误差与HDG之间的解析关系式，设计了基于惯导解算求解上述影响的方法。在匀速运动条件下，分别通过解析式与惯导解算两种方法计算了相同HDG引起的INS位置误差。解析式计算结果表明，±80 mGal（1 mGal=10-5 m/s2）范围内变化的HDG约可引起最大约3 000 m的INS位置误差；对两种方法计算结果的比较显示，所得INS位置误差的量级与变化情况基本一致，两组结果验证了各自方法的有效性。Abstract: The influence of horizontal disturbing gravity (HDG) on the positional error of high-precision Inertial Navigation Systems (INSs) was studied under different conditions of movement. A space-state equation expressing INS error with HDG was deduced and analytic expressions of INS position error with HDG were deduced under three conditions of movement. Additionally, a method of computing above influence based on inertial navigation calculation is designed. Under the condition of uniform motion, INS position error caused by the same HDG was calculated through analytic expressions and inertial navigation calculations. The results from analytic expressions show that disturbing gravity varied between ±80 mGal (1 mGal = 10-5 m/s2) causing about 3 000 m INS positional error at the maximum. A comparison of the results from two methods show that the level and change in INS positional error are basically consistent while the validity of each method was verified by these results.
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Keywords:
- disturbing gravity /
- inertial navigation system /
- position error /
- acceleration /
- ultra-precise
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图 5 通过惯导解算仿真HDG对INS的位置影响
Figure 5. Position Error of INS Caused by HDG Computed by Inertial Navigation Algorithm
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图 6 海洋航线上两种方法计算的位置误差比较
Figure 6. Comparison of Position Error Computed by two Methods Along MarineRoute
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图 7 陆地航线上两种方法计算的位置误差比较
Figure 7. Comparison of Position Error Computed by Two Methods Along Terrestrial Route
表 1 扰动重力对INS各误差量影响的传递函数
Table 1 Transfer Functions of Disturbing Gravity on Each Error Variation of INS
误差项 δgN(s) δgE(s) ψx(s) 0 $ - \frac{1}{{R\left( {{s^2} + \omega _s^2} \right)}} $ ψy(s) $ \frac{1}{{R\left( {{s^2} + \omega _s^2} \right)}} $ 0 ψz(s) 0 $ \frac{{\tan \varphi }}{{R\left( {{s^2} + \omega _s^2} \right)}} $ δvN(s) $ - \frac{s}{{\left( {{s^2} + \omega _s^2} \right)}} $ 0 δvE(s) 0 $ - \frac{s}{{\left( {{s^2} + \omega _s^2} \right)}} $ δφ(s) $ - \frac{1}{{R\left( {{s^2} + \omega _s^2} \right)}} $ 0 δλ(s) 0 $ - \frac{{\sec \varphi }}{{R\left( {{s^2} + \omega _s^2} \right)}} $ 
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表 2 HDG及其引起位置误差的统计信息
Table 2 Statistics of HDG and Corresponding Position Error
海洋航线 陆地航线 最大值 平均值 最大值 平均值 |δgN|/mGal 18.18 9.05 93.61 38.19 |δPN|/m 223.58 75.63 2 971.32 1 058.23 |δgE|/mGal 39.23 30.89 79.18 26.04 |δPE|/m 531.82 214.33 2583.78 787.55
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表 3 惯性传感器仿真条件
Table 3 Simulation Condition of Inertial Instruments
条件1 条件2 条件3 陀螺零偏/((°)·h-1) 0.000 5 0.005 0.05 陀螺随机漂移/((°)·h-1, 1σ) 0.001 0.01 0.1 加速度计零偏/(m·s-2) 5×10-6 5×10-5 5×10-4 加计白噪声/(m·s-2, 1σ) 1×10-5 1×10-4 1×10-3
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表 4 不同仿真条件下INS位置误差统计表
Table 4 Statistics of INS Position Error Under Different Simulation Conditions
|δPN|/m |δPE|/m 最大值 平均值 最大值 平均值 条件1 435.18 123.62 558.49 211.98 条件2 435.17 123.56 558.29 211.90 条件3 435.20 123.64 558.52 211.99
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