﻿ 极区惯导编排中地球近似模型的适用性分析
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Applicability analysis of the approximate model of the Earth with the arrangement of INS in polar region
LIN Xiuxiu, BIAN Hongwei, MA Heng, WANG Rongying
Electrical Engineering College, Navy University of Engineering, Wuhan 430033, China
Foundation support: The National Natural Science Foundation of China (Nos. 41876222;41506220)
First author: LIN Xiuxiu(1994—), female, master, majors in inertial navigation technology and application.E-mail:741083098@qq.com
Corresponding author: BIAN Hongwei, E-mail: 4985726@qq.com
Abstract: The arrangement of horizontal coordinate system based on the Earth's second approximate ellipsoid model is complicated in polar region, the arrangement itself has the principle error, While the first approximate sphere model has geometric errors, it has simple arrangement in polar regions, and the geometric error is smaller than that in the middle and low latitudes. The selection of the Earth model is becoming more and more prominent with the intensive study of the inertial navigation in polar region. To solve this problem, based on the definition of the Earth approximate model, the system error equations of SINS based on the first approximate model of the Earth is derived. Then comparing the inertial error of the Earth approximate model with the simulation and analyzing the applicability of the Earth approximate model. The simulation results show that the geometric errors of the first approximate model will accumulate with time, while the errors of the second approximate model change little with time. When the inertial navigation run in a long time, the first approximate model of the Earth is no longer suitable for polar area.
Key words: polar navigation     error analysis of inertial navigation     Earth approximate model     Earth first approximation     Earth second approximation

1 地球近似模型定义 1.1 球近似模型半径的选取

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 半径类型 半径/km 椭球上点到球面距离的平方和M N=1120 N=11 112 N=111 112 等表面积半径Ra 6 371.010 219 286.84 2 191 386.17 21 912 379.48 等体积半径Rv 6 371.004 219 099.51 2 189 514.19 21 893 660.90 椭球长半轴半径Re 6 378.137 498 333.62 4 979 895.44 49 795 513.57 椭球短半轴半径Rp 6 356.752 93.61 932.85 9 325.24 切换位置椭球体曲率半径Rs 6 357.398 246.49 2 464.90 24 649.00 最小二乘法拟合半径R 6 356.968 41.48 413.39 4 132.45

1.2 地球模型定义与对比

 图 1 球体模型与椭球模型定义对比图 Fig. 1 Comparison diagram between the sphere model and ellipsoid model

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2 横向坐标系惯导编排及其误差分析 2.1 横向坐标系惯导编排

 图 2 横向经纬度与横向坐标系示意图 Fig. 2 A schematic diagram of transverse longitude and latitude and transverse coordinate system

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2.2 横向坐标系误差分析

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3 地球近似模型适用性范围分析

3.1 无器件误差对比仿真

 图 3 极区地球近似模型无器件误差惯导24 h编排误差对比结果 Fig. 3 The comparison result of 24 hours INS arrangement error of non device error with the approximate model in polar region

 图 4 极区地球近似模型无器件误差惯导240 h编排误差对比结果 Fig. 4 The comparison result of 240 hours INS arrangement error of non device error with the approximate model in polar region

 图 5 极区地球近似模型无器件误差惯导360 h编排误差对比结果 Fig. 5 The comparison result of 360 hours INS arrangement error of non device error with the approximate model in polar region

 统计量 24 h 240 h 360 h ∇δφ′/m 0.033 711.2 2.59×106 ∇δλ′/m 0.017 638.7 2.46×106 ∇δvEt/(m/s) 7.19×10-6 0.81 3.23×103 ∇δvNt/(m/s) 2.12×10-5 0.92 3.34×103 ∇ϕEt/(′) 1.39×10-5 0.35 1.4×103 ∇ϕNt/(′) 1.72×10-5 0.38 1.27×103 ∇ϕUt/(′) 1.19×10-5 0.034 3.48×102

3.2 实际应用地球近似模型选用分析

 图 6 极区地球近似模型航海级器件误差24 h编排误差对比结果 Fig. 6 The comparison result of 24 hours INS arrangement error of seafaring level device error with the approximate model in polar region

 图 7 极区航海级器件误差地球近似模型编排误差120 h对比结果 Fig. 7 The comparison result of 120 hours INS arrangement error of seafaring level device error with the approximate model in polar region

 统计量 导弹 飞机 舰船 舰船 5 h 24 h 24 h 120 h ∇δφ′/m 0.16 76.4 2.47 348.8 ∇δλ′/m 1.49 153.6 2.81 516.5 ∇δvEt/(m/s) 0.001 0.08 0.007 0.59 ∇δvNt/(m/s) 0.002 0.04 3.4×10-4 0.42 ∇ϕEt/(′) 9.4×10-5 0.06 5.8×10-4 0.39 ∇ϕNt/(′) 8.6×10-4 0.05 3.7×10-4 0.19 ∇ϕUt/(′) 8.2×10-4 0.01 0.001 3 0.01

4 结论

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http://dx.doi.org/10.11947/j.AGCS.2019.20180073

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#### 文章信息

LIN Xiuxiu, BIAN Hongwei, MA Heng, WANG Rongying

Applicability analysis of the approximate model of the Earth with the arrangement of INS in polar region

Acta Geodaetica et Cartographica Sinica, 2019, 48(3): 303-312
http://dx.doi.org/10.11947/j.AGCS.2019.20180073