Effect of the ionospheric virtual height on the joint positioning accuracy of multi-station over-the-horizon radar system
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摘要: 在天波超视距雷达系统的短基线多站联合定位中，一般假设多站点电离层反射虚高保持一致，为确定这一假设对定位结果的影响，本文进行电离层探测试验，以研究电离层虚高对多站联合定位精度的影响。试验时分别架设两个接收站模拟短基线超视距雷达系统的接收站点，再在较远距离架设目标站点，利用来自目标站点的发射信号模拟目标的返回信号。本文假设参考站点到目标站点链路的电离层反射虚高和大圆距离是已知的，对于同一工作频率，利用参考站点-目标站点链路上的电离层虚高，去解算定位站点-目标站点之间的大圆距离。参考站点和定位站点相距约90 km情况下，结果显示：目标和定位站(道孚-武汉)大圆距离约为1 260 km时，两条链路的虚高均方根误差约为5.82 km，相应的大圆距离的定位均方根误差约为5.02 km，相对误差约为0.34%，当目标和定位站(乐山-武汉)大圆距离约为1 000 km时，误差分别约为5.5 km, 5.69 km和0.46%。试验结果和理论分析表明，可以从缩短接收站点的布局和降低电离层反射虚高两个方面进一步提高目标定位的精度。本文试验结果可为短基线天波超视距雷达的建设提供较为重要的参考价值。Abstract: In the short baseline multi-station joint positioning of skywave over-the-horizon-radar(OTHR) system, the ionospheric virtual height of different propagation links of radio waves is generally assumed to be equal. In order to search the effect of this assumption on the positioning results, we conduct observation experiments to study the influence of ionospheric virtual height on the accuracy of multi-station joint positioning. In the experiment, two receiver stations are set up to simulate the receiver station of the short baseline OTHR system, and then the target station is set up at a long distance. We simulate the reflected wave of the target by using the transmitted wave from the target station. This paper assumes that the ionospheric virtual height and the great circle distance of the link from the reference station to the target station are known. In this case, for the same operating frequency, the great circle distance between the positioning station and the target station is calculated by using the ionospheric reflected virtual height on the propagation link between the reference and target stations. The results show that when the distance between the reference station and the positioning station is about 90 km meanwhile the great circle distance between the target and the positioning station (Daofu-Wuhan) is about 1260 km, the root mean square error of the virtual height of the two links is about 5.82 km, the positioning root mean square error of the great circle distance is about 5.02 km, and the relative error is about 0.34%. When the great circle distance (Leshan-Wuhan) is about 1000 km, the errors are about 5.5 km, 5.69 km and 0.46%, respectively. The experimental results and theoretical analysis show that the accuracy of target positioning can be further improved by shortening the layout of receiving stations and reducing the ionospheric virtual height. The experimental results can provide some reference value for the construction of short baseline skywave OTHR.
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图 1 单站有源定位示意图(左)和根据Martyn等效定理构建的三角形（右）
Fig. 1 Schematic diagram of the single site location (left) and Triangle constructed according to Martyn's equivalence theorem (left)
图 2 虚高偏差对大圆距离解算的影响
Fig. 2 Effect of the virtual height deviation on the calculation of great circle distance
图 3 四个试验站点的地理位置示意图
Fig. 3 Geographical location of Daofu, Leshan, Xiantao and Wuhan stations
图 5 仙桃站和武汉站接收的斜测电离图（2021年3月12日15:00）
Fig. 5 The oblique ionograms recorded at Xiaotao and Wuhan stations at 15:00 on March 12, 2021
图 6 道孚-武汉链路的真实虚高差和大圆距离解算误差
Fig. 6 Real virtual height deviation and calculated error of the great circle distance of Daofu-Wuhan link
图 7 道孚-武汉链路数据标定时选取的频率
Fig. 7 Frequency selected for data calibration of Daofu-Wuhan link
图 8 乐山-武汉链路的真实虚高差和大圆距离解算误差
Fig. 8 Real virtual height deviation and calculated error of the great circle distance of Leshan-Wuhan link
图 9 乐山-武汉链路数据标定时选取的频率
Fig. 9 Frequency selected for data calibration of Leshan-Wuhan link
表 1 道孚-仙桃的虚高解算道孚-武汉大圆距离的误差
Tab. 1 The error using the virtual height of Daofu-Xiantao link to calculate the great circle distance of Daofu-Wuhan link
日期 虚高均方根误差/km 大圆距离均方根误差/km 相对误差/% 3月12日 6.03 5.18 0.34 3月13日 6.35 5.49 0.36 3月14日 5.04 4.35 0.32 平均值 5.82 5.02 0.34 
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表 2 乐山-仙桃的虚高解算乐山-武汉大圆距离的误差
Tab. 2 The error using the virtual height of Leshan-Xiantao link to calculate the great circle distance of Leshan-Wuhan link
日期 虚高均方根误差/km 大圆距离均方根误差/km 相对误差/% 3月12日 5.46 5.56 0.47 3月13日 4.91 5.22 0.41 3月14日 6.02 6.21 0.48 平均值 5.50 5.69 0.46
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