GNSS外辐射源雷达空中目标TDOA定位算法评估

谭传瑞; 李唐; 陈文谦; 王峰; 杨东凯; 吴世玉

doi:10.13700/j.bh.1001-5965.2023.0685

GNSS外辐射源雷达空中目标TDOA定位算法评估

doi: 10.13700/j.bh.1001-5965.2023.0685

1.
北京航空航天大学电子信息工程学院，北京 100191
2.
北京航空航天大学沈元学院，北京 100191
3.
北京遥感设备研究所，北京 100191

详细信息

通讯作者:
E-mail：wangf.19@163.com

中图分类号: TN958.97
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出版历程
- 收稿日期: 2023-10-24
- 录用日期: 2023-12-06
- 网络出版日期: 2023-12-19
- 整期出版日期: 2025-12-31

Evaluation of TDOA based air target localization algorithm using GNSS-based passive radar

1.
School of Electronic and Information Engineering，Beihang University，Beijing 100191，China
2.
SHENYUAN Honors College，Beihang University，Beijing 100191，China
3.
Beijing Institute of Remote Sensing Equipment，Beijing 100191，China

More Information

Corresponding author: E-mail：wangf.19@163.com

摘要

摘要:
对全球导航卫星系统(GNSS)外辐射源雷达空中目标到达时间差(TDOA)定位算法的性能进行评估，推导TDOA定位方程及方程的加权最小二乘解，引入高度角权重模型和信噪比(SNR)权重模型2种定权方案，分析权重模型、卫星数量、几何精度因子对定位误差的影响。进行仿真试验和外场试验，结果表明：与等权模型相比，高度角权重模型、信噪比权重模型均能有效降低TDOA算法的定位误差，高度角权重模型的降低效果略优于信噪比权重模型；对卫星数量的分析表明，定位中使用的卫星数量小于7颗时定位性能随卫星数量的增加而快速提升，但超过7颗后定位性能的提升速度放缓；对几何精度因子的分析表明，几何精度因子与定位误差的均值呈线性正相关。外场试验中对民航客机的最大定位误差为206.30 m、最小定位误差为13.85 m。
- 全球导航卫星系统 /
- 外辐射源雷达 /
- 空中目标 /
- 到达时间差 /
- 定位性能
Abstract:
The effectiveness of the air target localization method based on time difference of arrival (TDOA) is assessed using passive radar based on the global navigation satellite system (GNSS). The equations of localization and their weighted least squares solution are derived. To determine the weight matrix, an elevation-dependent model and a signal to noise ratio(SNR)-dependent model are introduced. Simulation and outdoor experiment results show that the elevation-dependent model and SNR-dependent model can effectively reduce the position error of the TDOA based air target localization algorithm compared with the unweighted model. When the number of satellites used for localization is fewer than seven, the position performance improves quickly as the number of satellites used increases. However, the improvement trend slows down if more than seven satellites are employed. The evaluation of geometric dilution of precision shows that there is a positive linear correlation between the geometric dilution of precision and position error. In outdoor experiment, the maximum position error of airliners is 206.30 m, and the minimum position error is 13.85 m.
- global navigation satellite system /
- passive radar /
- air target /
- time difference of arrival /
- position performance

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图 1 TDOA定位算法的几何示意图

Figure 1. Geometric schematic of the TDOA localization algorithm

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图 2 定位散点在$ x{O}y $平面的投影

Figure 2. Locate the projection of the scattering point in the xOy plane

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图 3 定位误差的协方差与CRLB对比

Figure 3. Covariance of positioning error plotted against CRLB

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图 4 定位性能随卫星数量变化曲线

Figure 4. Positioning performance versus number of satellites

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图 5 GDOP-定位误差均值散点图及其回归直线

Figure 5. GDOP-positioning error mean scatter plot and its regression straight line

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图 6 标准化残差的正态P-P图

Figure 6. Normal P-P plot of standardised residuals

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图 7 不同噪声强度下的定位误差

Figure 7. Positioning errors at different noise intensities

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图 8 试验场景

Figure 8. Test scenarios

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图 9 目标回波的时延-多普勒图像

Figure 9. Time-delay-Doppler images of target echoes

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图 10 各组数据的定位误差

Figure 10. Positioning error for each data set

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图 11 定位性能随卫星数量的变化曲线

Figure 11. Variation curve of positioning performance with the number of satellites

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图 12 GDOP-定位误差均值散点图及其回归直线

Figure 12. GDOP-positioning error mean scatter plot and its regression straight line

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图 13 标准化残差的正态P-P图

Figure 13. Normal P-P plot of standardised residuals

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图 14 不同权重模型的误差序列均值和标准差

Figure 14. Mean and standard deviation of error series for models with different weights

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表 1 仿真条件

Table 1. Simulation conditions

编号	$ x/ $m	$ y $/m	$ {\textit{z}} $/m
地面站	0	0	0
空中目标	833.88	930.84	1067.10
卫星1	2874701.46	18323941.72	12163715.47
卫星2	−17796907.72	15098203.19	27454679.68
卫星3	−10832994.37	20313279.47	−3114663.86
卫星4	−1480434.16	15176177.60	15471755.24
卫星5	−12042034.11	21659654.86	25834343.54
卫星6	−18396103.15	32511284.53	−3687283.66
卫星7	−14087596.33	−1462340.29	18377118.55
卫星8	−12585913.97	35077823.98	−4628896.76
卫星9	−2339303.01	22727493.15	28099180.15
卫星10	−32147874.59	20112733.37	−4036209.35
卫星11	14019148.46	20442049.95	692344.88

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表 2 试验所用设备及其性能

Table 2. Equipment used for the test and its performance

设备名称	设备性能
右旋天线	圆极化天线全向天线最大增益为5.5 dBi
左旋天线	圆极化天线波束范围为±10°; 最大增益为10 dBi
采集器	中频为15.48 MHz 采样率为64 MHz 量化位数为8 bit
计算机	Intel i5-7500 CPU 16 GB RAM

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表 3 每组数据的可见卫星和选星方案数量

Table 3. Number of visible satellites and satellite selection programmes per data set

数据编号	可见卫星数量	选星方案总数
1	6	22
2	7	64
3	11	1816
4	9	382
5	6	22
6	10	848
7	9	382
8	10	848
9	7	64

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