Comparison of AOA Localization in Ultrashort Wave under Various Azimuth Calculation Methods
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摘要: 考虑到方位角计算是AOA （angle of arrival）定位的基础之一，首先，提出了以大地坐标计算方位角的球面近似法和正轴圆柱投影-平面法；进而，建立了球面精确AOA定位方程、球面近似AOA定位方程和正轴圆柱投影-平面AOA定位方程；最后，采用无约束非线性规划方法建立了基于大地坐标的分别与上述方程相对应的3个最优化AOA定位模型，并以网格逐点搜索求解法进行了模型验证. 验证结果的分析表明：在不考虑测向误差时，球面精确AOA定位模型的精度最高，且与纬度无关，但其定位运算时间最长；球面近似AOA定位模型和正轴圆柱投影-平面AOA定位模型的精度均较高，后者的定位误差略大于前者，定位运算时间也长于前者；要提高AOA定位网的定位精度，既可提高各站点的测向精度，也可增加测向站点数，并应综合考虑定位时效性要求和精度要求选择合适的AOA定位模型.Abstract: Given that azimuth calculation is fundamental to angle-of-arrival (AOA) localization, the spherical approximation method and normal cylindrical projection-plane method for azimuth calculation on geodetic coordinates are proposed firstly. Furthermore, the AOA localization equations based on spherical accuracy calculation, spherical approximation calculation, and normal cylindrical projection-rectangle are established respectively. Finally, the unconstrained nonlinear programming method is used to establish the three optimization AOA localization models on geodetic coordinates, which correspond to the above equations respectively, and the models are verified by the point-by-point grid search method. The numerical results show without considering the direction-finding error, the spherical accuracy AOA localization model has the highest precision, which is independent of latitude, but its positioning operation time is the longest. As for the spherical approximation AOA localization model and the normal cylindrical projection-rectangle AOA localization model, both have a high precision, the positioning error of the latter is slightly higher than that of the former, and its positioning operation time is also longer than that of the former. The positioning accuracy of AOA localization network can be improved by increasing either the direction finding accuracy of each site or the number of direction finding sites. The appropriate AOA localization model is selected according to the overall positioning requirements of the timeliness and precision.
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Key words:
- passive location /
- AOA localization /
- azimuth calculation /
- optimal modeling /
- geodetic coordinates
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图 1 不考虑测向误差时5种方法的定位精度
Figure 1. Localization accuracy of five methods without considering direction-finding error
图 2 3站点定位网不同测向误差的定位精度
Figure 2. Localization accuracy of different direction-finding errors in 3-station network
图 3 4站点定位网不同测向误差的定位精度
Figure 3. Localization accuracy of different direction-finding errors in 4-station network
图 4 5站点定位网不同测向误差下的定位精度
Figure 4. Localization accuracy of different direction-finding errors in 5-station network
图 5 9站点定位网不同测向误差的定位精度
Figure 5. Localization accuracy of different direction-finding errors in 9-station network
图 6 16站点定位网不同测向误差的定位精度
Figure 6. Localization accuracy of different direction-finding errors in 16-station network
表 1 AOA定位仿真参数设置
Table 1. Setting of simulation parameters in AOA localization
参数 说明 定位网络构成 在东西长、南北长均约 20 km 的范围内，均匀布设 3、4、5、9、16 个站点构成的定位网络，其中有 4 个站点的网络无中心站点. 待定位信号源的位置 在定位网络之内，在经线上等间隔取 10 个点，在纬线上等间隔取 10 个点，共取 100 个不同的点. 测向误差 1） 不考虑误差 2） −5°～5° 随机均匀分布 3） −10°～10° 随机均匀分布 4） −20°～20° 随机均匀分布 AOA 定位误差 求 100 个定位误差的均方根 
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