A passive location algorithm based on TDOA and FDOA of dual-satellite in the condition of unfiled rank
-
摘要:
针对双星对地面已知高度目标辐射源到达时间差（TDOA）和到达频率差（FDOA）无源定位过程中存在卫星1位置矢量、两卫星位置矢量差以及两卫星速度矢量差三者共面问题，提出了一种获得目标位置三维解析解的算法，并指出当且仅当两卫星位置矢量和速度矢量四者共线时才无解。分析了共面但不共线和共线2种情况，给出了不同情况下的解析解，并且当两卫星位置矢量共线时可以将定位问题化简为简单的一元二次方程求解问题，可以有效降低求解复杂度和减少虚根数量。此外，当三矢量共面时还可以改善星下点区域的定位精度。仿真实验验证了所提算法的有效性。
-
关键词:
- 到达时间差(TDOA) /
- 到达频率差(FDOA) /
- 无源定位 /
- 解析解 /
- 双星
Abstract:To solve the problem that the position vector of the first satellite, the position difference vector between dual satellites and the speed difference vector between dual satellites are coplanar when the fixed emitter with known altitude is located by dual satellites using time difference of arrival (TDOA) and frequency difference of arrival (FDOA), an analytic solution in three-dimensional spaces was proposed. The condition for no solution is only that the two position vectors and two speed vectors of dual satellites are collinear. The paper analyzes the two conditions of both coplanar but non-collinear and collinear. The analytic solutions of different conditions are given. The problem of location can be simplified into solving quadratic equation with one unknown when the position vectors of dual satellites are collinear, which alleviates the complexity of the problem solving and reduces the computational complexity. Besides, the positioning accuracy is enhanced in nadir point of dual satellites when the three vectors are coplanar. The algorithm was proved useful by simulation experiments.
-
图 1 双星时频差无源定位示意图
Figure 1. Schematic of dual-satellite passive location using TDOA and FDOA
图 2 两卫星位置矢量共线时定位误差分布
Figure 2. Location error distribution when position vectors of dual satellites are collinear
图 3 三矢量共面但不共线时定位误差分布
Figure 3. Location error distribution when three vectors are co-planar but non-collinear
-
[1] 常啸鸣, 张晓林, 张强.基于加权矩阵的TDOA多站无源定位算法[J].北京航空航天大学学报, 2011, 37(11):1378-1383. http://bhxb.buaa.edu.cn/CN/abstract/abstract12122.shtmlCHANG X M, ZHANG X L, ZHANG Q.Method of TDOA multistation passive location based on weighted matrix[J].Journal of Beijing University of Aeronautics, 2011, 37(11):1378-1383(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract12122.shtml [2] 杨宇翔, 张汇川.同步三星目标运动状态快速检测方法[J].北京航空航天大学学报, 2014, 40(10):1392-1398. http://bhxb.buaa.edu.cn/CN/abstract/abstract13050.shtmlYANG Y X, ZHANG H C.Fast algorithm of motion state detection based on tri geo-satellites[J].Journal of Beijing University of Aeronautics, 2014, 40(10):1392-1398(in Chinese). http://bhxb.buaa.edu.cn/CN/abstract/abstract13050.shtml [3] 狄慧, 刘渝, 杨健.基于径向加速度精估计的PSO单星无源定位[J].宇航学报, 2014, 35(9):1036-1043. http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB201409009.htmDI H, LIU Y, YANG J.PSO single satellite passive localization based on radial acceleration accurate estimation[J].Journal of Astronautics, 2014, 35(9):1036-1043(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB201409009.htm [4] 白晶, 王国宏, 王娜, 等.测向交叉定位系统中的最优交会角研究[J].航空学报, 2009, 30(2):298-304. http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB200902020.htmBAI J, WANG G H, WANG N, et al.Study on optimum cut angles in bearing-only location systems[J].Acta Aeronautica et Astronautica Sinica, 2009, 30(2):298-304(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-HKXB200902020.htm [5] 曲长文, 徐征, 李炳荣, 等.一种新的基于角度和时差的稳健定位跟踪算法[J].信号处理, 2011, 27(2):230-235. http://www.cnki.com.cn/Article/CJFDTOTAL-XXCN201102014.htmQU C W, XU Z, LI B R, et al.A novel robust algorithm for passive location and tracking with angles and time difference of arrival measurements[J].Signal Processing, 2011, 27(2):230-235(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-XXCN201102014.htm [6] YIN J H, WAN Q, YANG S W, et al.A simple and accurate TDOA-AOA localization method using two stations[J].IEEE Signal Processing Letters, 2016, 23(1):144-148. doi: 10.1109/LSP.2015.2505138 [7] 贾兴江, 周一宇, 郭福成.双/多机测角频差定位算法研究[J].信号处理, 2011, 27(1):37-42. http://www.cnki.com.cn/Article/CJFDTOTAL-XXCN201101008.htmJIA X J, ZHOU Y Y, GUO F C.Research on hybrid DOA and FDOA passive localization using dual/multiple aircrafts[J].Signal Processing, 2011, 27(1):37-42(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-XXCN201101008.htm [8] CAO Y L, PENG L, LI J Z, et al.A new iterative algorithm for geolocating a known altitude target using TDOA and FDOA measurements in the presence of satellite location uncertainty[J].Chinese Journal of Aeronautics, 2015, 28(5):1510-1518. doi: 10.1016/j.cja.2015.08.015 [9] FOY W H.Position location solutions by Taylor-series estimation[J].IEEE Transaction on Aerospace and Electronic Systems, 1976, AES-12(2):187-194. doi: 10.1109/TAES.1976.308294 [10] TPRRIERI D J.Statistical theory of passive location systems[J].IEEE Transaction on Aerospace and Electronic Systems, 1984, AES-20(2):183-198. doi: 10.1109/TAES.1984.310439 [11] WEI H, PENG R, WAN Q, et.al.Multidimensional scaling analysis for passive moving target localization with TDOA and FDOA measurements[J].IEEE Transaction on Signal Processing, 2010, 58(3):1677-1688. doi: 10.1109/TSP.2009.2037666 [12] WANG G, LI Y, ANSARI N.A semidefinite relaxation method for source localization using TDOA and FDOA measurements[J].IEEE Transaction on Vehicle Technology, 2013, 62(2):853-862. doi: 10.1109/TVT.2012.2225074 [13] YU H, HUANG G, GAO J.Constrained total least-squares localization algorithm using time difference of arrival and frequency difference of arrival measurements with sensor location uncertainties[J].IET Radar Sonar & Navigation, 2012, 6(9):891-899. [14] HO K C, CHAN Y T.Geolocation of a known altitude object from TDOA and FDOA measurements[J].IEEE Transaction on Aerospace and Electronic Systems, 1997, 33(3):770-783. doi: 10.1109/7.599239 [15] 郭福成, 樊昀.双星时差频差联合定位方法及其误差分析[J].宇航学报, 2008, 29(4):1381-1386. http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB200804055.htmGUO F C, FAN Y.A method of dual-satellites geolocation using TDOA and FDOA and its precision analysis[J].Journal of Astronautics, 2008, 29(4):1381-1386(in Chinese). http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB200804055.htm [16] 杨宇翔, 夏畅雄, 同武勤.高低轨双星定位中的时变时频差参数估计[J].信号处理, 2012, 28(10):1465-1474. doi: 10.3969/j.issn.1003-0530.2012.10.017YANG Y X, XIA C X, TONG W Q.Estimation of the time varying TDOA and FDOA in the GEO-LEO dual-satellites location system[J].Signal Processing, 2012, 28(10):1465-1474(in Chinese). doi: 10.3969/j.issn.1003-0530.2012.10.017 -
下载:
点击查看大图
计量
- 文章访问数: 907
- HTML全文浏览量: 132
- PDF下载量: 414
- 被引次数: 0
