一种基于观测站数目最小化的TDOA/FDOA无源定位算法

doi:10.7527/S1000-6893.2019.22902

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一种基于观测站数目最小化的TDOA/FDOA无源定位算法

孙霆, 董春曦, 董阳阳, 刘明明

西安电子科技大学电子工程学院, 西安 710071

收稿日期:2019-01-10 修回日期:2019-02-15 出版日期:2019-09-15 发布日期:2019-03-15
通讯作者: 董春曦 E-mail:chxdong@mail.xidian.edu.cn
基金资助:
陕西省自然科学基础研究计划（2018JQ6046）

A TDOA/FDOA passive location algorithm with the minimum number of stations

SUN Ting, DONG Chunxi, DONG Yangyang, LIU Mingming

School of Electronic Engineering, Xidian University, Xi'an 710071, China

Received:2019-01-10 Revised:2019-02-15 Online:2019-09-15 Published:2019-03-15
Supported by:
Natural Science Basic Research Project of Shaanxi Province (2018JQ6046)

摘要/Abstract

摘要： 在三维（3D）运动目标无源定位系统中，无模糊定位最少需要4个观测站。而传统的两步加权最小二乘（TSWLS）及其改进的闭式算法至少需要5个观测站进行求解，当减少一个观测站时，这些闭式算法往往无法提供可靠解。针对这一问题，提出一种最小化观测站数目的到达时间差（TDOA）与到达频率差（FDOA）定位算法。该算法是一种闭式解法并且能够在三维场景下仅使用4个观测站进行定位。该算法分为两步：第1步分离传统的TSWLS算法中未知参数空间，建立了一组新的等式，并且利用加权最小二乘（WLS）算法得到目标位置与速度的初始值；第2步利用泰勒级数展开算法将中间变量线性化，对目标位置和速度初始值进一步校正。理论分析证明了在适当的噪声水平下该算法能够达到克拉美罗界（CRLB）。此外，计算机仿真表明仅使用4个观测站时，该算法对于近场以及远场目标参数的估计精度在测量噪声较小时可以实现CRLB；并且还表明使用5个观测站估计时，该算法比TSWLS及其改进算法能更好地适应大的测量噪声。

关键词: 无源定位, 到达时间差(TDOA), 到达频率差(FDOA), 观测站数目, 加权最小二乘

Abstract: In the Three-Dimension (3D) moving target passive positioning scenario, the minimum number of stations required for unambiguous localization is four. However, the traditional Two-Step Weighted Least Squares (TSWLS) and its improved closed-form algorithms require at least five stations. When reducing one station, these closed-form methods often cannot provide available solution. To solve this problem, a Time Difference of Arrival (TDOA) and Frequency Difference of Arrival (FDOA) based positioning algorithm which minimizes the number of stations is proposed in this paper. This algorithm is a closed-form solution and can locate the source with only four stations in the 3D scenario. This method has two steps:in the first step, a new set of equations is established by separating the unknown parameter space of the TSWLS from the known parameters, and the initial values of the source position and velocity are obtained by Weight Least Squares (WLS). In the second step, using taylor series expansion technique, the intermediates are linearized to further correct the initial values. Theoretical analysis proves that the proposed method can reach the Cramér-Rao Lower Bound (CRLB) at the appropriate noise level. In addition, simulations prove that both the far field and the near field parameter estimation accuracy of proposed method can achieve the CRLB at low noise level when only four stations are used.It also shows the positioning performance of the proposed algorithm can better adapt to large measurement noise than TSWLS or its improved algorithms when using five stations.

Key words: passive localization, Time Difference of Arrival (TDOA), Frequency Difference of Arrival (FDOA), number of stations, weighted least square

中图分类号:

V247
TN971

孙霆, 董春曦, 董阳阳, 刘明明. 一种基于观测站数目最小化的TDOA/FDOA无源定位算法[J]. 航空学报, 2019, 40(9): 322902-322902.

SUN Ting, DONG Chunxi, DONG Yangyang, LIU Mingming. A TDOA/FDOA passive location algorithm with the minimum number of stations[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(9): 322902-322902.

参考文献 22

[1]	胡来招. 无源定位[M]. 北京:国防工业出版社, 2005:1-29. HU L Z. Passive locating[M]. Beijing:National Defence Industry Press, 2005:1-29(in Chinese).
[2]	LIU C, FANG D, YANG Z, et al. RSS distribution-based passive localization and its application in sensor networks[J]. IEEE Transactions on Wireless Communications, 2016, 15(4):2883-2895.
[3]	ASSAF A E, ZAIDI S, AFFES S, et al. Low-cost localization for multihop heterogeneous wireless sensor networks[J]. IEEE Transactions on Wireless Communications, 2016, 15(1):472-484.
[4]	WANG Y, HO K C. An asymptotically efficient estimator in closed-form for 3D AOA localization using a sensor network[J]. IEEE Transactions on Wireless Communications, 2015, 14(12):6524-6535.
[5]	NOROOZI A, OVEIS A H, SEBT M A. Iterative target localization in distributed MIMO radar from bistatic range measurements[J]. IEEE Signal Processing Letters, 2017, 24(10):1709-1713
[6]	朱建丰, 陈玥, 郝本建, 等. 基于合成孔径阵列的雷达辐射源被动定位技术研究[J]. 电子学报, 2017, 45(10):22-26. ZHU J F, CHEN Y, HAO B J, et al. Passive radar source localization using synthetic aperture antenna array[J]. Acta Electronica Sinica, 2017, 45(10):22-26(in Chinese).
[7]	PETERS D J. A Bayesian method for localization by multistatic active sonar[J]. IEEE Journal of Oceanic Engineering, 2017, 42(1):135-142.
[8]	SIMAKOV S. Localization in airborne multistatic sonars[J]. IEEE Journal of Oceanic Engineering, 2008, 33(3):278-288.
[9]	FOY W H. Position-location solutions by Taylor-series estimation[J]. IEEE Transactions on Aerospace & Electronic Systems, 1987, 12(2):187-194.
[10]	周成, 黄高明, 单鸿昌, 等. 基于最大似然估计的TDOA/FDOA无源定位偏差补偿算法[J]. 航空学报, 2015, 36(3):979-986. ZHOU C, HUANG G M, SHAN H C, et al. Bias compensation algorithm based on maximum likelihood estimation for passive localization using TDOA and FDOA measurements[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(3):979-986(in Chinese).
[11]	ZHU G H, FENG D Z. Bi-iterative method for moving source localisation using TDOA and FDOA measurements[J]. Electronics Letters, 2015, 51(1):8-10.
[12]	QU X M, XIE L H, TAN W R. Iterative constrained weighted least squares source localization using TDOA and FDOA measurements[J]. IEEE Transactions on Signal Processing, 2017, 65(15):3990-4003.
[13]	HO K C, XU W W. An accurate algebraic solution for moving source location using TDOA and FDOA measurements[J]. IEEE Transactions on Signal Processing, 2004, 52(9):2453-2463.
[14]	HO K C, LU X, KOVAVISARUCH L. Source localization using TDOA and FDOA measurements in the presence of receiver location errors:Analysis and solution[J]. IEEE Transactions on Signal Processing, 2007, 55(2):684-696.
[15]	YANG K, JIANG L, LUO Z Q. Efficient semidefinite relaxation for robust geolocation of unknown emitter by satellite cluster using TDOA and FDOA measurements[C]//2011 IEEE International Conference on Acoustics, Speech and Signal Process. Piscataway, NJ:IEEE Press, 2011:2584-2587.
[16]	WANG G, LI Y, ANSARI N. A semidefinite relaxtion method for source localization using TDOA and FDOA measurements[J]. IEEE Transactions on Vehicular Technology, 2013, 62(2):852-863.
[17]	WEI H W, PENG R, WAN Q, et al. Multidimensional scaling analysis for passive moving target localization with TDOA and FDOA measurements[J]. IEEE Transactions on Signal Processing, 2010, 58(3):1677-1688.
[18]	曹景敏, 万群, 欧阳鑫信, 等. 观测站有位置误差的多维标度时频差定位算法[J]. 信号处理, 2017, 33(1):1-9. CAO J M, WAN Q, OUYANG X X, et al. Multidimensional scaling-based passive emitter localization from time difference of arrival and frequency difference of arrival measurements with sensor location uncertainties[J]. Journal of Signal Processing, 2017, 33(1):1-9(in Chinese).
[19]	刘洋, 杨乐, 郭福成, 等. 基于定位误差修正的运动目标TDOA/FDOA无源定位算法[J]. 航空学报, 2015, 36(5):1617-1626. LIU Y, YANG L, GUO F C, et al. Moving targets TDOA/FDOA passive localization algorithm based on localization error refinement[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(5):1617-1626(in Chinese).
[20]	NOROOZI A, OVEIS A H, HOSSEINI M R, et al. Improved algebraic solution for source localization from TDOA and FDOA measurements[J]. IEEE Wireless Communications Letters, 2018, 7(3):352-355.
[21]	KAY S M. Fundamentals of statistical signal processing volumn I:Estimation theory[M]. Upper Saddle River, NJ:Prentice Hall, 1998:23-45.
[22]	张贤达. 矩阵分析与应用[M]. 北京:清华大学出版社, 2004:144-151 ZHANG X D. Matrix analysis and application[M]. Beijing:Tsinghua University Press, 2004:144-151(in Chinese).

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一种基于观测站数目最小化的TDOA/FDOA无源定位算法

A TDOA/FDOA passive location algorithm with the minimum number of stations

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