无需先验测量误差的定位节点选择方法

doi:10.12305/j.issn.1001-506X.2024.01.04

摘要/Abstract

摘要：

针对现有定位节点选择算法依赖先验测量误差的问题, 研究了一种不依赖先验测量误差的时差与频差无源定位节点选择方法, 该方法将两步加权最小二乘定位算法中目标估计误差协方差作为目标函数。在给定可用定位节点数目的情况下, 通过引入一组布尔量构建关于目标函数为带约束的最小估计误差寻优问题, 通过半定松弛技术将非凸问题转为半定规划问题进行求解, 依据最小化问题特性, 使得所提算法不依赖先验测量误差。仿真结果表明, 不依赖测量误差的方法与穷举搜索法相比在定位性能上无太大差别; 相比于穷尽搜索算法, 所提方法复杂度低、实时性好。同时, 仿真结果进一步表明在对运动目标定位过程中, 及时调整定位节点组合的必要性。

关键词: 无源定位, 到达时间差, 到达频率差, 半定规划, 节点优选

Abstract:

In response to the problem of existing localization node selection algorithms relying on prior measurement error, this paper studies a passive localization node selection method for time difference of arrival and frequency difference of arrival (TDOA-FDOA) that does not rely on prior measurement error. This method takes the covariance of the target estimation error in the two-stage weighted least squares (TSWLS) localization algorithm as the objective function. Given the number of available positioning nodes, a minimum estimation error optimization problem with constraints on the objective function is constructed by introducing a set of boolean variables. The non-convex problem is transformed into a semi definite programming semi-definite programming (SDP) problem through semi-definite relaxation (SDR) technique for solution. Based on the characteristics of the minimization problem, the proposed algorithm does not rely on prior measurement error. The simulation results show that there is no significant difference in positioning performance between methods that do not rely on measurement error and exhaustive search methods; Compared to exhaustive search algorithms, the proposed method has lower complexity and better real-time performance. The simulation results further demonstrate the necessity of timely adjusting the combination of positioning nodes in the process of locating moving targets.

Key words: passive localization, time difference of arrival (TOOA), frequency difference of arrival (FDOA), semi-definite programming (SDP), node selection optimization

中图分类号:

TN911.23

汤建龙, 解佳龙, 陈弘凯. 无需先验测量误差的定位节点选择方法[J]. 系统工程与电子技术, 2023, 46(1): 35-41.

Jianlong TANG, Jialong XIE, Hongkai CHEN. Selection method for localization node without priori measurement error[J]. Systems Engineering and Electronics, 2023, 46(1): 35-41.

图/表 7

表1

图1

图2

图3

图4

图5

图6

参考文献 30

1	赵国庆. 雷达对抗原理[M]. 2版西安: 西安电子科技大学出版社, 2012.
	ZHAO G Q . Principles of radar countermea-sure[M]. 2nd ed Xi'an: Xidian University Press, 2012.
2	ZHAO Y , LI Z , CHENG N , et al. Joint UAV position and power optimization for accurate regional localization in space-air integrated localization network[J]. Internet of Things Journal, 2021, 8 (6): 4841- 4854. doi: 10.1109/JIOT.2020.3030064
3	JIA T , HO K C , WANG H , et al. Effect of sensor motion on time delay and Doppler shift localization: analysis and solution[J]. IEEE Trans.on Signal Processing, 2019, 67 (22): 5881- 5895. doi: 10.1109/TSP.2019.2946025
4	VERHEYDE T, BLAIS A, MACABIAU C, et al. SmartCoop algorithm: improving smart-phones position accuracy and reliability through collaborative positioning[C]//Proc. of the International Conference on Localization and GNSS, 2021.
5	LI J , ZHAO Y J , LI D H . Accurate single observer passive coherent location estimation based on Tdoa and DOA[J]. Chinese Journal of Aeronautics, 2014, 27 (4): 913- 923. doi: 10.1016/j.cja.2014.06.004
6	KRISHNAVENI B V, REDDY K S, REDDY P R. An introduction to the TOA measurement for UWB indoor localization systems[C]//Proc. of the 5th Conference on Information and Communication Technology, 2021.
7	LIU Y , GUO F C , YANG L , et al. An improved algebraic solution for TDOA localization with sensor position errors[J]. IEEE Communications Letters, 2015, 19 (12): 2218- 2221. doi: 10.1109/LCOMM.2015.2486769
8	ZOU Y B , LIU H P , WAN Q . An iterative method for moving target localization using TDOA and FDOA measurements[J]. IEEE Access, 2017, 6, 2746- 2754.
9	周恭谦, 杨露菁, 刘忠. 改进的非完全约束加权最小二乘TDOA/FDOA无源定位方法[J]. 系统工程与电子技术, 2018, 40 (8): 1686- 1692.
	ZHOU G Q , LIU L J , LIU Z . Improved incomplete constrained weighted least squares TDOA/FDOA passive location method[J]. Systems Engineering and Electronics, 2018, 40 (8): 1686- 1692.
10	LE T K , HO K C . Joint source and sensor localization by angles of arrival[J]. IEEE Trans.on Signal Processing, 2020, 68, 6521- 6534. doi: 10.1109/TSP.2020.3037412
11	WIN M Z , DAI W , SHEN Y , et al. Network operation strategies for efficient localization and navigation[J]. Proceedings of the IEEE, 2018, 106 (7): 1224- 1254. doi: 10.1109/JPROC.2018.2835314
12	SHAMAIAH M, BANERJEE S, VIKALO H. Greedy sensor selection: leveraging submod-ulearity[C]//Proc. of the IEEE Conference on Decision and Control, 2010: 2572-2577.
13	HU X, FOWLER M L. Sensor selection for multiple sensor emitter location systems[C]//Proc. of the IEEE Aerospace Conference, 2008.
14	JOSHI S , BOYD S . Sensor selection via convex optimization[J]. IEEE Trans.on Signal Processing, 2009, 57 (2): 451- 462. doi: 10.1109/TSP.2008.2007095
15	YANG X J , NIU R . Adaptive sensor selection for nonlinear tracking via sparsity-promoting approaches[J]. IEEE Trans.on Aerospace and Electronic Systems, 2018, 58 (4): 1966- 1982.
16	ZHAO Y , LI Z , HAO B J , et al. How to select the best sensors for TDOA and TDOA/AOA localization?[J]. China Communications, 2019, 16 (2): 134- 145.
17	HASHEMI A , GHASEMI M , VIKALO H , et al. Randomized greedy sensor selection: leveraging weak submodularity[J]. Transactions on Automatic Control, 2021, 66 (1): 199- 212. doi: 10.1109/TAC.2020.2980924
18	余德荧, 李厚朴, 纪兵, 等. 基于灰狼优化算法的快速选星方法[J]. 系统工程与电子技术, 2023, 45 (5): 1489- 1495.
	YU D Y , LI H P , JI B , et al. A fast satellite selection method based on grey wolf optimization algorithm[J]. Systems Engineering and Electronics, 2023, 45 (5): 1489- 1495.
19	SUN T , DONG C X , MAO Y , et al. Moving target localization in multiple-input multiple-output radar systems without the prior knowledge of measurement noise powers[J]. IEEE Communications Letters, 2020, 24 (9): 1957- 1960. doi: 10.1109/LCOMM.2020.3001950
20	ZHANG H W , ZHENG Z , WANG W Q , et al. Source localization using TDOA and FDOA measurements under unknown noise power knowledge[J]. IET Signal Processing, 2020, 14 (7): 435- 439. doi: 10.1049/iet-spr.2019.0406
21	LIU S , MASAZADE E , FARDAD M , et al. Sensor selection with correlated measurements for target tracking in wireless sensor networks[J]. IEEE Trans.on Signal Processing, 2016, 64 (13): 3509- 3520. doi: 10.1109/TSP.2016.2550005
22	DAI Z C , WANG G , JIN X P , et al. Nearly optimal sensor selection for tdoa-based source localization in wireless sensor networks[J]. IEEE Trans.on Vehicular Technology, 2020, 69 (10): 12031- 12042. doi: 10.1109/TVT.2020.3011118
23	CAO N X , CHOI S , MASAZADE E , et al. Sensor selection for target tracking in wireless sensor networks with uncertainty[J]. IEEE Trans.on Signal Processing, 2016, 64 (20): 5191- 5204. doi: 10.1109/TSP.2016.2595500
24	郝本建, 王林林, 李赞, 等. 面向TDOA被动定位的定位节点选择方法[J]. 电子与信息学报, 2019, 41 (2): 462- 468.
	HAO B J , WANG L L , LI Z , et al. Sensor selection method for TDOA passive localization[J]. Journal of Electronics & Information Technology, 2019, 41 (2): 462- 468.
25	NOROOZI A , OVEIS A H , HOSSEINI S M , et al. Improved algebraic solution for source localization from TDOA and FDOA measurements[J]. IEEE Wireless Communications Letters, 2018, 7 (3): 352- 355. doi: 10.1109/LWC.2017.2777995
26	HO K C . Bias reduction for an explicit solution of source localization using TDOA[J]. IEEE Trans.on Signal Processing, 2012, 60 (5): 2101- 2114. doi: 10.1109/TSP.2012.2187283
27	LI Q , CHEN B X , YANG M L . Time difference of arrival passive localization sensor selection method based on Tabu search[J]. Sensors, 2020, 20 (22): 6547. doi: 10.3390/s20226547
28	周荣艳, 陈建峰, 李晓强, 等. 基于目标高斯分布的定位系统节点最优部署方法[J]. 系统工程与电子技术, 2021, 43 (7): 1791- 1796.
	ZHOU R Y , CHEN J F , LI X Q , et al. Optimal deployment method of sensors in localization system based on targets with Gaussian distribution[J]. Systems Engineering and Electronics, 2021, 43 (7): 1791- 1796.
29	WANG G , LI Y M , NASARI N . A semidefinite relaxation method for source localization using TDOA and FDOA measurements[J]. IEEE Trans.on Vehicular Technology, 2013, 62 (2): 853- 862. doi: 10.1109/TVT.2012.2225074
30	赵越. 无线定位网络节点优化理论与关键技术研究[D]. 西安: 西安电子科技大学, 2020.
	ZHAO Y. Research on node operations in wireless localization networks[D]. Xi'an: Xidian University, 2020.

选择数目k	穷尽搜索法耗时	本文算法耗时
4	0.275	0.330
6	4.269	0.333
8	43.487	0.347
10	205.261	0.327

[1]	张铠宇, 于昊天, 卢雨. 一种基于双站协同的时差频差定位方法[J]. 系统工程与电子技术, 2023, 45(9): 2698-2705.
[2]	何胜阳, 杜杰朋, 赵雅琴, 王宝莹, 赵亮, 吴龙文. 基于TDOA的无人机集群协同单目标定位[J]. 系统工程与电子技术, 2023, 45(1): 1-8.
[3]	王伟, 王钦钊, 沈岚, 王波, 丁怀. 基于概率累积的非通视无源定位方法[J]. 系统工程与电子技术, 2022, 44(1): 64-69.
[4]	方冰, 韩冰. MISO无线携能通信系统保密波束形成方法[J]. 系统工程与电子技术, 2021, 43(6): 1692-1698.
[5]	苏志刚, 武瑞, 郝敬堂. 分布式无源定位技术的定位精度提高方法[J]. 系统工程与电子技术, 2020, 42(9): 1890-1896.
[6]	吴龙文, 王宝莹, 魏俊杰, 何胜阳, 赵雅琴. 基于AOA的双机无源定位模型及其解算方法[J]. 系统工程与电子技术, 2020, 42(5): 978-986.
[7]	蒋伊琳, 刘梦楠, 郜丽鹏, 陈涛. 运动多站无源时差/频差联合定位方法[J]. 系统工程与电子技术, 2019, 41(7): 1441-1449.
[8]	朱晓丹, 朱伟强, 陈卓. 基于TOA变化率有偏估计的单通道无源定位[J]. 系统工程与电子技术, 2019, 41(7): 1459-1467.
[9]	王生亮, 刘根友, 高铭, 王嘉琛, 王彬彬. 改进的自适应遗传算法在TDOA定位中的应用[J]. 系统工程与电子技术, 2019, 41(2): 254-258.
[10]	王旭东, 董文杰, 吴楠. 基于TDOA/AOA混合的高精度室内可见光定位算法[J]. 系统工程与电子技术, 2019, 41(10): 2371-2377.
[11]	冯奇, 曲长文, 李廷军. 基于约束加权最小二乘的无源定位闭式解算方法[J]. 系统工程与电子技术, 2017, 39(2): 263-268.
[12]	刘帅琦, 王布宏, 李夏, 田继伟, 曹帅. 二维混合MIMO相控阵雷达收发波束空间设计[J]. 系统工程与电子技术, 2017, 39(10): 2221-2227.
[13]	郝振兴, 罗继勋, 胡朝晖. 空基双探测端分布式定位系统的航迹控制[J]. 系统工程与电子技术, 2016, 38(8): 1886-1891.
[14]	李宁, 曹祯, 邓中亮, 韩可. 干扰源定位中到达时间差参数估计方法[J]. 系统工程与电子技术, 2016, 38(5): 994-.
[15]	李振强1, 黄振2, 陈曦2, 葛宁1. 时频差精度的时变性影响及补偿估计方法[J]. 系统工程与电子技术, 2016, 38(3): 481-486.