A novel method for TDOA localization in presence of synchronization clock bias and sensor position uncertainty

WANG Ding; YIN Jiexin; GAO Lu; YANG Bin

doi:10.7527/S1000-6893.2021.25405

ACTA AERONAUTICAET ASTRONAUTICA SINICA >

2022 , Vol. 43 >Issue 7: 325405 - 325405

DOI: https://doi.org/10.7527/S1000-6893.2021.25405

Electronics and Electrical Engineering and Control

A novel method for TDOA localization in presence of synchronization clock bias and sensor position uncertainty

WANG Ding ,
YIN Jiexin ,
GAO Lu ,
YANG Bin

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1. Institute of Information System Engineering, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China;
2. National Digital Switching System Engineering and Technology Research Center, Zhengzhou 450002, China;
3. Beijing Institute of Space Long March Vehicle, Beijing 100076, China

Received date: 2021-02-21

Revised date: 2021-07-21

Online published: 2021-07-20

Supported by

National Natural Science Foundation of China (62071029, 61772548, 61901526); Key Scientific and Technological Projects in Henan Province (192102210092); Research and Development Fund of PLA Strategic Support Force Information Engineering University (F4108, F4109)

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Abstract

Synchronous clock bias and sensor position uncertainty seriously affect Time Difference of Arrival (TDOA) positioning performance. To solve this problem, based on the principle of Weighted MultiDimensional Scaling (WMDS), this paper proposes a novel TDOA location method, which can effectively restrain the influence of these two kinds of errors. First, an elimination matrix is constructed to mitigate the effect of clock offset. Subsequently, the location relationship is formed based on the WMDS approach, and the estimation results of the locations of the emitter and the sensors are obtained. Finally, the synchronization clock bias is determined based on the criterion of the maximum likelihood estimator. The proposed method makes use of the dimension and eigenstructure information of the scalar product matrix, and thus has stronger robustness to all kinds of errors. A theoretical performance analysis shows that the Mean Square Error (MSE) of the proposed estimator for all the unknowns can reach the corresponding Cramér-Rao Lower Bound(CRLB). Simulation results verify that the new estimator is asymptotically efficient, and its threshold effect occurs later than that of some existing TDOA localization methods.

Key words： emitter localization; Time Difference of Arrival(TDOA); Weighted MultiDimensional Scaling(WMDS); synchronization clock bias; sensor location uncertaintyhttp

Cite this article

WANG Ding , YIN Jiexin , GAO Lu , YANG Bin . A novel method for TDOA localization in presence of synchronization clock bias and sensor position uncertainty[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022 , 43(7) : 325405 -325405 . DOI: 10.7527/S1000-6893.2021.25405

References

[1] 马方立,徐扬,徐鹏.基于大地经纬度的二维TDOA无源定位[J].通信学报, 2019, 40(5):136-143. MA F L, XU Y, XU P. 2D-TDOA passive location based on geodetic longitude and latitude[J]. Journal on Communications, 2019, 40(5):136-143(in Chinese).
[2] WANG G, CHEN H Y. An importance sampling method for TDOA-based source localization[J]. IEEE Transactions on Wireless Communications, 2011, 10(5):1560-1568.
[3] XU E Y, DING Z, DASGUPTA S. Reduced complexity semidefinite relaxation algorithms for source localization based on time difference of arrival[J]. IEEE Transactions on Mobile Computing, 2011, 10(9):1276-1282.
[4] 房嘉奇,冯大政,李进. TDOA中的修正牛顿及泰勒级数方法[J].西安电子科技大学学报, 2016, 43(6):27-33. FANG J Q, FENG D Z, LI J. Research on modified Newton and Taylor-series methods in TDOA[J]. Journal of Xidian University, 2016, 43(6):27-33(in Chinese).
[5] YANG K, AN J P, BU X Y, et al. Constrained total least-squares location algorithm using time-difference-of-arrival measurements[J]. IEEE Transactions on Vehicular Technology, 2010, 59(3):1558-1562.
[6] 李万春,魏平,肖先赐.一种稳健的TDOA无源定位方法及其性能分析[J].中国科学F辑:信息科学, 2009, 39(4):476-482. LI W C, WEI P, XIAO X C. A robust TDOA-based location method and its performance analysis[J]. Science in China Series F:Information Sciences, 2009, 39(4):476-482(in Chinese).
[7] 王鼎,胡涛.无源定位技术-二次等式约束最小二乘估计理论与方法[M].北京:电子工业出版社, 2018:45-57. WANG D, HU T. The least-squares estimation theory and method in passive location with quadratic equality constraints[M]. Beijing:Publishing House of Electronics Industry, 2018:45-57(in Chinese).
[8] SMITH J, ABEL J. Closed-form least-squares source location estimation from range-difference measurements[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1987, 35(12):1661-1669.
[9] HUANG Z, LU J. Total least squares and equilibration algorithm for range difference location[J]. Electronics Letters, 2004, 40(5):323-325.
[10] CHAN Y T, HO K C. A simple and efficient estimator for hyperbolic location[J]. IEEE Transactions on Signal Processing, 1994, 42(8):1905-1915.
[11] WEI H W, WAN Q, CHEN Z X, et al. Multidimensional scaling-based passive emitter localisation from range-difference measurements[J]. IET Signal Processing, 2008, 2(4):415.
[12] WANG Y L, WU Y, YI S C, et al. Complex multidimensional scaling algorithm for time-of-arrival-based mobile location:A unified framework[J]. Circuits, Systems, and Signal Processing, 2017, 36(4):1754-1768.
[13] 陈少昌,贺慧英,禹华钢.传感器位置误差条件下的约束总体最小二乘时差定位算法[J].航空学报, 2013, 34(5):1165-1173. CHEN S C, HE H Y, YU H G. Constrained total least-squares for source location using TDOA measurements in the presence of sensor position errors[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(5):1165-1173(in Chinese).
[14] 朱颖童,董春曦,刘松杨,等.存在观测站位置误差的转发式时差无源定位[J].航空学报, 2016, 37(2):706-716. ZHU Y T, DONG C X, LIU S Y, et al. Passive localization using retransmitted TDOA measurements in the presence of sensor position errors[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(2):706-716(in Chinese).
[15] 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.
[16] 左燕,周夏磊,蒋陶然.传感器位置误差下外辐射源雷达三维定位代数解算法[J].电子与信息学报, 2020, 42(3):555-562. ZUO Y, ZHOU X L, JIANG T R. Algebraic solution for 3D localization of multistatic passive radar in the presence of sensor position errors[J]. Journal of Electronics&Information Technology, 2020, 42(3):555-562(in Chinese).
[17] CAO J M, WAN Q, OUYANG X X, et al. Multidimensional scaling-based passive emitter localisation from time difference of arrival measurements with sensor position uncertainties[J]. IET Signal Processing, 2017, 11(1):43-50.
[18] YANG L, HO K C. An approximately efficient TDOA localization algorithm in closed-form for locating multiple disjoint sources with erroneous sensor positions[J]. IEEE Transactions on Signal Processing, 2009, 57(12):4598-4615.
[19] SUN M, YANG L, HO D K C. Efficient joint source and sensor localization in closed-form[J]. IEEE Signal Processing Letters, 2012, 19(7):399-402.
[20] WANG D, YIN J X, TANG T, et al. A two-step weighted least-squares method for joint estimation of source and sensor locations:A general framework[J]. Chinese Journal of Aeronautics, 2019, 32(2):417-443.
[21] ZOU Y B, LIU H P. Semidefinite programming methods for alleviating clock synchronization bias and sensor position errors in TDOA localization[J]. IEEE Signal Processing Letters, 2020, 27:241-245.
[22] WANG D, YIN J X, CHEN X, et al. On the use of calibration emitters for TDOA source localization in the presence of synchronization clock bias and sensor location errors[J]. EURASIP Journal on Advances in Signal Processing, 2019, 2019:37.
[23] GHOLAMI M R, GEZICI S, STROM E G. TDOA based positioning in the presence of unknown clock skew[J]. IEEE Transactions on Communications, 2013, 61(6):2522-2534.
[24] AHMAD A, SERPEDIN E, NOUNOU H, et al. Joint node localization and time-varying clock synchronization in wireless sensor networks[J]. IEEE Transactions on Wireless Communications, 2013, 12(10):5322-5333.
[25] RUI L Y, HO K C. Algebraic solution for joint localiza-tion and synchronization of multiple sensor nodes in the presence of beacon uncertainties[J]. IEEE Transactions on Wireless Communications, 2014, 13(9):5196-5210.
[26] XIONG H, CHEN Z Y, YANG B Y, et al. TDOA localization algorithm with compensation of clock offset for wireless sensor networks[J]. China Communications, 2015, 12(10):193-201.
[27] WANG Y, HO K C. TDOA source localization in the presence of synchronization clock bias and sensor position errors[J]. IEEE Transactions on Signal Processing, 2013, 61(18):4532-4544.
[28] 王鼎,尹洁昕,刘瑞瑞,等.同步时钟偏差存在下的时差定位性能分析及改进的定位方法[J].电子学报, 2018, 46(6):1281-1288. WANG D, YIN J X, LIU R R, et al. Performance analysis and improvement for TDOA source localization in the presence of synchronization clock bias[J]. Acta Electronica Sinica, 2018, 46(6):1281-1288(in Chinese).
[29] VIBERG M, OTTERSTEN B. Sensor array processing based on subspace fitting[J]. IEEE Transactions on Signal Processing, 1991, 39(5):1110-1121.
[30] KAY S M.统计信号处理基础-估计与检测理论[M].罗鹏飞,张文明,刘忠,等,译.北京:电子工业出版社, 2011:129-158. KAY S M. Fundamentals of statistical signal processing-Estimation and detection theory[M]. LUO P F, ZHANG W M, LIU Z, et al. translated. Beijing:Publishing House of Electronics Industry, 2011:129-158(in Chinese).
[31] TORRIERI D J. Statistical theory of passive location systems[J]. IEEE Transactions on Aerospace and Electronic Systems, 1984, 20(2):183-198.

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