ACTA AERONAUTICAET ASTRONAUTICA SINICA >
A TDOA/FDOA cooperative localization method for multiple disjoint sources based on weighted multidimensional scaling analysis
Received date: 2022-03-04
Revised date: 2022-03-28
Accepted date: 2022-05-30
Online published: 2022-05-09
Supported by
National Natural Science Foundation of China(62171469);Key Scientific and Technological Projects in Henan Province(192102210092);Research and Development Fund of PLA Strategic Support Force Information Engineering University(F4108)
TDOA/FDOA localization is an important wireless positioning mechanism for moving emitters， and its location accuracy is greatly affected by measurement errors of TDOA/FDOA and prior measurement errors of sensor models （including sensor position and velocity）. To improve the localization performance under the condition of high-level measurement errors， a TDOA/FDOA cooperative localization method for multiple disjoint sources is proposed based on weighted multidimensional scaling analysis in this paper. The proposed method consists of two calculation stages： Stage-a and Stage-b. Specifically， in Stage-a， two groups of scalar product matrices in multidimensional scaling analysis are employed to form the positioning relationship， which is further used to yield the solutions for the locations of multiple disjoint sources and sensors by constructing a weighting matrix. In Stage-b， a constrained minimization model is established based on the intermediate variables introduced in multidimensional scaling analysis to determine the estimation errors in Stage-a. By solving this optimization problem， the expression for the localization errors in Stage-a are obtained， so as to refine the position and velocity estimates of the multiple disjoint sources as well as the sensors. In addition， the first-order error analysis is employed to prove that the proposed method can asymptotically reach the Cramér-Rao Bound （CRB） accuracy. Simulation results show that the new method outperforms the existing TDOA/FDOA positioning methods.
Ding WANG , Jiexin YIN , Xinguang ZHANG , Na’e ZHENG . A TDOA/FDOA cooperative localization method for multiple disjoint sources based on weighted multidimensional scaling analysis[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023 , 44(7) : 327105 -327105 . DOI: 10.7527/S1000-6893.2022.27105
| 1 | LIU Y N， NIU H Q， LI Z L. A multi-task learning convolutional neural network for source localization in deep ocean［J］. The Journal of the Acoustical Society of America， 2020， 148（2）： 873. |
| 2 | MA F H， LIU Z M， YANG L， et al. Source localization in large-scale asynchronous sensor networks［J］. Digital Signal Processing， 2021， 109： 102920. |
| 3 | HE J， LI L N， SHU T， et al. Mixed near-field and far-field source localization based on exact spatial propagation geometry［J］. IEEE Transactions on Vehicular Technology， 2021， 70（4）： 3540-3551. |
| 4 | 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. |
| 5 | 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 Transactions on Vehicular Technology， 2020， 69（10）： 12031-12042. |
| 6 | ZHANG L， ZHANG T， SHIN H S. An efficient constrained weighted least squares method with bias reduction for TDOA-based localization［J］. IEEE Sensors Journal， 2021， 21（8）： 10122-10131. |
| 7 | YEREDOR A， ANGEL E. Joint TDOA and FDOA estimation： A conditional bound and its use for optimally weighted localization［J］. IEEE Transactions on Signal Processing， 2011， 59（4）： 1612-1623. |
| 8 | LIU Z X， WANG R， ZHAO Y J. Computationally efficient TDOA and FDOA estimation algorithm in passive emitter localisation［J］. IET Radar， Sonar & Navigation， 2019， 13（10）： 1731-1740. |
| 9 | FOY W H. Position-location solutions by Taylor-series estimation［J］. IEEE Transactions on Aerospace and Electronic Systems， 1976， AES-12（2）： 187-194. |
| 10 | WANG Y L， WU Y. An efficient semidefinite relaxation algorithm for moving source localization using TDOA and FDOA measurements［J］. IEEE Communications Letters， 2017， 21（1）： 80-83. |
| 11 | YU H G， HUANG G M， GAO J， et al. An efficient constrained weighted least squares algorithm for moving source location using TDOA and FDOA measurements［J］. IEEE Transactions on Wireless Communications， 2012， 11（1）： 44-47. |
| 12 | 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， YANG 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 （in Chinese）. | |
| 13 | 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. |
| 14 | LIU C F， YUN J W. A joint TDOA/FDOA localization algorithm using Bi-iterative method with optimal step length［J］. Chinese Journal of Electronics， 2021， 30（1）： 119-126. |
| 15 | 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. |
| 16 | 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. |
| 17 | SONG H B， WEN G J， ZHU L X， et al. A novel TSWLS method for moving target localization in distributed MIMO radar systems［J］. IEEE Communications Letters， 2019， 23（12）： 2210-2214. |
| 18 | CHEN Z X， WEI H W， WAN Q， et al. A supplement to multidimensional scaling framework for mobile location： A unified view［J］. IEEE Transactions on Signal Processing， 2009， 57（5）： 2030-2034. |
| 19 | 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. |
| 20 | WEI H W， LU P Z. On optimality of weighted multidimensional scaling for range-based localization［J］. IEEE Transactions on Signal Processing， 2020， 68： 2105-2113. |
| 21 | 李万春. 加权多维标量的接收信号强度定位方法［J］. 信号处理， 2013， 29（12）： 1713-1717. |
| LI W C. Novel weighted multidimensional scaling method for received signal strength based source location［J］. Journal of Signal Processing， 2013， 29（12）： 1713-1717 （in Chinese）. | |
| 22 | CHAN F K W， SO H C. Efficient weighted multidimensional scaling for wireless sensor network localization［J］. IEEE Transactions on Signal Processing， 2009， 57（11）： 4548-4553. |
| 23 | LIN L X， SO H C， CHAN F K W. Multidimensional scaling approach for node localization using received signal strength measurements［J］. Digital Signal Processing， 2014， 34： 39-47. |
| 24 | 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. |
| 25 | 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. |
| 26 | HO K C， LU X N， 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. |
| 27 | SUN X Y， LI J D， HUANG P Y， et al. Total least-squares solution of active target localization using TDOA and FDOA measurements in WSN［C］∥22nd International Conference on Advanced Information Networking and Applications-Workshops （aina workshops 2008）. Piscataway： IEEE Press， 2008： 995-999. |
| 28 | YU H， GAO J， HUANG G. Constrained total least-squares localisation 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. |
| 29 | 曲付勇， 孟祥伟. 基于约束总体最小二乘方法的到达时差到达频差无源定位算法［J］. 电子与信息学报， 2014， 36（5）： 1075-1081. |
| QU F Y， MENG X W. Source localization using TDOA and FDOA measurements based on constrained total least squares algorithm［J］. Journal of Electronics ＆ Information Technology， 2014， 36（5）： 1075-1081 （in Chinese）. | |
| 30 | 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）. | |
| 31 | LIU Z X， HU D X， ZHAO Y S， et al. An algebraic method for moving source localization using TDOA， FDOA， and differential Doppler rate measurements with receiver location errors［J］. EURASIP Journal on Advances in Signal Processing， 2019， 2019： 1-15. |
| 32 | LU X N， HO K C. Taylor-series technique for moving source localization in the presence of sensor location errors［C］∥2006 IEEE International Symposium on Circuits and Systems. Piscataway： IEEE Press， 2006： 1075-1078. |
| 33 | WU H， SU W M， GU H. A novel Taylor series method for source and receiver localization using TDOA and FDOA measurements with uncertain receiver positions［C］∥Proceedings of 2011 IEEE CIE International Conference on Radar. Piscataway： IEEE Press， 2011： 1037-1040. |
| 34 | SUN M， HO K C. An asymptotically efficient estimator for TDOA and FDOA positioning of multiple disjoint sources in the presence of sensor location uncertainties［J］. IEEE Transactions on Signal Processing， 2011， 59（7）： 3434-3440. |
| 35 | HAO B J， LI Z， SI J B， et al. Joint source localisation and sensor refinement using time differences of arrival and frequency differences of arrival［J］. IET Signal Processing， 2014， 8（6）： 588-600. |
| 36 | GAO L Y， LIU M Z， YUE J Y， et al. Source number estimation based on improved singular value decomposition at low SNR［C］∥2019 IEEE 9th International Conference on Electronics Information and Emergency Communication. Piscataway： IEEE Press， 2019： 1-4. |
| 37 | 麻凯利， 王川川. 基于深度学习的信源数估计方法［J］. 航天电子对抗， 2019， 35（3）： 7-11. |
| MA K L， WANG C C. Source number estimation method based on deep learning［J］. Aerospace Electronic Warfare， 2019， 35（3）： 7-11 （in Chinese）. | |
| 38 | ICHIGE K， HAMADA S， KASHIWAGI K， et al. Robust source number estimation based on denoising preprocessing［C］∥2020 Sensor Signal Processing for Defence Conference （SSPD）. Piscataway： IEEE Press， 2020： 1-5. |
| 39 | JIANG B， LU A N， XU J. An improved signal number estimation method based on information theoretic criteria in array processing［C］∥2019 IEEE 11th International Conference on Communication Software and Networks. Piscataway： IEEE Press， 2019： 193-197. |
| 40 | ROGERS J， BALL J E， GURBUZ A C. Robust estimation of the number of coherent radar signal sources using deep learning［J］. IET Radar， Sonar & Navigation， 2021， 15（5）： 431-440. |
| 41 | VIBERG M， OTTERSTEN B. Sensor array processing based on subspace fitting［J］. IEEE Transactions on Signal Processing， 1991， 39（5）： 1110-1121. |
| 42 | ZHANG L， YANG B， LUO M K. Joint delay and Doppler shift estimation for multiple targets using exponential ambiguity function［J］. IEEE Transactions on Signal Processing， 2017， 65（8）： 2151-2163. |
| 43 | ZHANG X D， LI H B， HIMED B. Maximum likelihood delay and Doppler estimation for passive sensing［J］. IEEE Sensors Journal， 2019， 19（1）： 180-188. |
| 44 | NG B C， NEHORAI A. Active array sensor localization［J］. Signal Processing， 1995， 44（3）： 309-327. |
| 45 | WANG L， HON T K， REISS J D， et al. Self-localization of ad-hoc arrays using time difference of arrivals［J］. IEEE Transactions on Signal Processing， 2016， 64（4）： 1018-1033. |
| 46 | BERTSEKAS D P. Nonlinear programming［M］. 2nd ed. Belmont： Athena Scientific， 1999. |
| 47 | 高祺. 多传感器多目标跟踪的数据关联算法研究［D］. 西安： 西安电子科技大学， 2013. |
| GAO Q. Research on multisensor-multitarget tracking data association algorithm［D］. Xi’an： Xidian University， 2013 （in Chinese）. |
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