基于重要性采样的TOA与FOA无源定位算法

刘瑞瑞; 王云龙; 尹洁昕; 王鼎; 吴瑛

doi:10.1631/FITEE.1601657

Your Location：

Home >

Browse articles >

基于重要性采样的TOA与FOA无源定位算法

常规文章 | Updated：2022-05-19

- 基于重要性采样的TOA与FOA无源定位算法
- Passive source localization using importance sampling based on TOA and FOA measurements
- 信息与电子工程前沿（英文） 2017年18卷第8期页码：1167-1179
- Affiliations：
  
  National Digital Switching System Engineering & Technology Research Center, Zhengzhou 450001, China
- Author bio：
  
  Yun-long WANG, E-mail: chriswayulo@sina.com
- Funds：
  
  Project supported by the National Natural Science Foundation of China (No. 61201381) and the China Postdoctoral Science Foundation (No. 2016M592989)
- DOI：10.1631/FITEE.1601657
  中图分类号： TN91
- 收稿：2016-10-25，
  
  修回：2017-;8-18，
  
  纸质出版：2017-08
- Accepted：
Scan QR Code
刘瑞瑞, 王云龙, 尹洁昕, 等. 基于重要性采样的TOA与FOA无源定位算法[J]. 信息与电子工程前沿（英文）, 2017,18(8):1167-1179.

Rui-rui LIU, Yun-long WANG, Jie-xin YIN, et al. Passive source localization using importance sampling based on TOA and FOA measurements[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(8): 1167-1179.
刘瑞瑞, 王云龙, 尹洁昕, 等. 基于重要性采样的TOA与FOA无源定位算法[J]. 信息与电子工程前沿（英文）, 2017,18(8):1167-1179. DOI： 10.1631/FITEE.1601657.

Rui-rui LIU, Yun-long WANG, Jie-xin YIN, et al. Passive source localization using importance sampling based on TOA and FOA measurements[J]. Frontiers of Information Technology & Electronic Engineering, 2017, 18(8): 1167-1179. DOI： 10.1631/FITEE.1601657.

摘要

最大似然类的无源定位方法可以达到较高的定位精度，但其计算量非常大。由于时频参数联合定位模型本身的非线性和非凸性非常大，繁重的计算量在TOA与FOA联合定位系统中表现尤为明显。本文针对这一问题，通过Pincus全局最优理论和蒙特卡洛重要性采样技术降低了最大似然类定位算法的计算复杂度，并且保证算法可以收敛到全局最优解。本文主要的贡献是构建了一个高斯分布的概率密度函数来近似原始的代价函数方便后续的采样，我们称之为重要性函数。该方法所带来性能上的提升是因为选择了最优的重要性函数并且Pincus保证算法收敛到全局最小值。这一处理大大降低了计算量，由于算法进行了泰勒级数展开，需要初始估计值。通过采样处理并且对样本进行加权，本文算法对初始估计值具有良好的鲁棒性。最后，实验证明本文所提算法可以达到克拉美罗限，且性能要优于现有算法。

Abstract

Passive source localization via a maximum likelihood (ML) estimator can achieve a high accuracy but involves high calculation burdens

especially when based on time-of-arrival and frequency-of-arrival measurements for its internal nonlinearity and nonconvex nature. In this paper

we use the Pincus theorem and Monte Carlo importance sampling (MCIS) to achieve an approximate global solution to the ML problem in a computationally efficient manner. The main contribution is that we construct a probability density function (PDF) of Gaussian distribution

which is called an important function for efficient sampling

to approximate the ML estimation related to complicated distributions. The improved performance of the proposed method is attributed to the optimal selection of the important function and also the guaranteed convergence to a global maximum. This process greatly reduces the amount of calculation

but an initial solution estimation is required resulting from Taylor series expansion. However

the MCIS method is robust to this prior knowledge for point sampling and correction of importance weights. Simulation results show that the proposed method can achieve the Cramér-Rao lower bound at a moderate Gaussian noise level and outperforms the existing methods.

关键词

Keywords

references

F. Alizadeh , , , D. Goldfarb . . Second-order cone programming . . Math. Prog. , , 2003 . . 95 ( ( 1 ): ): 3 - - 51 . . DOI: 10.1007/s10107-002-0339-5 http://doi.org/10.1007/s10107-002-0339-5 . .

A. Beck , , , P. Stoica , , , J. Li . . Exact and approximate solutions of source localization problems . . IEEE Trans. Signal Process. , , 2008 . . 56 ( ( 5 ): ): 1770 - - 1778 . . DOI: 10.1109/TSP.2012.2191778 http://doi.org/10.1109/TSP.2012.2191778 . .

C.G. Broyden . . The convergence of a class of double-rank minimization algorithms 1: general considerations . . IMA J. Appl. Math. , , 1970 . . 6 ( ( 1 ): ): 76 - - 90 . . DOI: 10.1093/imamat/6.1.76 http://doi.org/10.1093/imamat/6.1.76 . .

Y.T. Chan , , , H.Y.C. Hang , , , P.C. Ching . . Exact and approximate maximum likelihood localization algorithms , , 2006 . . 55 ( ( 1 ): ): 10 - - 16 . . DOI: 10.1109/TVT.2005.861162 http://doi.org/10.1109/TVT.2005.861162 . .

K.W. Cheung , , , H.C. So , , , W.K. Ma , , , 等 . . Least squares algorithms for time-of-arrival-based mobile location . . IEEE Trans. Signal Process. , , 2004 . . 52 ( ( 4 ): ): 1121 - - 1130 . . DOI: 10.1109/TSP.2004.823465 http://doi.org/10.1109/TSP.2004.823465 . .

T.F. Coleman , , , Y. Li , , , I. An . . Trust region approach for nonlinear minimization subject to bounds . . SIAM J. Optim. , , 2006 . . 6 ( ( 2 ): ): 418 - - 445 . . DOI: 10.1137/0806023 http://doi.org/10.1137/0806023 . .

L. Dong . . Cooperative localization and tracking of mobile ad hoc networks . . IEEE Trans. Signal Process. , , 2012 . . 60 ( ( 7 ): ): 3907 - - 3913 . . DOI: 10.1109/TSP.2012.2191778 http://doi.org/10.1109/TSP.2012.2191778 . .

V. Elvira , , , L. Martino , , , D. Luengo , , , 等 . . Heretical multiple importance sampling . . IEEE Signal Process. Lett. , , 2016 . . 23 ( ( 10 ): ): 1474 - - 1478 . . DOI: 10.1109/LSP.2016.2600678 http://doi.org/10.1109/LSP.2016.2600678 . .

U. Engel . . A geolocation method using TOA and FOA measurements . . positioning, navigation and communication. IEEE Workshop on Positioning , , 2009 . . p.77 - - 82 . . DOI: 10.1109/WPNC.2009.4907807 http://doi.org/10.1109/WPNC.2009.4907807 . .

R. Fletcher , , , C.M. Reeves . . Function minimization by conjugate gradients . . Comput. J. , , 1964 . . 7 ( ( 2 ): ): 149 - - 154 . . DOI: 10.1090/S0025.5718.1970.0274029.X http://doi.org/10.1090/S0025.5718.1970.0274029.X . .

W.H. Foy . . Position-location solutions by Taylor-series estimation . . IEEE Trans. Aerosp. Electron. Syst. , , 1976 . . AES-12 ( ( 2 ): ): 187 - - 194 . . DOI: 10.1109/TAES.1976.308294 http://doi.org/10.1109/TAES.1976.308294 . .

Z. Fu , , , X. Sun , , , Q. Liu , , , 等 . . Achieving efficient cloud search services: multi-keyword ranked search over encrypted cloud data supporting parallel computing . . IEICE Trans. Commun. , , 2015 . . 98 ( ( 1 ): ): 190 - - 200 . . DOI: 10.1109/TSP.2012.2191778 http://doi.org/10.1109/TSP.2012.2191778 . .

B. Gu , , , X. Sun , , , V.S. Sheng . . Structural minimax probability machine . . IEEE Trans. Neur. Netw. Learn. Syst. , , 2017 . . 28 ( ( 7 ): ): 1646 - - 1656 . . DOI: 10.1109/TNNLS.2016.2544779 http://doi.org/10.1109/TNNLS.2016.2544779 . .

J.G. Huang , , , D. Xie , , , X. Li , , , 等 . . Maximum likelihood DOA estimator based on importance sampling . . IEEE Region 10 Conf. , , 2006 . . p.1 - - 4 . . DOI: 10.1109/TENCON.2006.344051 http://doi.org/10.1109/TENCON.2006.344051 . .

S.M. Kay . . Fundamentals of Statistical Signal Processing, Volume Ⅰ: Estimation Theory . . Prentice-Hall, London , , 1993 . . p.111 - - 136 . . . .

S.M Kay . . Intuitive Probability and Random Processes Using MATLAB . . Springer, Berlin , , 2006 . . DOI: 10.1007/b104645 http://doi.org/10.1007/b104645 . .

C. Knapp , , , G. Carter . . The generalized correlation method for estimation of time delay . . IEEE Trans. Acoust. Speech Signal Process. , , 1976 . . 24 ( ( 4 ): ): 320 - - 327 . . DOI: 10.1109/TASSP.1976.1162830 http://doi.org/10.1109/TASSP.1976.1162830 . .

Z. Ma , , , K.C. Ho . . TOA localization in the presence of random sensor position errors . . IEEE Int. Conf. on Acoustics, Speech and Signal Processing , , 2011 . . p.2468 - - 2471 . . DOI: 10.1109/ICASSP.2011.5946984 http://doi.org/10.1109/ICASSP.2011.5946984 . .

A. Masmoudi , , , F. Bellili , , , S. Affes , , , 等 . . A maximum likelihood time delay estimator in a multipath environment using importance sampling . . IEEE Trans. Signal Process. , , 2013 . . 61 ( ( 1 ): ): 182 - - 193 . . DOI: 10.1109/TSP.2012.2222402 http://doi.org/10.1109/TSP.2012.2222402 . .

Z. Pan , , , J. Lei , , , Y. Zhang , , , 等 . . Fast motion estimation based on content property for low-complexity H . . 265/ HEVC encoder. IEEE Trans. Broadcast. , , 2016 . . 62 ( ( 3 ): ): 1 - - 10 . . DOI: 10.1109/TBC.2016.2580920 http://doi.org/10.1109/TBC.2016.2580920 . .

K. Papakonstantinou , , , D. Slock . . Hybrid TOA/AOD/ Doppler-shift localization algorithm for NLOS environments . . Int. Symp. on Personal, Indoor and Mobile Radio Communications , , 2009 . . p.1948 - - 1952 . . DOI: 10.1109/PIMRC.2009.5450008 http://doi.org/10.1109/PIMRC.2009.5450008 . .

N. Patwari , , , J.N. Ash , , , S. Kyperountas , , , 等 . . Locating the nodes: cooperative localization in wireless sensor networks . . IEEE Signal Process. Mag. , , 2005 . . 22 ( ( 4 ): ): 54 - - 69 . . DOI: 10.1109/MSP.2005.1458287 http://doi.org/10.1109/MSP.2005.1458287 . .

M. Pincus . . A closed form solution of certain programming problems . . Oper. Res. , , 1968 . . 16 ( ( 3 ): ): 690 - - 694 . . DOI: 10.1287/opre.16.3.690 http://doi.org/10.1287/opre.16.3.690 . .

R. Ramlall , , , J. Chen , , , A.L. Swindlehurst . . Non-line-of-sight mobile station positioning algorithm using TOA, AOA, and Doppler-shift . . Ubiquitous Positioning Indoor Navigation and Location Based Service , , 2014 . . p.180 - - 184 . . DOI: 10.1109/UPINLBS.2014.7033726 http://doi.org/10.1109/UPINLBS.2014.7033726 . .

T.S. Rappaport , , , J.H. Reed , , , B.D. Woerner . . Position location using wireless communications on highways of the future . . IEEE Commun. Mag. , , 1996 . . 34 ( ( 10 ): ): 33 - - 41 . . DOI: 10.1109/35.544321 http://doi.org/10.1109/35.544321 . .

D.F. Shanno . . Conditioning of quasi-Newton methods for function minimization . . Math. Comput. , , 1970 . . 24 ( ( 111 ): ): 647 - - 656 . . DOI: 10.1090/S0025.5718.1970.0274029.X http://doi.org/10.1090/S0025.5718.1970.0274029.X . .

J. Shen , , , A.F. Molisch , , , J. Salmi . . Accurate passive location estimation using TOA measurements . . IEEE Trans. Wirel. Commun. , , 2012 . . 11 ( ( 6 ): ): 2182 - - 2192 . . DOI: 10.1109/TWC.2012.040412.110697 http://doi.org/10.1109/TWC.2012.040412.110697 . .

B.Y. Shikur , , , T. Weber . . Localization in NLOS environments using TOA, AOD, and Doppler-shift . . 11th Workshop on Positioning, Navigation and Communication , , 2014 . . p.1 - - 6 . . DOI: 10.1109/WPNC.2014.6843297 http://doi.org/10.1109/WPNC.2014.6843297 . .

L. Vandenberghe , , , S. Boyd . . Semidefinite programming . . SIAM Rev. , , 1998 . . 38 ( ( 1 ): ): 49 - - 95 . . DOI: 10.1137/1038003 http://doi.org/10.1137/1038003 . .

G. Wang , , , H. Chen . . An importance sampling method for TDOA-based source localization . . IEEE Trans. Wirel. Commun. , , 2011 . . 10 ( ( 5 ): ): 1560 - - 1568 . . DOI: 10.1109/TWC.2011.030311.101011 http://doi.org/10.1109/TWC.2011.030311.101011 . .

H. Wang , , , S. Kay . . Maximum likelihood angle-Doppler estimator using importance sampling . . IEEE Trans. Aerosp. Electron. Syst. , , 2010 . . 46 ( ( 2 ): ): 610 - - 622 . . DOI: 10.1109/TAES.2010.5461644 http://doi.org/10.1109/TAES.2010.5461644 . .

H. Wang , , , S. Kay , , , S. Saha . . An importance sampling maximum likelihood direction of arrival estimator . . IEEE Trans. Signal Process. , , 2008 . . 56 ( ( 10 ): ): 5082 - - 5092 . . DOI: 10.1109/TSP.2008.928504 http://doi.org/10.1109/TSP.2008.928504 . .

Y. Wang , , , Y. Wu . . An improved direct position determination algorithm with combined time delay and Doppler . . J. Xi'an Jiaotong Univ. , , 2015 . . 49 ( ( 4 ): ): 123 - - 129 . . DOI: 10.7652/xjtuxb201504020 http://doi.org/10.7652/xjtuxb201504020 . .

Y. Wang , , , Y. Wu . . An efficient semidefinite relaxation algorithm for moving source localization using TDOA and FDOA measurements . . IEEE Commun. Lett. , , 2016 . . 21 ( ( 1 ): ): 80 - - 83 . . DOI: 10.1109/LCOMM.2016.2614936 http://doi.org/10.1109/LCOMM.2016.2614936 . .

A.J. Weiss . . On the accuracy of a cellular location system based on RSS measurements . . IEEE Trans. Veh. Technol. , , 2003 . . 52 ( ( 6 ): ): 1508 - - 1518 . . DOI: 10.1109/TVT.2003.819613 http://doi.org/10.1109/TVT.2003.819613 . .

Z. Xia , , , X. Wang , , , L. Zhang , , , 等 . . A privacy-preserving and copy-deterrence content-based image retrieval scheme in cloud computing . . IEEE Trans. Inform. Forens. Secur. , , 2016 . . 11 ( ( 11 ): ): 2594 - - 2608 . . DOI: 10.1109/TSP.2012.2191778 http://doi.org/10.1109/TSP.2012.2191778 . .

J.X. Yin , , , Y. Wu , , , D. Wang . . On 2-D direction-of-arrival estimation performance for rank reduction estimator in presence of unexpected modeling errors . . Circ. Syst. Signal Process. , , 2014 . . 33 ( ( 2 ): ): 515 - - 547 . . DOI: 10.1007/s00034-013-9654-8 http://doi.org/10.1007/s00034-013-9654-8 . .

J.X. Yin , , , Y. Wu , , , D. Wang . . An auto-calibration method for spatially and temporally correlated noncircular sources in unknown noise fields . . Multidimens. Syst. Signal Process. , , 2016 . . 27 ( ( 2 ): ): 1 - - 29 . . DOI: 10.1007/s11045-015-0316-9 http://doi.org/10.1007/s11045-015-0316-9 . .

W. Zhang , , , G. Zhang . . An efficient algorithm for TDOA/FDOA estimation based on approximate coherent accumulative of short-time CAF . . Int. Conf. on Wireless Communications and Signal Processing , , 2011 . . p.1 - - 4 . . DOI: 10.1109/WCSP.2011.6096807 http://doi.org/10.1109/WCSP.2011.6096807 . .

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

暂无数据