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Bias compensation algorithm based on maximum likelihood estimation for passive localization using TDOA and FDOA measurements
Received date: 2014-09-09
Revised date: 2014-11-19
Online published: 2015-03-31
Supported by
National Natural Science Foundation of China(60901069), National High-tech Research and Development Program of China (2013AAXXXX061)
In the time differences/frequency differences of arrival (TDOA/FDOA) passive localization system, the nonlinear nature of the localization problem creates bias to a location estimate. When the measurement noise is large and the geolocation geometry is poor, the bias of localization is significant. In order to solve the problem, a novel bias compensation localization algorithm based on maximum likelihood estimation is proposed. The algorithm locates the target in three steps. Firstly, it starts by solving the target location using the maximum likelihood estimator. Secondly, using the estimated location and noisy data measurements, the theoretical bias of the target location estimate is derived in the second step. Finally, the bias compensated result is derived by subtracting theoretical bias from the maximum likelihood solution. Theoretical analysis and actual results verify that the theoretical bias of target position and velocity matches very well with simulation when the noise is small, and the bias compensation algorithm can reduce the bias effectively while keeping the same root mean square error (RMSE) with the original maximum likelihood algorithm, meanwhile the target localization performance is improved effectively.
TDOA and FDOA measurements ZHOU Cheng , HUANG Gaoming , SHAN Hongchang , GAO Jun . Bias compensation algorithm based on maximum likelihood estimation for passive localization using TDOA and FDOA measurements[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015 , 36(3) : 979 -986 . DOI: 10.7527/S1000-6893.2014.0317
[1] Xu Z, Qu C W, Wang C H. Performance analysis for multiple moving observers passive localization in the presence of systematic errors[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(3): 629-635 (in Chinese). 徐征, 曲长文, 王昌海. 系统误差条件下的多运动站无源定位性能分析[J]. 航空学报, 2013, 34(3): 629-635.
[2] Ozgur B, Kenneth K D. Localization of more sources than sensors via joint-sparse beyasian learning[J]. IEEE Signal Processing Letters, 2014, 21(2): 131-134.
[3] Wang Z H, Seyed A, Reza Z. Omnidirectional mobile NLOS identification and localization via multiple cooperative nodes[J]. IEEE Transactions on Mobile Computing, 2012, 11(12): 2047-2059.
[4] Chen W, Li X. Sensor localization in concave environments[J]. ACM Transactions on Sensor Networks, 2008, 4(1): 1-31.
[5] Canclini A, Antonacci F, Sarti A, et al. Acoustic source localization with distributed asynchronous microphone networks[J]. IEEE Transactions on Audio, Speech, and Language Processing, 2013, 21(2): 439-443.
[6] Satoshi K, Hiroshi M, Yuuki T, et al. Microphone array for 2D sound localization and capture[J]. Springer Tracts in Advanced Robotics, 2006, 21(1): 45-54.
[7] Chen T Y, Liu C S, Zakharov V. Source localization using matched-phase matched-field processing with phase descent search[J]. IEEE Journal of Oceanic Engineering, 2012, 37(2): 261-269.
[8] Natanael N M, Eduardo F S F, Jose M S. Narrow-band short-time frequency-domain blind signal separation of passive sonar signals[J]. Lecture Notes in Computer Science, 2009, 5441(1): 686-693.
[9] Li J D, Sun X Y, Huang P Y, et al. Performance analysis of active target localization using TDOA and FDOA measurements in WSN[C]//IEEE 22nd International Conference on Advanced Information Networking and Applications Workshops. Piscataway, NJ: IEEE, 2008: 585-589.
[10] Liu X G. Analysis on the error of single/multiple airborne observer(s) passive localization[D]. Changsha: National University of Defense Technology, 2010 (in Chinese). 刘晓光. 单/多机空空无源定位误差分析[D]. 长沙: 国防科学技术大学, 2010.
[11] Rui L Y, Ho K C. Bias analysis of source localization using the maximum likelihood estimator[C]//2012 IEEE International Conference on Acoustics, Speech and Signal Processing. Piscataway, NJ: IEEE, 2012: 2605-2608.
[12] Ho K C. Bias reduction for an explicit solution of source localization using TDOA[J]. IEEE Transactions on Signal Processing, 2012, 60(5): 2101-2113.
[13] Barton R J, Rao D. Performance capabilities of long-range UWB-IR TDOA localization systems[J]. EURASIP Journal on Advances in Signal Processing, 2008, 2008(81): 1-17.
[14] Dogancay K. Bias compensation for the bearings-only pseudolinear target track estimator[J]. IEEE Transactions on Signal Processing, 2006, 54(1): 59-68.
[15] Rui L Y, Ho K C. Bias compensation for target tracking from range based maximum likelihood position estimates[C]//2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop. Piscataway, NJ: IEEE, 2012: 193-196.
[16] Hao B J, Li Z, Qi P H, et al. Effective bias reduction methods for passive source localization using TDOA and GROA[J]. Science China Information Sciences, 2013, 56(7): 1-12.
[17] 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.
[18] Foy W H. Position-location solutions by Taylor series estimation[J]. IEEE Transactions on Aerospace Electronic System, 1976, 12(3): 187-194.
[19] Zhang X D. Matrix analysis and applications[M]. Beijing: Tsinghua University Press, 2004: 64-70 (in Chinese). 张贤达. 矩阵分析与应用[M]. 北京: 清华大学出版社, 2004: 64-70.
[20] Kay S M. Fundamentals of statistical signal processing, estimation theory[M]. New York: Prentice-Hall, 1993: 20-30.
[21] Wang G , Li Y M, Nirwan A. A semi-definite relaxation method for source localization using TDOA and FDOA measurements[J]. IEEE Transactions on Vehicular Technology, 2013, 62(2): 853-862.
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