Application Research of LM Algorithm in TDOA-based Three-dimensional Positioning

doi:10.19678/j.issn.1000-3428.0056130

Abstract

Abstract: The Taylor algorithm for TDOA-based three-dimensional positioning is affected by external conditions,which leads to a large-scale solution failure.To address the problem,a simulation software for the TDOA-based three-dimensional positioning algorithm is developed to carry out simulation for the application of the Taylor algorithm in TDOA-based three-dimensional positioning,and the environmental restrictions of the Taylor algorithm in the TDOA-based three-dimensional positioning application are found.In order to reduce the unnecessary impact of the external environment on the positioning performance and avoid the large-area non-convergence in the positioning results,the LM algorithm is proposed as a solution to TDOA-based three-dimensional positioning.Results of simulation show that the LM algorithm overcomes the limitations of the Taylor algorithm in the use of conditions,improves the positioning accuracy while ensuring the result convergence,and has robustness.The feasibility of the LM algorithm is verified as a solution to TDOA-based three-dimensional positioning.

Key words: TDOA technology, three-dimensional positioning, Taylor algorithm, LM algorithm, convergence

摘要： 针对Taylor算法在TDOA三维定位中受到外界条件的影响而导致大范围求解失败的问题，开发TDOA三维定位算法仿真软件并对Taylor算法在TDOA三维定位中的应用进行仿真，找到Taylor算法在TDOA三维定位应用中的环境限制因素。为了降低外部环境对定位性能产生不必要的影响，避免定位结果产生大面积不收敛的现象，将LM算法作为TDOA三维定位的求解算法。仿真结果表明，与Taylor算法相比，LM算法克服了Taylor算法的使用条件限制，在保证结果收敛的前提下提高了定位精度，且具有鲁棒性，验证了LM算法作为TDOA三维定位求解算法的可行性。

关键词: TDOA技术, 三维定位, Taylor算法, LM算法, 收敛

CLC Number:

TP393

WEI Zihui, ZHANG Yaofa, ZHAO Jixun, XIE Yunlong, LI Xiaoting, FANG Lide. Application Research of LM Algorithm in TDOA-based Three-dimensional Positioning[J]. Computer Engineering, 2020, 46(9): 193-197,204.

韦子辉, 张要发, 赵计勋, 解云龙, 李小亭, 方立德. LM算法在TDOA三维定位中的应用研究[J]. 计算机工程, 2020, 46(9): 193-197,204.

/ / Recommend / Download Citations

URL: http://www.ecice06.com/EN/10.19678/j.issn.1000-3428.0056130

http://www.ecice06.com/EN/Y2020/V46/I9/193

Figures/Tables 8

References

[1] LI Yan,YUAN Hongyu,YU Jiaqiao,et al.A survey of the application of genetic algorithms in optimization problems[J].Shandong Industrial Technology,2019(12):242-243,180.(in Chinese) 李岩,袁弘宇,于佳乔,等.遗传算法在优化问题中的应用综述[J].山东工业技术,2019(12):242-243,180.
[2] KRAMER O.Genetic algorithm essentials[EB/OL].[2019-09-12].https://link.springer.com/content/pdf/bfm%3A978-3-319-52156-5%2F1.pdf.
[3] ZHANG Mengdan,ZHAN Zhihui,LI Jingjing,et al.Tournament selection based artificial bee colony algorithm with elitist strategy[C]//Proceedings of International Conference on Technologies and Applications of Artificial Intelligence.Berlin,Germany:Springer,2014:387-396.
[4] JERIN L I,SARAVANA S S,VICTOR R M,et al.An elitist strategy genetic algorithm for integrated layout design[J].The International Journal of Advanced Manufacturing Technology,2013,66:1573-1589.
[5] FANG B T.Simple solutions for hyperbolic and related position fixes[J].IEEE Transactions on Aerospace and Electronic Systems,1990,26(5):748-753.
[6] FRIEDLANDER B.A passive localization algorithm and its accuracy analysis[J].IEEE Journal of Oceanic Engineering,1987,12(1):234-245.
[7] SCHAU H,ROBINSON A.Passive source localization employing intersecting spherical surfaces from time-of-arrival differences[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1987,35(8):1223-1225.
[8] ABEL J,SMITH J.The spherical interpolation method for closed-form passive source localization using rangedifference measurements[C]//Proceedings of IEEE International Conference on Acoustics,Speech,and Signal Processing.Washington D.C.,USA:IEEE Press,1987:471-474.
[9] 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.
[10] FOY W.Position-location solutions by Taylor-series estimation[J].IEEE Transactions on Aerospace and Electronic Systems,1976,12(2):187-194.
[11] JIANG Kangrong.Research on positioning algorithm based on TDOA in cellular network[D].Nanjing:Nanjing University of Posts and Telecommunications,2016.(in Chinese) 蒋康荣.蜂窝网络中基于TDOA的定位算法研究[D].南京:南京邮电大学,2016.
[12] YANG Fanfan.Research and implementation of wireless location algorithm based on UWB[D].Shenyang:Northeastern University,2014.(in Chinese)杨凡凡.基于UWB的无线定位算法的研究与实现[D].沈阳:东北大学,2014.
[13] ZHANG Wei,MA Hong,WU Tao,et al.A location algorithm of ground interference sources using satellites FDOA measurements based on taylor series expansion[J].Radio Communications Technology,2019,45(4):385-390.(in Chinese)张威,马宏,吴涛,等.一种基于泰勒级数展开的卫星FDOA地面干扰源定位算法[J].无线电通信技术,2019,45(4):385-390.
[14] FU Shichen,LI Yiming,ZONG Kai,et al.Ultra-wideband pose detection method based on TDOA positioning model for boom-type roadheader[J].AEU-International Journal of Electronics and Communications,2019,99:70-80.
[15] CHENG Peng,LIU Aijun,WANG Ke,et al.Gradient descent algorithm for frequency offset estimation of faster-than-nyquist signal[J].Journal of Signal Processing,2017,33(9):1199-1207.(in Chinese)程鹏,刘爱军,王柯,等.超奈奎斯特信号载波频偏估计的梯度下降算法[J].信号处理,2017,33(9):1199-1207.
[16] LI Nana,YE Na,SU Rijian,et al.Fast inversion algorithm for magnetic nanoparticle temperature based on Gauss-Newton algorithm[J].Journal of Huazhong University of Science and Technology(Nature Science Edition),2018,46(10):105-109,132.(in Chinese)李娜娜,叶娜,苏日建,等.基于高斯牛顿法的磁纳米温度快速反演算法[J].华中科技大学学报(自然科学版),2018,46(10):105-109,132.
[17] IZMAILOV A F,SOLODOV M V,USKOV E I.A globally convergent Levenberg-Marquardt method for equality-constrained optimization[J].Computational Optimization and Applications,2019,72(1):215-239.
[18] LEVENBERG K.A method for the solution of certain non-linear problems in leastsquares[J].Quarterly of Applied Mathematics,1994,2(2):164-168.
[19] MARQUARDT D W.An algorithm for least-squares estimation of nonlinear parameters[J].Journal of the Society for Industrial and Applied Mathematics,1963,11(2):431-441.
[20] ZHAO Ruixue,FAN Jinyan.On a new updating rule of the Levenberg-Marquardt parameter[J].Journal of Scientific Computing,2018,74(2):1146-1162.
[21] ZHU Qiang,LI Shaokang,XU Zhen.Study of solving nonlinear least squares under large residual based on Levenberg-Marquardt algorithm[J].China Measurement & Testing Technology,2016,42(3):12-16.(in Chinese)祝强,李少康,徐臻.LM算法求解大残差非线性最小二乘问题研究[J].中国测试,2016,42(3):12-16.

Please choose a citation manager

Content to export