西安电子科技大学学报 ›› 2019, Vol. 46 ›› Issue (4): 16-21.doi: 10.19665/j.issn1001-2400.2019.04.003

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一种利用声音能量的两步SDR定位算法

田强1,冯大政1,李进2,胡豪爽1   

  1. 1.西安电子科技大学 雷达信号处理国家重点实验室,陕西 西安 710071
    2.西安电子科技大学 综合业务网理论及关键技术国家重点实验室,陕西 西安 710071
  • 收稿日期:2019-03-23 出版日期:2019-08-20 发布日期:2019-08-15
  • 作者简介:田 强(1990—),男,西安电子科技大学博士研究生,E-mail: qtianxd@126.com
  • 基金资助:
    国家自然科学基金(61801363)

New two-step semidefinite relaxation method for acoustic energy-based localization

TIAN Qiang1,FENG Dazheng1,LI Jin2,HU Haoshuang1   

  1. 1.National Key Lab. of Radar Signal Processing, Xidian University, Xi’an 710071, China
    2.State Key Lab. of Integrated Service Networks, Xidian University, Xi’an 710071, China
  • Received:2019-03-23 Online:2019-08-20 Published:2019-08-15

摘要:

针对基于声音能量定位具有高度非线性、非凸特性而难以直接求解的问题,提出了一种两步半正定松弛定位算法。该算法将非线性定位方程转化为关于目标位置和信号发射能量的加权最小二乘估计问题,然后分成两步进行求解:第1步根据最小二乘准则将未知的信号发射能量表示成目标位置的函数,并将其从代价函数中消除;第2步利用凸松弛技术,将非凸的代价函数转化成半正定规划问题,并优化求解出目标位置。从理论上证明了该方法对代价函数的凸松弛变换是紧的。仿真实验表明,与现有的方法相比,该方法具有较高的定位精度,尤其在测量误差较大时具有明显的优势。

关键词: 无线传感器网络, 声音能量, 目标定位, 半正定规划, 加权最小二乘

Abstract:

A new two-step semidefinite relaxation method is proposed to deal with the nonlinear and non-convex problem of acoustic energy-based localization in wireless sensor networks. The proposed algorithm transforms the nonlinear positioning equations into a weighted least squares estimation problem of the unknown source location and signal transmit power, which is then solved in two steps. First, the signal transmit power is eliminated from the cost function by expressing it as a function of the source position in the least square sense. In the second step, the weighted least squares formulation is converted into a semidefinite programming(SDP) optimization problem by using a new convex relaxation technique. The tightness of the semidefinite relaxation method is theoretically proved. Simulation results indicate that compared with the previous methods, the proposed algorithm has a higher localization accuracy, especially when the measurement error is relatively large.

Key words: wireless sensor networks, acoustic energy, source localization, semidefinite programming, weighted leasts quares

中图分类号: 

  • TN912