Open Access
 Issue JNWPU Volume 38, Number 1, February 2020 31 - 39 https://doi.org/10.1051/jnwpu/20203810031 12 May 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1 问题描述与系统模型

 图 1无线传感器网定位模型

## 2 基于稀疏表示定位

### 2.1 正交匹配追踪算法

 算法1  标准正交匹配追踪 输入:z, K, D 输出: w     初始化  s=Ø, k=0, w=0, r0=z     当k < K & max(DTrk)>C进入循环        (ζ, t)←max(DTrk)         s←s∪t         ws←argminθ‖z-Dsws‖         rk+1←z-Dsws         k=k+1     循环结束

### 2.2 快速正交匹配追踪

 算法2  基于QR分解的快速正交匹配跟踪算法 输入: z, K, D 输出: w 初始化    s=Ø, k=0, r0=z, Ψ0=[], R=[]p0={＜r0, dn＞}n=1, 2, …, N 当k < K    进入循环     循环结束cK=ΨKTz w=RK-1cK

## 3 仿真分析

### 3.1 无噪情况下定位性能对比

 图 2理想情况下不同OMP算法性能对比

### 3.2 传感器个数对于定位性能和计算效率的影响

 图 3传感器个数与估计精度的关系
 图 4传感器个数与计算时间的关系

### 3.3 目标个数对于定位性能和计算效率的影响

 图 5目标数目与估计精度的关系
 图 6目标数目与计算时间的关系

### 3.4 网格大小对于定位性能和计算效率的影响

 图 7网格大小与估计精度的关系
 图 8网格大小与计算时间的关系

## 4 结论

rik=qiTak, 其中i=1, 2, …k-1, k=1, 2…n

R为上三角矩阵

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## All Figures

 图 1无线传感器网定位模型 In the text
 图 2理想情况下不同OMP算法性能对比 In the text
 图 3传感器个数与估计精度的关系 In the text
 图 4传感器个数与计算时间的关系 In the text
 图 5目标数目与估计精度的关系 In the text
 图 6目标数目与计算时间的关系 In the text
 图 7网格大小与估计精度的关系 In the text
 图 8网格大小与计算时间的关系 In the text

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