﻿ 基于动态质心迭代与偏差修正的室内定位方法
 计算机系统应用  2018, Vol. 27 Issue (11): 265-270 PDF

1. 福建师范大学福清分校 电子与信息工程学院, 福清 350300;
2. 福建师范大学 协和学院 信息技术系, 福州 350117

Indoor Positioning Method Based on Dynamic Centroid Iteration and Error Correction
SU Guo-Dong1, XU Shi-Wu2, CAI Bi-Li1
1. The School of Electronic and Information Engineering, Fuqing Branch of Fujian Normal University, Fuqing 350300, China;
2. Department of Information Technology, Concord University College, Fujian Normal University, Fuzhou 350117, China
Foundation item: Education and Research Project for Young and Middle-aged teachers of Fujian Province in 2016 (Science and Technology Class) (JAT160573, JAT160574)
Abstract: Radio Frequency Identification Technology (RFID) is one of the key technologies of indoor positioning. The traditional LANDMARC location algorithms have poor positioning accuracy. To solve this problem, a novel location algorithm is proposed by combining the dynamic centroid iteration and error correction. It updates nearest neighbors in turn by employing the centroid of the neighboring area as next reference tag which takes the minimum location relationship as the criterion, and achieves the pre-positioning coordinate until the location relationship with the target tag is lower than the threshold. The correction factor is adopted to compensate error of the pre-positioning coordinate by relocating each of k-nearest neighbors. Simulation results show that the proposed algorithm performs better in terms of positioning accuracy than LANDMARC.
Key words: LANDMARC     minimum location relationship     dynamic centroid iteration     error correction

1 引言

2 LANDMARC算法简介

LANDMARC算法的核心思想是通过利用引入参考标签替代部署阅读器, 借助阅读器对参考标签和目标标签的接收信号强度感知并对比. 原则上, 实际位置越接近目标标签的参考标签, 其在阅读器上的感知应该与目标标签更为相似. 故此, 找出它们之间的关联度, 并借助已知坐标的参考标签, 从而估计目标标签的坐标.

 ${E_{ij}} = \sqrt {\sum\limits_{p = 1}^M {{{({S_{ip}} - {\theta _{jp}})}^2}{\rm{ }}} } {\rm{ (}}i = 1,2,\cdots,U;j = 1,2,\cdots,N)$ (1)

 $E = \left[ {\begin{array}{*{20}{c}} {{E_{11}}}&{{E_{12}}}&{\cdots}&{{E_{1N}}} \\ {{E_{21}}}&{{E_{22}}}&{\cdots}&{{E_{2N}}} \\ {\cdots}&{\cdots}&{\cdots}&{\cdots} \\ {{E_{U1}}}&{{E_{U2}}}&{\cdots}&{{E_{UN}}} \end{array}} \right]$ (2)

 $({x_i},{y_i}) = \sum\limits_{j = 1}^k {w(i,j)*({x_{ij}},{y_{ij}})}$ (3)

 $w(i,j){\rm{ = }}\frac{{\frac{1}{{E_{ij}^2}}}}{{\sum\limits_{j = 1}^k {\frac{1}{{E_{ij}^2}}} }}{\rm{ }}$ (4)

3 动态质心迭代与自偏差修正算法研究 3.1 动态质心迭代算法

3.2 自偏差修正算法

 ${\rm{ }}\left\{ {\begin{array}{*{20}{c}} {{x_i} = (1 + {\beta _{ix}})*{{x'}_i}} \\ {{y_i} = (1 + {\beta _{iy}})*{{y'}_i}} \end{array}} \right.$ (5)

${\beta _i}x$ : x坐标的修正系数, 其值为式(9);

${\beta _{iy}}$ : y坐标的修正系数, 其值为式(10).

 ${\rm{ }}{x_{il}} = (1 + {\beta _{ix}})*{x'_{il}}$ (6)

 ${\varepsilon _i}^{\rm{2}}{\rm{ = }}\frac{{\sum\limits_{l = 1}^k {{\varepsilon _{il}}^2} }}{k} = \frac{{\sum\limits_{l = 1}^k {{{[{x_{il}} - (1 + {\beta _{ix}}){{x'}_{il}}]}^2}} }}{k}$ (7)

 $f({\beta _{ix}}) = {\varepsilon _i}^{\rm{2}} = \frac{{\sum\limits_{l = 1}^k {{{[{x_{il}} - (1 + {\beta _{ix}}){{x'}_{il}}]}^2}} }}{k}$ (8)

${\beta _i}x$ 求导, 并令其值为0, 即 ${f'_{{\beta _{ix}}}} = 0$ . 整理可得:

 ${\beta _i}x{\rm{ = }}\frac{{\sum\limits_{l = 1}^k {({x_{il}} - {{x'}_{il}})} }}{{\sum\limits_{l = 1}^k {{{x'}_{il}}} }}$ (9)

 ${\beta _i}y{\rm{ = }}\frac{{\sum\limits_{l = 1}^k {({y_{il}} - {{y'}_{il}})} }}{{\sum\limits_{l = 1}^k {{{y'}_{il}}} }}$ (10)
3.3 算法流程图

 图 1 动态质心迭代及偏差修正算法流程图

4 仿真实验与结果分析 4.1 仿真环境

4.2 结果分析

 图 2 仿真布局图

 图 3 LANDMARC和质心迭代改进算法仿真结果图

 图 4 LANDMARC质心迭代及偏差修正算法仿真结果图

 图 5 LANDMARC和改进算法各目标标签定位误差直方图

5 结论与展望

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