﻿ 一种基于多普勒效应的拟牛顿室内定位算法
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 浙江大学学报(理学版)  2017, Vol. 44 Issue (3): 322-326  DOI:10.3785/j.issn.1008-9497.2017.03.013 0

### 引用本文 [复制中英文]

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ZHANG Xiaoyan, SUN Tingting, XU Xinmin. A quasi-Newton indoor localization algorithm based on the Doppler effect[J]. Journal of Zhejiang University(Science Edition), 2017, 44(3): 322-326. DOI: 10.3785/j.issn.1008-9497.2017.03.013.
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### 文章历史

1. 浙江长征职业技术学院，浙江 杭州 310023;
2. 浙江大学 信息与电子工程学院，浙江 杭州 310027

A quasi-Newton indoor localization algorithm based on the Doppler effect
ZHANG Xiaoyan1 , SUN Tingting2 , XU Xinmin2
1. Zhejiang Changzheng Vocational and Technical College, Hangzhou 310023, China;
2. College of Information and Electronic Engineering, Zhejiang University, Hangzhou 310027, China
Abstract: To avoid the clock synchronization between objective node and beacon nodes in indoor location system, a new distance measuring method based on the Doppler effect is proposed. A quasi-Newton indoor localization algorithm is implemented for distance measurement. The initial parameters for quasi-Newton are obtained randomly. Quasi-Newton is used to get each single position. Then, all the relative positions would be iterated to adjust the original position for localization. Matlab simulations show that the location error is less than 0.5 m when SNR is 10. Then, particle swarm optimization is applied to improve the performance of convergence.
Key words: Doppler effect    quasi-Newton    indoor localization
0 引言

1 定位测距模型 1.1 测距原理

 $f' = \left( {\frac{{v \pm {v_o}}}{{v \mp {v_s}}}} \right)f.$ (1)

 ${d_j}^i = v \bullet ({t_{R1}} - {t_{T1}});$ (2)
 图 1 目标节点和一个信标节点的信号发射接收时间显示 Fig. 1 Transmit and receive times of signals betweenan objective node and a beacon node

 ${d_j}{_{ + 1}^i} = v \bullet ({t_{R2}} - {t_{T2}}).$ (3)

 ${D_{j, j}}{_{ + 1}^i} = v \bullet \left[{({t_{R2}}-{t_{R1}})-({t_{T2}}-{t_{T1}})} \right] = v \bullet \left[{({t_{R2}}-{t_{R1}})-T/2} \right].$ (4)

1.2 定位模型

 图 2 目标节点运动时相对于某一信标节点的距离 Fig. 2 Distance between a beacon node andan objective node in motion

 ${D_{j, j}}{_{ + 1}^i} = {d_{j + 1}}^i - {d_j}^i = \sqrt {{{({x_{j + 1}} - {m_i})}^2} + {{({y_{j + 1}} - {n_i})}^2}} - \sqrt {{{({x_j} - {m_i})}^2} + {{({y_i} - {n_i})}^2}} .$ (5)

 $\min ({{\rm{\varepsilon }}_{j, j + 1}}^2).$ (6)

 ${{\rm{\varepsilon }}_{j, j + 1}}^i = {\hat D_{j, j + 1}}^i - {D_{j, j + 1}}^i, i = 1, 2, \ldots, N,$

2 迭代定位算法 2.1 起始位置分析

 ${D_{0, j}}^i = {d_j}^i - {d_0}^i = \sqrt {{{({x_j} - {m_i})}^2} + {{({y_j} - {n_i})}^2}} - \sqrt {{{({x_0} - {m_i})}^2} + {{({y_0} - {n_i})}^2}} .$ (7)

 ${\sum\limits_{j = 0}^{{N_{p - 1}}} {\sum\limits_{i = 1}^N {({{\rm{\varepsilon }}_{j, j + 1}}^i)} } ^2},$ (8)

2.2 迭代算法

 图 3 算法流程图 Fig. 3 Flow chat of algorithm

2.3 定位仿真误差分析

 图 4 (a)对角路径，(b)闭合路径 Fig. 4 (a)Diagonal path, (b)closed path 实际轨迹，——估计轨迹

 图 5 对角路径和闭合路径的定位误差 Fig. 5 Error of diagonal path location andclosed path location
2.4 初始值分析

 图 6 随机选取初始猜测值时，初始位置横纵坐标的收敛情况 Fig. 6 Convergence of original positions withrandom initial values

 图 7 随机选取的初始猜测值分布图 Fig. 7 Distribution of random initial values

 图 8 基于PSO算法的初始位置收敛结果 Fig. 8 Convergence of original positions based on PSO
3 总结

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