﻿ 基于离散时间信号相关性的交通事件检测算法
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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (11): 1508-1513.  DOI: 10.11908/j.issn.0253-374x.2018.11.006 0

### 引用本文

SUN Qian, GUO Zhongyin. Automatic Incident Detection Algorithm Based on Discrete Time Signal Correlation[J]. Journal of Tongji University (Natural Science), 2018, 46(11): 1508-1513. DOI: 10.11908/j.issn.0253-374x.2018.11.006

### 文章历史

Automatic Incident Detection Algorithm Based on Discrete Time Signal Correlation
SUN Qian , GUO Zhongyin
Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China
Abstract: An automatic incident detection algorithm based on discrete time signal correlation was proposed. Traffic information data were converted to discrete-time signals and the correlation was calculated to locate the same traffic stream passing the upper and lower sections. The characteristics of correlation coefficients were explained. The results show that the algorithm is visual and easy to understand. The algorithm performs well under low-saturated traffic conditions and has better adaptability.
Key words: traffic incident    signal processing    signal correlation

1 离散时间信号相关性算法 1.1 离散时间信号相关性理论

 ${R_{xy}}\left( \tau \right) = \sum {x\left( n \right)y\left( {n + \tau } \right)}$ (1)

 $\begin{array}{l} X\left( k \right) = \sum\limits_{n = 0}^{N - 1} {x\left( n \right){{\rm{e}}^{ - {\rm{j}}\frac{{2{\rm{\pi }}}}{N}nk}}} \\ Y\left( k \right) = \sum\limits_{n = 0}^{N - 1} {y\left( n \right){{\rm{e}}^{ - {\rm{j}}\frac{{2{\rm{\pi }}}}{N}nk}}} \end{array}$

 $\begin{gathered} {W_{xy}}\left( k \right) = X\left( k \right){Y^ * }\left( k \right) \hfill \\ {R_{xy}}\left( \tau \right) = f\left( {{W_{xy}}\left( k \right)} \right) \hfill \\ \end{gathered}$

 $\begin{gathered} {\rho _{xy}}\left( \tau \right) = \frac{{{R_{xy}}\left( \tau \right) - {\mu _x}{\mu _y}}}{{{\sigma _x}{\sigma _y}}} \hfill \\ {\mu _x} = \sqrt {\mathop {\lim }\limits_{\tau \to \infty } {R_{xx}}\left( \tau \right)} , {\mu _y} = \sqrt {\mathop {\lim }\limits_{\tau \to \infty } {R_{yy}}\left( \tau \right)} \hfill \\ {\sigma _x} = \sqrt {{R_{xx}}\left( 0 \right)} , {\sigma _y} = \sqrt {{R_{yy}}\left( 0 \right)} \hfill \\ \end{gathered}$

1.2 离散时间信号相关性应用

 图 1 离散时间信号分布 Fig.1 Distribution of discrete time signal

 图 2 相关系数分布 Fig.2 Distribution of correlation coefficient

2 交通离散时间信号相关性特征分析 2.1 互相关系数特征分析

 $F = k\left( {1/N - a} \right)$
 图 3 信号长度与互相关系数关系 Fig.3 Relationship between signal length and correlation coefficient

 图 4 斜率等值线 Fig.4 Contour map of slop
2.2 事件与非事件条件下相关性特征分析

 图 5 6 h相关系数分布 Fig.5 Distribution of correlation coefficient in 6 h

 图 6 自动交通事件检测流程 Fig.6 Flow chart of AID
 图 7 相关性发展图 Fig.7 Development of correlation
 图 8 扰动发展图 Fig.8 Development of disturbance
3 交通事件检测试验 3.1 检测试验

AID算法性能的评价指标包括交通事件检测率(DR)、误报率(FAR)和平均检测时间(MTTR).检测率和误报率用于评价AID算法的检测性能，平均检测时间能够评价算法的检测效率.3个指标存在互相制约的关系.

 图 9 误报率和检测率关系 Fig.9 Relationship between FAR and DR

3.2 结果分析

 图 10 低饱和交通环境下参数变化 Fig.10 Variation of parameters under low saturated traffic environment

 图 11 高饱和交通环境下参数变化 Fig.11 Variation of parameters under high saturated traffic environment
4 结语

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