光电工程  2020, Vol. 47 Issue (4): 190661      DOI: 10.12086/oee.2020.190661

1. 西安理工大学自动化与信息工程学院，陕西 西安 710048;
2. 陕西省智能协同网络军民共建重点实验室，陕西 西安 710048

The research on fog's positioning performance of vehicles based on visible light
Zhang Ying1,2, Yang Jing1, Yang Yufeng1
1. School of Automation and Information Engineering, Xi'an University of Technology, Xi'an, Shaanxi 710048, China;
2. Shaanxi Civil-Military Collaboration Key Laboratory of Intelligence Coodination Networks, Xi'an, Shaanxi 710048, China
Abstract: In order to analyze the performance of vehicle positioning using LED traffic lights in foggy environment, the influences of receiving angle, road width, and signal-to-noise ratio (SNR) at the receiver in foggy environment on vehicle positioning range are discussed. The simulation results show that the optimal signal reception angle is 25°; when the vehicle is within 20 m of the LED traffic light, the road width has a greater impact on the received power of the signal; near the traffic light, the positioning distance of the vehicle on the second lane is 2.2 m shorter than that of the vehicle in the first lane; the SNR of the receiver at night is better than during the day, and the positioning range at night is greater than during the day; compared with sunny weather, the SNR in the fog days decrease significantly, which will greatly affect the positioning range of the vehicle, so to ensure safe driving, vehicles need more braking time when driving in foggy days.
Keywords: LED traffic light    visibility    signal to noise ratio    positioning range

1 引言

2 系统模型 2.1 LED交通灯定位系统模型

 $d = \sqrt {{x^2} + {{(3 - y)}^2} + {{(H - h)}^2}} ,$ (1)
 图 1 LED交通灯定位系统模型 Fig. 1 LED traffic light position system model

 $\varphi {\rm{ = }}|\arccos (x/d)|。$ (2)

 $\psi {\rm{ = }}\arccos \left( {\frac{1}{d} \cdot \sin (\theta + \arctan (\frac{{H - h}}{x}))\sqrt {{x^2} + {{(H - h)}^2}} } \right)。$ (3)

 $H{(0)_{{\rm{Los}}}} =\\ \left\{ \begin{gathered} \frac{{(m + 1)A}}{{2{\rm{ \mathsf{ π} }}{d^2}}}{\cos ^m}(\varphi ){T_{\rm{s}}}(\psi )g(\psi )\cos (\psi )\tau (d), \;\;\;0 \leqslant \psi \leqslant {\psi _{\rm{c}}} \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;0, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\psi > {\psi _{\rm{c}}} \\ \end{gathered} \right.,$ (4)

 $\tau (d) = \exp ( - \mu d),$ (5)

 ${p_{\rm{r}}} = {p_{\rm{t}}}H{(0)_{{\rm{Los}}}}\\ {\rm{ = }}\left\{ \begin{gathered} {p_{\rm{t}}}\frac{{(m + 1)A}}{{2{\rm{ \mathsf{ π} }}{d^2}}}{\cos ^m}(\varphi ){T_{\rm{s}}}(\psi )g(\psi )\cos (\psi )\tau (d), \;\;\;0 \leqslant \psi \leqslant {\psi _{\rm{c}}} \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;0, \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\psi > {\psi _{\rm{c}}} \\ \end{gathered} \right.。$ (6)
2.2 雾的衰减模型

 等级 水平能见度/m 0(浓雾) < 50 1(大雾) 50~200 2(中雾) 200~500 3(轻雾) 500~1000 4(薄雾) 1000~2000

 ${\mu _{{\rm{vis}}}}{\rm{ = }}\frac{{3.192}}{V}{\left( {\frac{\lambda }{{550}}} \right)^{ - \kappa }},$ (7)

 $\kappa=\left\{\begin{array}{cc} 0.16 V+0.34, & 1 \mathrm{km} 2.3 系统的噪声 利用交通灯进行车辆定位时，会受到背景光影响。如太阳辐射的环境光和街灯、车辆、静态霓虹灯标志牌和广告屏幕等带来的人造光。其中，太阳辐射诱发的散粒噪声是系统在白天时噪声的主要来源，表示为 $\sigma _{{\rm{shot}}}^2 = 2qR{p_{\rm{r}}}B + 2q{I_{{\rm{bg}}}}{I_2}B, $(9) 式中：q为电子电荷常量，B为系统带宽，Ibg为背景光电流，I2为背景噪声带宽系数，R为光电转换效率。人造光诱发的热噪声是夜间的主要噪声来源，表示为 $\sigma _{{\rm{th}}}^2 = \frac{{8{\rm{ \mathsf{ π} }}kT}}{G}cA{I_2}{B^2} + \frac{{16{{\rm{ \mathsf{ π} }}^2}kTG}}{{{G_{\rm{m}}}}}{c^2}{A^2}{I_3}{B^3}, $(10) 式中：G是系统电压增益，c是单位面积电容，T是绝对温度，K是波尔兹曼常数，Gm场效应管的跨导。 表 2 系统参数 Table 2 System parameters  参数 数值 LED波长/nm 525 LED功率半角/(°) 15 接收机最大视角/(°) 25 透镜折射率 1.7 光电感应面积/cm2 1 光电转换速率 0.35 平均发射功率/W 0.314 LED灯高度/m 5.5 发射角度/(°) 30 道路宽度/m 7 光电探测器高度/m 1 绿灯坐标 (0, 3, 5.5) 因此，系统总噪声为 ${\sigma ^2} = \sigma _{{\rm{shot}}}^2 + \sigma _{{\rm{th}}}^2。$(11) 该系统选用OOK调制，信噪比可表示为[13] ${R_{{\rm{SNR}}}} = {(R{p_{\rm{r}}})^2}/{\sigma ^2}。\$ (12)
3 仿真分析

3.1 衰减系数和能见度的关系

 图 2 传输衰减与能见度的关系 Fig. 2 Relationship between transmission attenuation and visibility
3.2 接收角度和光信号水平传输距离的关系

 图 3 接收角度与光信号水平传输距离的关系 Fig. 3 Relationship between receiving angle and horizontal transmission distance of optical signal
3.3 接收端接收功率和光信号水平传输距离的关系

 图 4 接收功率与光信号水平传输距离的关系 Fig. 4 Relationship between received power and horizontal transmission distance of optical signal
3.4 系统的信噪比分析

 图 5 白天不同能见度情况下信噪比和定位距离之间的关系。 Fig. 5 Show the relationship between signal-to-noise ratio and positioning distance for different visibility during the day. (a)第一车道时信噪比与定位距离的关系；(b)第二车道时信噪比与定位距离的关系 (a) The relationship between the signal-to-noise ratio and the positioning distance in the first lane; (b) The relationship between the signal-to-noise ratio and the positioning distance in the second lane

 图 6 夜晚不同能见度情况下信噪比和定位距离之间的关系。 Fig. 6 Show the relationship between signal-to-noise ratio and positioning distance for different visibility at night. (a)第一车道时信噪比与定位距离的关系；(b)第二车道时信噪比与定位距离的关系 (a) The relationship between the signal-to-noise ratio and the positioning distance in the first lane; (b) The relationship between the signal-to-noise ratio and the positioning distance in the second lane

4 结论

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