An Asynchronous Visible Light Positioning Method Based on New On-Off Keying Coded Pulse-pair
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摘要: 发光二极管(LED)照明的普及为高精度室内定位提供了一种绿色低成本的解决方案，作为最经济的LED调制方式，开关键控(OOK)由于开关速度、响应时间和节点间同步等的限制，存在定位精度差等问题。该文提出一种基于新型开关键控编码脉冲对的室内信标构造方法及其对应的异步可见光定位模型，各LED仅需按所提规则进行开关键控，光电探测器(PD)端可以获得最大后验概率准则下的最优位置估计。经验证，当信道(含LED和接收机)具有理想带宽、200 MHz和100 MHz带宽时，在30 dB的信噪比(SNR)条件下，终端以90%的概率使得定位精度分别可以达到6 mm, 7 mm和1 cm。在相同条件下，与异步码分多址(CDMA)进行定位、传统OOK基于指纹进行定位以及传统OOK基于接收信号强度进行定位这3种方法相比，该文提出的方法可以获得明显较好的定位效果。另外，当带内信噪比从30 dB恶化至15 dB时，终端的定位精度还能稳健地保持在厘米量级。Abstract: The popularity of Light-Emitting Diode (LED) lighting provides a green and low-cost solution for high-accuracy indoor positioning. As the most economical LED modulation method, On-Off Keying (OOK) has poor positioning accuracy due to the defects of switching speed, response time, and synchronization between nodes. In this paper, an indoor positioning beacon based on the new OOK coded pulse-pair and its corresponding asynchronous visible light positioning model is proposed. Herein, each LED only needs to perform OOK according to the proposed rules, and the optimal position of the PhotoDetector (PD) terminal under the maximum posterior probability criterion can be estimated. It is verified that when the channel (including LED and receiver) has ideal bandwidth, 200 MHz, and 100 MHz bandwidth, the terminal can achieve a positioning accuracy of 6 mm, 7 mm, and 1 cm with a 90% probability under the condition of 30 dB Signal-to-Noise Ratio (SNR). Under the same conditions, compared with asynchronous Code Division Multiple Access (CDMA) positioning, traditional OOK positioning based on fingerprint and traditional OOK positioning based on received signal strength, the proposed method in this paper can get a significantly better positioning effect. In addition, when the SNR deteriorates from 30 dB to 15 dB, the positioning accuracy of the terminal can also be robustly maintained in the order of centimeters.
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Key words:
- Indoor positioning /
- Asynchronous visible light /
- On-Off Keying (OOK) /
- Coded pulse-pair /
- High accuracy
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表 1 所提定位模型算法
(1) 设置位置误差容限$ \varepsilon $、脉冲宽度$ {T_w} $、脉冲对间隔$ {T_I} $、LED的坐标$\left( {x_i^{{\rm{Led}}},y_i^{{\rm{Led}}},z_i^{{\rm{Led}}} } \right)$、LED的辐射功率$ P $、参考位置的坐标
$\left( {x_0^{{\rm{Pd}}},y_0^{{\rm{Pd}}},z_0^{{\rm{Pd}}} } \right)$、时域搜索步进因子$ \alpha $。(2) 将终端固定在参考位置，开始检测脉冲，并对脉冲对计数$ k $，测量第$ i $个LED在第$ k $个脉冲对间隔内可分辨的脉冲${\boldsymbol{y}}_i^0\left( k \right)$及脉冲到达时间
${\boldsymbol{t}}_i^0\left( k \right)$，计算距离${\boldsymbol{d}}_i^0$及信道增益${\boldsymbol{h}}_i^0$：${\boldsymbol{h} }_i^0{\text{ = } }\dfrac{1}{ {K \times \sqrt P } }\displaystyle\sum\limits_{k = 0}^{K - 1} { {\boldsymbol{y} }_i^0\left( k \right)}$(3) 计算4个LED发射第$ 0 $组脉冲对的时间为：${ {\boldsymbol{\phi} } _i}\left( 0 \right) = \dfrac{1}{K}\displaystyle\sum\limits_{k = 0}^{K - 1} {\left( { {\boldsymbol{t} }_i^0\left( k \right) - { { {\boldsymbol{d} }_i^0}/ {\rm{c}}} - k \times {T_I} } \right)}$ 时间误差为：${\delta ^2} = \dfrac{1}{K}{\displaystyle\sum\limits_{k = 0}^{K - 1} {\left( {{\boldsymbol{t}}_i^0\left( k \right) - \left( { { {{\boldsymbol{d}}_i^0}/ c} + {{\boldsymbol{\phi}} _i}\left( k \right)} \right)} \right)} ^2}$ 4个LED的发射第$ k $个脉冲对的时间为：${{\boldsymbol{\phi}} _i}\left( k \right) = {{\boldsymbol{\phi}} _i}\left( 0 \right) + k \times {T_I}$ (4) 计算第$ i $个LED可能的发射时间集合：${ {\boldsymbol{\varPhi } }_i}{\text{ = } }\left\{ { { {\boldsymbol{\phi} } _i}\left( k \right) - 3\delta :{ {\alpha \varepsilon }/ {\rm{c} } }:{\phi _i}\left( k \right) + 3\delta } \right\}$
(5) 在集合${ {\boldsymbol{\varPhi } }_i}$中，计算似然比$ \gamma $：$\gamma {\text{ = } }\displaystyle\sum\limits_{k = 1}^K {\displaystyle\sum\limits_{i = 1}^4 {\left| { {{\boldsymbol{y}}_i}\left( k \right) - \sqrt {P \times {\boldsymbol{w}}_{ {\phi _i} }^s\left( k \right) \times {T_w} } \times {\boldsymbol{h}}_i^s} \right|} }$并剔除不满足式(9)约束的组合。(6) 找到$ \gamma $的最大值对应的${\hat {\boldsymbol{\phi}} _i}\left( k \right)$和$\hat {\boldsymbol{s}}$，分别为满足最大后验概率准则的发射时间和终端位置的最优估计。 
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表 2 算法验证参数
图3(a)、图4(a)、图4(c) 图3(b)、图4(b)、图4(d) 图5 信噪比(dB) 30 30, 20, 15 LED及终端带宽(MHz) 200, 100, 50 200, 100, 50 LED的数量 4 6 4 LED的坐标 [1.25 1.25 3; 3.75 1.25 3;
1.25 3.75 3; 3.75 3.75 3][1 1.5 3; 2.5 1.5 3; 4 1.5 3; 1 3.5 3; 2.5 3.5 3; 4 3.5 3] [1.25 1.25 3; 3.75 1.25 3;
1.25 3.75 3; 3.75 3.75 3]
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