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 自动化学报  2017, Vol. 43 Issue (2): 227-237 PDF

A Multi-channel Decoupled Event Triggered Transmission Mechanism and Its Application to Optic-electric Sensor Network
CHEN Ye, LI Yin-Ya, QI Guo-Qing, SHENG An-Dong
College of Automation, Nanjing University of Science and Technology, Nanjing 210094
Foundation Item: Supported by National Natural Science Foundation of China (61104186, 61273076)
Corresponding author. CHEN Ye Ph. D. candidate at the College of Automation, Nanjing University of Science and Technology. His research interest covers information fusion and event-triggered estimation algorithm. Corresponding author of this paper
Recommended by Associate Editor CHEN Ji-Ming
Abstract: This paper deals with the problem of the communication constraint caused by energy limitation on the sensor network fusion system. We propose a multi-channel decoupled event-triggered measurement transmission mechanism which is based on the designed event-triggered condition for each output component of each sensor separately. Meanwhile we propose the condition which guarantees the boundary of the estimation error. The algorithm proposed in this article ensures the accuracy of the fusion system while the data transmitted is reduced at each time instant. The effectiveness and the feasibility of the proposed mechanism is verified through the optic-electric sensor network experiment in the fire control system and the simulation for comparison between our method and three other techniques.
Key words: Centralized fusion estimation algorithm     a multi-channel decoupled event-triggered mechanism     data transmission amount rate     the optic-electric sensor network

1 问题描述

 $\pmb x_{k+1}=A\pmb x_{k}+\pmb w_{k}$ (1)

 $\pmb y_{k}^{i}=C^{i}\pmb x_{k}+\pmb v_{k}^{i}, \quad 1\leq i \leq M, ~i \in \bf{N}$ (2)

 $r_{k}^{i}= \begin{cases} 0 ,& \mbox{若}~ \pmb{y}_{k}^{i} - \tilde{\pmb{y}}_{k}^{i} \in \xi_{W_{k}^{i},\delta_{i}}, ~ 1 \leq i \leq M \\ 1, & \mbox{其他} \end{cases} \label{whole_eq}$ (3)

$\pmb u_{k}^{i}=\|\pmb y_{k}^{i} -\tilde{\pmb{y}}_{k}^{i} \|$, 则式(3) 中条件根据$\xi_{W_{k}^{i}, \delta}$定义可化为

 $\sum\limits_{l=1}^{m} W_{k}^{i}(l,l)\times \pmb u_{k}^{i}(l,1)^2$

 图 1 多通道解耦的事件触发估计算法 Figure 1 The multi-channel decoupled event triggered estimation algorithm

 $\bar{r}_{k}^{i,l}= \begin{cases} 0, & \mbox{若}~G^{l}(\pmb y_{k}^{i}-\tilde{\pmb{y}}_{k}^{i}) \in \xi_{{\bar{W}_{k,i}^{l}},\bar{\delta}_{i}^{l}} \\ 1, & \mbox{其他} \end{cases}\label{decoupled_eq}$ (4)

$\bar{r}_{k}^{i, 1}=\bar{r}_{k}^{i, 2}=\cdots=\bar{r}_{k}^{i, m}$, 多通道解耦事件触发机制与事件触发机制(3) 等价.

2 多通道解耦事件触发估计算法

 $\label{xuni_eq} \pmb z_{k}^{i}= T_{k}^{i}\pmb y_{k}^{i}-(T_{k}^{i}-I)\pmb \eta_{k}^{i}=\notag \\[1mm] T_{k}^{i}C^{i}\pmb x_{k}+T_{k}^{i}\pmb v_{k}^{i}-(T_{k}^{i}-I)\pmb \eta_{k}^{i}$ (5)

 $\Omega_{k}^{i}=\left\{ \pmb \varpi|G^{l}(\pmb y_{k}^{i}-\pmb \varpi)\in \xi_{\bar{W}_{k,i}^{l},\bar{\delta}_{i}^{l}} \right\}$

 $p_{\pmb x_{k}|\bar{r}_{k}^{i,l}}(\pmb x_{k}|0) \propto \int_{\tilde{{\pmb y}}+\xi_{\bar{W}_{k,i}^{l},\bar{\delta}_{i}^{l}}} p_{\pmb v_{k}^{i}}(\pmb \varrho-C^{i}\pmb x_{k})\text{d}\pmb \varrho p_{\pmb x_{k}}(\pmb x_{k}) \label{eq_posterior}$ (6)

 $T_{k}^{i}\pmb v_{k}^{i}=\pmb \varsigma_{k}^{i} \\[1mm] (T_{k}^{i}-I)\pmb \eta_{k}^{i}=\pmb \varepsilon_{k}^{i}$

 $p_{\pmb \varsigma_{k}^{i}-\pmb \varepsilon_{k}^{i}}(\pmb \varsigma_{k}^{i})= \int_{{\bf{R}}^{m}}p_{\pmb \varepsilon_{k}^{i}}(\pmb \varepsilon_{k}^{i})p_{\pmb \varsigma_{k}^{i}}(\pmb \varsigma_{k}^{i}+\pmb \varepsilon_{k}^{i}) \text{d} \pmb \varepsilon_{k}^{i} \propto\\[1mm] \int_{\xi_{\bar{W}_{k,i}^{l},\bar{\delta}_{i}^{l}}}p_{\pmb \varsigma_{k}^{i}}(\pmb \varsigma_{k}^{i}+\pmb \varepsilon_{k}^{i})\text{d}\pmb \varepsilon_{k}^{i}$

 $p_{\pmb z_{k}^{i}|\pmb x_{k}}(\pmb z_{k}^{i}|\pmb x_{k})=p_{\pmb \varsigma_{k}^{i}-\pmb \varepsilon_{k}^{i}}(\pmb z_{k}^{i}-C^{i}\pmb x_{k})\propto \\[1mm] \qquad \int_{\xi_{\bar{W}_{k,i}^{l},\bar{\delta}_{i}^{l}}}p_{\pmb \varsigma_{k}^{i}}(\pmb z_{k}^{i}-C^{i}\pmb x_{k}+\pmb \varepsilon_{k}^{i})\text{d}\pmb \varepsilon_{k}^{i}$

 $p_{\pmb x_{k}|\pmb z_{k}^{i}}(\pmb x_{k}|\pmb z_{k}^{i}) \propto \\[1mm] \qquad\int_{\xi_{\bar{W}_{k,i}^{l},\bar{\delta}_{i}^{l}}}p_{\pmb \varsigma_{k}^{i}}(\pmb z_{k}^{i}-C^{i}\pmb x_{k}+\pmb \varepsilon_{k}^{i})\text{d}\pmb \varepsilon_{k}^{i} p_{\pmb x_{k}}(\pmb x_{k})$

 $p_{\pmb x_{k}|\pmb z_{k}^{i}}(\pmb x_{k}|\pmb z_{k}^{i})=p_{\pmb x_{k}|\bar{r}_{k}^{i,l}}(\pmb x_{k}|0)$

 $Q=q \left[ \begin{array}{cccc} \frac{\Delta^{3}}{3} &\frac{\Delta^{2}}{2} &0 &0 \\ \frac{\Delta^{2}}{2} &\Delta &0 &0 \\ 0 &0 &\frac{\Delta^{3}}{3} &\frac{\Delta^{2}}{2} \\ 0 &0 &\frac{\Delta^{2}}{2} &\Delta \end{array} \right]$

 $\pmb{y}_{k}^{i}=\left[ \begin{array}{cccc} 1 &0 &0 &0 \\ 0 &0 &1 &0 \end{array} \right]\pmb{x}_{k}+\pmb{v}_{k}^{i}, \\ 1 \leq i \leq M,\ \, i \in \bf{N}$

 $R_{k}^{i}=\text{diag}\{5\sqrt{i} \quad 5\sqrt{i}\}$

 图 2 $\delta_{i}=30$, $\bar{\delta}_{i}^{1}=\bar{\delta}_{i}^{2}=15$时3号传感器发送x位置及y位置量测分量至融合中心的概率 Figure 2 The probability of the x position and y position measurement sent by sensor No. 3 to fusion center per second when $\delta_{i}=30$, $\bar{\delta}_{i}^{1}=\bar{\delta}_{i}^{2}=15$

 $f_{dc}=\frac{\sum\limits_{k=1}^{T}\sum\limits_{i=1}^{M}\sum\limits_{l=1}^{m}\bar{r}_{k}^{i,l}}{mMT} \\[2mm] f_{c}=\frac{\sum\limits_{k=1}^{T}\sum\limits_{i=1}^{M}r_{k}^{i}}{MT}$
 图 3 $\delta_{i}=6$, $\bar{\delta}_{i}^{1}=\bar{\delta}_{i}^{2}=3$时传感器网络每时刻传输数据量及对应估计精度 Figure 3 The RMSE of the estimation of the network and its corresponding data transmission amount per second when $\delta_{i}=6$, $\bar{\delta}_{i}^{1}=\bar{\delta}_{i}^{2}=3$
 图 4 $\delta_{i}=12$, $\bar{\delta}_{i}^{1}=\bar{\delta}_{i}^{2}=6$时传感器网络每时刻传输数据量及对应估计精度 Figure 4 The RMSE of the estimation of the network and its corresponding data transmission per second when $\delta_{i}=12$, $\bar{\delta}_{i}^{1}=\bar{\delta}_{i}^{2}=6$
 图 5 $\delta_{i}=30$, $\bar{\delta}_{i}^{1}=\bar{\delta}_{i}^{2}=15$时传感器网络每时刻传输数据量及对应估计精度 Figure 5 The RMSE of the estimation of the network and its corresponding data transmission per second when $\delta_{i}=30$, $\bar{\delta}_{i}^{1}=\bar{\delta}_{i}^{2}=15$

 图 6 多通道解耦事件触发机制与文献[17]中多通道耦合机制下传感器网络每时刻数据传输量及对应估计精度 Figure 6 The RMSE of the estimation of the network and its corresponding data transmission per second of multi-channel coupled and decoupled mechanism in [17]
 图 7 多通道解耦事件触发机制与文献[18]中多通道耦合机制下传感器网络每时刻数据传输量及对应估计精度 Figure 7 The RMSE of the estimation of the network and its corresponding data transmission per second of multi-channel coupled and decoupled mechanism in [18]

5 应用实例

 $\pmb X_{k+1}=F_{k}\pmb X_{k}+\pmb w_{k}$

k时刻光电传感器i对运动目标的量测方程如下:

 $\begin{cases} \varphi_{k}^{i}={\rm{arctan}}\left( \frac{y_{k}}{x_{k}} \right)+\tilde{\varphi}_{k}^{i} \\[2mm] \theta_{k}^{i}={\rm{arctan}}\left( \frac{z_{k}}{\sqrt{x_{k}^{2}+y_{k}^{2}}}\right)+ \tilde{\theta}_{k}^{i}\\[4mm] d_{k}^{i}=\sqrt{x_{k}^{2}+y_{k}^{2}+z_{k}^{2}}+\tilde{d}_{k}^{i} \end{cases}$

 图 8 多通道解耦事件触发机制下的光电传感网络目标跟踪示意图 Figure 8 The diagram of target tracking of the optic-electric sensor network with the multi-channel decoupled event triggered mechanism

 图 9 目标运动轨迹水平投影 Figure 9 The horizontal projection of target motion trajectory

 $X_{0}=[1\,000\quad 10\quad 1\,000\quad 10\quad 1\,000\quad 10]^{\rm T} \\[0.3mm] P_{0}=10^2\times I$

 图 10 航路A三种通信机制下对目标估计精度及通信量 Figure 10 The RMSE and communication amounts under three communication mechanism for lane A
 图 11 航路B三种通信机制下对目标估计精度及通信量 Figure 11 The RMSE and communication amounts under three communication mechanism for lane B
 图 12 航路C三种通信机制下对目标估计精度及通信量 Figure 12 The RMSE and communication amounts under three communication mechanism for lane C

6 结论

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