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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
Received: 2016-01-27, Accepted: 2016-04-09.
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

 1 Yue Yuan-Long, Zuo Xin, Luo Xiong-Lin. Improving measurement reliability with biased estimation for multi-sensor data fusion. Acta Automatica Sinica, 2014, 40 (9): 1843–1852. ( 岳元龙, 左信, 罗雄麟. 提高测量可靠性的多传感器数据融合有偏估计方法. 自动化学报, 2014, 40 (9): 1843–1852. ) 2 Xue Dong-Guo, Chen Bo, Zhang Wen-An, Yu Li. Kalman fusion estimation for networked multi-sensor fusion systems with communication constraints. Acta Automatica Sinica, 2015, 41 (1): 203–208. ( 薛东国, 陈博, 张文安, 俞立. 通信受限下网络化多传感器系统的Kalman融合估计. 自动化学报, 2015, 41 (1): 203–208. ) 3 Zhao Guo-Rong, Han Xu, Lu Jian-Hua. A decentralized fusion estimator using data-driven communication strategy subject to bandwidth constraints. Acta Automatica Sinica, 2015, 41 (9): 1649–1658. ( 赵国荣, 韩旭, 卢建华. 一种基于数据驱动传输策略的带宽受限的分布式融合估计器. 自动化学报, 2015, 41 (9): 1649–1658. ) 4 Cattivelli F S, Lopes C G, Sayed A H. Diffusion recursive least-squares for distributed estimation over adaptive networks. IEEE Transactions on Signal Processing, 2008, 56 (5): 1865–1877. DOI:10.1109/TSP.2007.913164 5 Bokareva T, Hu W, Kanhere S, Ristic B, Gordon N, Bessell T, Rutten M, Jha S. Wireless sensor networks for battlefield surveillance. In:Proceedings of the 2006 Land Warfare Conference. Brisbane, Australia:APDR, 2006. 1-8 6 Huo H W, Xu Y Z, Yan H R, Mubeen S, Zhang H K. An elderly health care system using wireless sensor networks at home. In:Proceedings of the 3rd International Conference on Sensor Technologies and Applications. Athens/Glyfada, Greece:IEEE, 2009. 158-163 http://ieeexplore.ieee.org/abstract/document/5210943/ 7 Santini S, Ostermaier B, Vitaletti A. First experiences using wireless sensor networks for noise pollution monitoring. In:Proceedings of the 3rd ACM Workshop on Real-World Wireless Sensor Networks. Glasgow, Scotland:ACM, 2008. 61-65 http://dl.acm.org/citation.cfm?id=1435490 8 Gungor V C, Hancke G P. Industrial wireless sensor networks:challenges, design principles, and technical approaches. IEEE Transactions on Industrial Electronics, 2009, 56 (10): 4258–4265. DOI:10.1109/TIE.2009.2015754 9 Gungor V C, Lu B, Hancke G P. Opportunities and challenges of wireless sensor networks in smart grid. IEEE Transactions on Industrial Electronics, 2010, 57 (10): 3557–3564. DOI:10.1109/TIE.2009.2039455 10 Trimpe S, D'Andrea R. Event-based state estimation with variance-based triggering. IEEE Transactions on Automatic Control, 2014, 59 (12): 3266–3281. DOI:10.1109/TAC.2014.2351951 11 Åström K J, Bernhardsson B M. Comparison of Riemann and Lebesgue sampling for first order stochastic systems. In:Proceedings of the 41st IEEE Conference on Decision and Control. Las Vegas, NV, USA:IEEE, 2002. 2011-2016 http://ieeexplore.ieee.org/abstract/document/1184824/ 12 Feeney L M, Nilsson M. Investigating the energy consumption of a wireless network interface in an ad hoc networking environment. In:Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies. Anchorage, Alaska, USA:IEEE, 2001. 1548-1557 http://ieeexplore.ieee.org/abstract/document/916651/ 13 Shnayder V, Hempstead M, Chen B, Allen G W, Welsh M. Simulating the power consumption of large-scale sensor network applications. In:Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems. Baltimore, Maryland, USA:ACM, 2004. 188-200 http://dl.acm.org/citation.cfm?id=1031518 14 Imer O C, Basar T. Optimal estimation with limited measurements. In:Proceedings of the 44th IEEE Conference on Decision and Control. Seville, Spain:IEEE, 2005. 1029-1034 http://ieeexplore.ieee.org/abstract/document/1582293/ 15 Rabi M, Moustakides G V, Baras J S. Multiple sampling for estimation on a finite horizon. In:Proceedings of the 45th IEEE Conference on Decision and Control. San Diego, USA:IEEE, 2006. 1351-1357 http://ieeexplore.ieee.org/abstract/document/4178072/ 16 Li L C, Lemmon M, Wang X F. Event-triggered state estimation in vector linear processes. In:Proceedings of the 2010 American Control Conference. Baltimore, Maryland, USA:IEEE, 2010. 2138-2143 http://ieeexplore.ieee.org/abstract/document/5531338/ 17 Wu J F, Jia Q S, Johansson K H, Shi L. Event-based sensor data scheduling:trade-off between communication rate and estimation quality. IEEE Transactions on Automatic Control, 2013, 58 (4): 1041–1046. DOI:10.1109/TAC.2012.2215253 18 Shi D W, Chen T W, Shi L. An event-triggered approach to state estimation with multiple point-and set-valued measurements. Automatica, 2014, 50 (6): 1641–1648. DOI:10.1016/j.automatica.2014.04.004 19 Battistelli G, Benavoli A, Chisci L. Data-driven communication for state estimation with sensor networks. Automatica, 2012, 48 (5): 926–935. DOI:10.1016/j.automatica.2012.02.028 20 Anderson B D O, Moore J B. Detectability and stabilizability of time-varying discrete-time linear systems. SIAM Journal on Control and Optimization, 1981, 19 (1): 20–32. DOI:10.1137/0319002 21 Duan Z S, Han C Z, Li X R. Comments on "unbiased converted measurements for tracking". IEEE Transactions on Aerospace and Electronic Systems, 2004, 40 (4): 1374–1377. DOI:10.1109/TAES.2004.1386889