基于传感器网络的分布式集员滤波问题的研究

摘要：由于网络技术、无线通信技术、微机电技术和微处理器技术等方面的进步，传感器网络应用成为了研究热点并取得长足发展。本文研究了基于事件触发机制的分布式集员滤波问题，利用递推线性矩阵不等式组（RecursiveLinearMatrixInequalities，RLMIs）给出了非线性时变系统受到传感器饱和约束下的滤波器设计方法。

首先，本文建立起了较为一般的待研究系统模型，同时考虑了扇形非线性约束，噪声未知但有界的干扰噪声以及传感器饱和等三个现象。其次，针对事件触发机制，提出了一个新的椭球触发条件。随后建立起待设计的滤波器存在的充分性条件，并给出设计策略。在此基础之上，考虑了两个优化问题，一个是固定触发阈值寻求最优化的滤波性能，另一个则是在给定的滤波精度之下探求所能容许的最大触发时间。最后，通过仿真算例验证了所给出理论算法的正确性与有效性。

关键词：分布式滤波，集员滤波，非线性时变系统，传感器网络，传感器饱和约束，未知但有界噪声

Title Research On Problems Of Distributed Set-membership Filtering Over Sensor Networks

Abstract：Due to the advances in technology which contains networking，wireless communications， microfabrication，and microprocessors，the topic of sensor networks has become a popular

research area. In this paper，a new distributed event-based set-membership filtering is adopted. It utilizes event-triggering mechanism to improve the traditional approach to estimating filtering measurements. The problem that nonlinear time-varying system with sensor saturations also has been addressed with recursive linear matrix inequality and set-membership filtering scheme.

First, the system model is established where the sector-bounded nonlinearity, unknown but bounded noises, and sensor saturations are all taken into consideration. Then, a new ellipsoidal triggering condition is presented in which the threshold is adjustable to make the compromise between filtering performance and communication cost. Sufficient conditions are derived for the existence of the desired filter, based on which two optimization problems are formulated. One is to seek the optimal filtering performance with fixed triggering threshold, whereas the other is to find out the maximum tolerable triggering threshold with satisfactory filtering accuracy. Finally, numerical example is provided to show the correctness and applicability of the presented theoretical results.

Keywords distributed filtering, set-membership filtering，nonlinear time-varying system， sensor networks， sensor saturation， unknown but bounded noise

1引言1

1.1研究背景及意义1

1.2传感器网络概述2

1.2.1传感器的物理构成2

1.2.2传感器的拓扑结构2

1.3基于传感器网络的状态估计问题3

1.3.1信息缺失对系统的影响3

1.3.2时变系统自身对滤波算法的影响3

1.3.3滤波算法对传感器网络性能的影响3

1.4研究内容4

1.5本文章节内容的安排4

2滤波器的设计问题建模（公式化）6

2.1非线性时变系统的状态空间模型6

2.2事件触发机制7

2.3基于事件触发的滤波器结构8

3基于事件触发的分布式集员滤波设计10

3.1两个用到的引理10

3.2满足固定三元组的滤波器设计10

3.3受制于平均滤波误差的滤波器设计15

3.4优化算法16

4算例仿真分析20结论27致谢28参考文献29附录A31

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