In this article, the distributed set-membership fusion filtering problem is investigated for a class of nonlinear 2-D shift-varying systems subject to unknown-but-bounded noises over sensor networks. The sensors are communicated with their neighbors according to a given topology through wireless networks of limited bandwidth. With the purpose of relieving the communication burden as well as enhancing the transmission security, a logarithmic-type encoding–decoding mechanism is introduced for each sensor node so as to encode the transmitted data with a finite number of bits. A distributed set-membership filter is designed to determine the local ellipsoidal set that contains the system state by only utilizing the data from the local sensor node and its neighbors, where the proposed filter scheme is truly distributed with desirable scalability. Then, a new ellipsoid-based fusion rule is developed for the designed set-membership filters in order to form the fused ellipsoidal set that has a globally smaller volume than all local ellipsoidal sets. With the aid of the mathematical induction technique, the set theory, and the convex optimization approach, sufficient conditions are derived for the existence of the desired distributed set-membership filters and the fusion weights. Then, the filter parameters and the fusion weights are acquired by solving a set of constrained optimization problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed fusion filtering algorithm.

中文翻译：

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传感器网络上非线性二维系统的分布式集成员融合过滤：一种编码-解码方案

在本文中，研究了传感器网络上受未知但有界噪声影响的一类非线性二维移变系统的分布式集合成员融合滤波问题。传感器根据给定的拓扑结构通过有限带宽的无线网络与它们的邻居进行通信。为了减轻通信负担并增强传输安全性，为每个传感器节点引入对数型编码解码机制，以便用有限位数对传输数据进行编码。分布式集成员过滤器旨在通过仅利用来自本地传感器节点及其邻居的数据来确定包含系统状态的本地椭圆集，其中所提出的过滤器方案是真正分布式的，具有理想的可扩展性。然后，为设计的集合成员过滤器开发了一种新的基于椭圆体的融合规则，以形成具有比所有局部椭圆体集更小的全局体积的融合椭圆体集。借助数学归纳法、集合论和凸优化方法，推导出所需分布式集合成员过滤器和融合权重存在的充分条件。然后，通过求解一组约束优化问题获得滤波器参数和融合权重。最后，给出了一个说明性的例子来证明所提出的融合过滤算法的有效性。