Distributed Set-Membership Fusion Filtering for Nonlinear 2-D Systems Over Sensor Networks: An Encoding–Decoding Scheme
针对传感器网络上受有界噪声影响的非线性二维时变系统，提出一种带对数型编解码机制的分布式集员融合滤波方法，通过局部滤波和椭球融合规则得到全局更小的状态估计集，并求解滤波器参数与融合权重。
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.