Distributed Filtering for Multi-Rate Nonlinear Quantization Systems With Fading Channels and Sensor Resolutions: Handling Amplify-and-Forward Relays

This paper addresses the distributed recursive filtering problem for a class of time-varying multi-rate nonlinear systems which are subject to fading channels, sensor resolutions and quantization effects. For the purpose of prolonging the transmission distance, the amplify-and-forward (AaF) relay is deployed in the wireless communication channel. The iterative method is employed to convert the underlying multi-rate system into a single-rate one. Before entering communication network for transmission, measurement outputs are quantized using a logarithmic quantizer. Moreover, a new equivalent delay-free measurement sequence is defined by the measurement reorganization technology to tackle random transmission delays. Our main aim is to design a distributed recursive filter such that an upper bound for the filtering error covariance is determined and subsequently minimized by properly choosing the filtering gains. Next, the performance of the proposed filtering algorithm is analyzed through establishing a sufficient condition for the boundedness of the filtering error covariance. Finally, a numerical simulation is used to testify the applicability and effectiveness of the developed filtering algorithm. Note to Practitioners—In practical process industries, signals from sensors are typically encapsulated into data packets for transmission to estimators via wireless communication network. As the limited transmission capability of the sensors, the transmission distance are limited, extending the propagation distance and enhancing the communication quality become a crucial design problem for filters in wireless network system. In this context, some efficient relay-based strategies have been introduced to facilitate signal transmission over long-distance communication channels. Up to now, relay-based communication plays an important role in 5G mobile network, autonomous aerial vehicle formation, navigation, and so on. Besides, the sensor resolutions, multi-rate samplings, fading channels, and quantization effects are also considered in this paper due to the technical/physical constraints, which may complicate the transmission behaviors of wireless communication. Therefore, in this paper, the distributed filtering problem is investigated in multi-rate nonlinear systems subject to sensor resolutions, fading channels and quantization effects under the relay-based mechanism. The proposed filtering algorithm is bounded under certain conditions, which ensures the reliability of the system. Future work is planned to extend the proposed filtering method to more complicated systems with cyber-attacks and bit rate constraints.