This paper focuses on the distributed filtering problem for a class of time-varying networked systems with sensor gain degradation and energy constrained communication protocol.To satisfy the requirement of power consumption and reduce the schedule computing complexity,centralized cyclic finite-time communication strategy optimization is taken into account.The networked system considered in this paper consists of spatially distributed sensors linked to their neighbor sensors,where each sensor node suffers from different gain degradation,and the transmission decisions of all the communication channels obey the centralized transmission schedule strategy identically.First,we present scattered communication action based on single-sensor transmission modeling with an energy constraint.Subsequently,an optimal communication protocol considering expected average error covariance is derived between the target system and each sensor node over the distributed sensor systems,based on a centralized finite-time scheme.Finally,by transforming the overall estimation error covariance of the systems at each sampling time into quadratic form,a conditionally unbiased least-square recursive distributed filtering technique over the networked system is designed at each sensor node.The system stability condition under such an optimal schedule is also accomplished with bounded covariance.A numerical example is provided to demonstrate the utility and effectiveness of the distributed filtering technique using the proposed optimized energy constrained communication protocol.