This technical note is concerned with the distributed Kalman filtering problem for a class of networked multi-sensor fusion systems (NMFSs) with communication bandwidth constraints. To satisfy finite communication bandwidth, only partial components of the local vector estimation signals are transmitted to the fusion center (FC) at each time step, where multiple binary variables are introduced to model this component transmitting process. A novel compensation strategy is proposed to restructure the untransmitted components of each local estimate at the FC end, and a recursive distributed fusion kalman filter (DFKF) is designed in the linear minimum variance sense. Moreover, a simple suboptimal judgement criterion is proposed to determine a group of binary variables such that the mean square error of the designed DFKF is minimal at each time step. An illustrative example is given to show the effectiveness of the proposed methods.