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For large-scale distributed systems, the evolution of system dynamics is dominated by current states and boundary conditions simultaneously. This work describes a distributed consensus filtering for a class of large-scale distributed systems with unknown boundary conditions, which are monitored by a set of sensors. Because of the difference of spatial positions among the sensor network, only the single state variables or both the states and outside input jointly could be estimates with Kalman information filtering, respectively. On diffusion processing, we fuse the common state estimations of the local information filters using consensus averaging algorithms and algebraic graph theory. Stability and performance analysis is provided for this distributed filtering algorithm. Finally, we consider an application of distributed estimation to a heat conduction process. The performance of the proposed distributed algorithm is compared to the centralized Kalman filtering

Consensus Information Filtering for Large-Scale Systems with Application to Heat Conduction Process