Distributed input and state estimation for linear discrete-time systems

This paper provides a solution for distributed input and state estimation, simultaneously. A set of sensors with the capability of exchanging information is used to collect data from a discrete-time system. Various distributed implementations of Kalman filter have already been developed to track system states in such a setup when the system is subject to noise with known stochastic properties. However, practical systems might be subject to unknown input signals as well as stochastic noise, which leads to a biased state estimation. This study proposes new distributed filters that calculate state estimation in the presence of unknown inputs. In addition, the filter provides an estimation of the unknown inputs. A consensus-based distributed estimation algorithm is proposed in this paper. The algorithm gives an optimal unbiased minimum variance estimation if perfect consensus is achieved. Simulation results show the efficiency of the method.