Optimal Distributed Filter for State and Unknown Input Estimations in Multi-Sensor Networks

This brief is aimed at estimating the state and unknown input of a linear system in the multi-sensor network. First, a distributed filter consisting of the unknown input estimator and the state estimator is proposed, in which the unknown input estimator only uses its own information while the state estimator uses its in-neighbors' information. Second, the optimal gain matrices are obtained by employing the weighted least squares method and minimizing the performance function, which allow to realize the optimal unbiased estimation of the proposed filter. Third, a sufficient condition about the given filter's convergence is derived. Finally, a simulation is given for validating the given methodologies.