Koopman enhanced distributed computing Kalman filtering for stochastic dynamic discrete systems in smart grids

For stochastic dynamic discrete systems, a new Koopman-enhanced distributed computing Kalman filtering (KE-DC-KF) is proposed, which is used to solve the state estimation problem when the system model is unknown and each sensor in the sensor network can only observe one-dimensional or multidimensional data of the system state. In the identification step, in order to identify the Koopman invariant subspace, the eigenfunction set is extracted from the minimizing the least-mean-square (LMS) errors over nonlinear observation data set to span the subspace. A multi-layer perceptrons (MLPs) structure is used to realize the eigenfunction set. Based on the Koopman observer form, the Koopman-enhanced distributed computing Kalman filtering is proposed for the first time. Then, convergence analysis is performed on the basis of the Lyapunov equation to guarantee the boundedness of KE-DC-KF estimate error. Finally, an example is given to verify the effectiveness of the filtering method.