Stochastic Filtering in Electromagnetics

This article presents the estimation of electric and magnetic fields using the Kalman filter (KF). The electric and magnetic fields in the entire space have been estimated using the scalar and vector potential. For this estimation, the measurements at a sparse discrete set of spatial pixels have been used. To implement the KF, the state space model has been obtained using the wave equations with sources satisfied by the scalar and vector potential. The proposed method has been implemented on a Hertzian dipole antenna. The fields estimated using KF have been compared with the recursive least squares (RLS) method. The KF presents better estimation than RLS, as it is an optimal estimator. This work uses the Kronecker product for compact representation of discretized fields in the form of vectors and partial differential operators in the form of matrices.