Electromagnetic fields and its error distribution predicted from magnetic field measured around metallic enclosure by using inverse-forward analysis

Let us consider the situation in which an electromagnetic wave is leaking through an aperture on a metallic box so that an electromagnetic field distribution is formed outside the box. By measuring the magnetic field distribution on the surface S1 near the box surface, the current distribution on the metallic box surface can be estimated (inverse analysis). Next, the electromagnetic field distribution on an arbitrary surface S2 outside the box can be predicted from the product of the above current distribution and a coefficient matrix (forward analysis). In this paper, the greatest likelihood estimation method is used for the inverse analysis. When the electromagnetic field distributions on surface S2 are predicted from the nearby magnetic field distribution by the inverse–forward analysis, there appear prediction error distributions that depend on the setting of the lattice meshes on surface S1, the box surface, and surface S2 in addition to the measurement errors. In this paper, the prediction error distributions dependent on the setting are obtained. In order to discuss the effectiveness of the above inverse–forward analysis, the magnetic field distribution on surface S1 where the measurement was carried out is derived by forward analysis from the current distribution on the box as a special case. The results are compared with the measured values. The comparison reveals good agreement. In order to consider the maximum electromagnetic interference level to obtain the maximum possible measurement error distribution, the distributions where all measurement points have the same value are assumed and the prediction error distributions are computed. Based on this assumption, the measurement error distribution is expressed in terms of the product of the unit matrix with the constant σ0, indicating the standard deviation of the measured error distribution (measurement error matrix). Then, the predicted error distribution of the electric field obtained by inverse–forward analysis is determined by the constant σ0 and the setting of the lattice meshes on surface S1, the box surface, and surface S2. Hence, if the maximum possible measurement error is assumed, the electromagnetic field distributions on an arbitrary surface can be computed with the associated prediction error. When some measure to reduce the leakage from a metal box is applied and its effect is studied, the prediction error distributions appear equally if the same lattice meshes as above are used in