This paper presents the method for an estimation of discharge current waveform in short gap discharge by radiated electromagnetic fields. The method of current waveform estimation is to use the one antenna method (single field method) with a measured electric or magnetic field at given field point by a time domain antenna. In order to verify the availability of the estimation theory, the discharge current waveform estimation was performed by one antenna methods using the measured electric fields of Wilson & Ma and compared with experiments. In addition diagnosis technique for power equipments is able to prevent from large accidents by finding signs of tile accidents before they happen. From the results of the estimation of discharge current, we have a possibility for the application of insulation diagnosis technique for power equipments using S$F_6$ gas. From this point of view, this paper simulated discharge progress and partial discharge by using needle-plan electrodes system in S$F_6$, studied the distribution of frequency spectrum of the radiated electromagnetic waves using a biconical antenna and a spectrum analyzer. From the experimental results of this study, according to the consideration of the mutual relation between frequency spectrum of the radiated electromagnetic waves and discharge progress, it was confirmed that detecting Partial discharge and estimating discharge progress in S$F_6$ could be Possible.