The ultra-high frequency (UHF) radiation source localization method for electrical equipment is a key technology for partial discharge (PD) localization. PD signals exhibit wide frequency bands (300 MHz-3 GHz), rapid rising edges (the shortest rise time reaching sub-nanoseconds or even hundreds of picoseconds), which are always accompanied by significant background noise. These characteristics impose stringent requirements on the sampling frequency and analog bandwidth of measurement systems. Conventional measurement systems struggle to effectively capture and completely record the rapid rising edge waveforms of PD pulse signals. To solve these problems, a radiation source localization method based on interpolation calculation and multi-scale wavelet transform is proposed. This method enables effective detection of rapid rising pulse signal arrival times under lower sampling rates. Interpolation is applied to the pulse signal, followed by multi-scale wavelet transform on the interpolated signal. The maximum wavelet coefficient is extracted to replace the original pulse signal. Based on the maximum wavelet coefficient, the energy accumulation algorithm is used to calculate the signal's arrival time. Simulation analyses and experimental validations demonstrate that this method significantly improves the temporal resolution of UHF pulse signals and exhibits robust noise resistance in high-noise electromagnetic environments.