We propose a self-sufficient online method that simultaneously performs transmission line characterization and event localization. Our proposed method eliminates the need for offline transmission line characterization or line parameter modeling based on the transmission line model. The method is based on traveling wave theory and adding a measurement device in a double-sided traveling wave event localization setup. The theoretical background of the method is derived, which is based on a complex continuous wavelet transform. The accuracy of the transmission line characterization method is evaluated using a frequency-dependent transmission line simulation model. The method was developed independently of the type of event and is evaluated in a variety of experimental setups that take into account different lengths of the monitored line section, line characteristics, location of the third measurement device, and location of the event. The localization accuracy is compared with other proposed online methods. The proposed method improves event localization and exhibits high characterization accuracy within a relative error of 1 %, even when mimicking real environmental conditions where noise and desynchronization between measurement devices occur.