The set of data processing techniques used on ASDEX Upgrade to automatically evaluate edge density profile characteristics from broadband data, obtained with the frequency-modulated continuous-wave reflectometer, has recently been upgraded to include (i) an adaptive algorithm that automatically optimizes the length of the window used in the spectrogram analysis of broadband signals and (ii) a new method to estimate the edge pedestal density based on the evolution of the local derivative of the group delay curve, removing the need for user supplied parameters. These tools are especially important in cases where the group delay of the reflected signals varies significantly in a short probing frequency range, such as when the profile exhibits a density shoulder at the edge. The application of these techniques in ASDEX Upgrade H-mode density limit discharges, to automatically obtain the time evolution of the edge pedestal parameters, namely, its density, position, and width, shows a clear improvement both on the time-frequency resolution of the group delay characteristic and on the detection of the density shoulder.