The THz-field-driven streak camera has proven to be a powerful diagnostic-technique that enables the shot-to-shot characterization of the duration and the arrival time jitter of free electron laser (FEL) pulses. Here we investigate the performance of three computational approaches capable to determine the duration of FEL pulses with complex temporal structures from single-shot measurements of up to three simultaneously recorded spectra. We use numerically simulated FEL pulses in order to validate the accuracy of the pulse length retrieval in average as well as in a single-shot mode. We discuss requirements for the THz field strength in order to achieve reliable results and compare our numerical study with the analysis of experimental data that were obtained at the FEL in Hamburg - FLASH.