In this work the performance of the Sucessive Interference Cancelation (SIC) architecture combined with Matching Pursuit (SIC/MP) and Least Squares (SIC/LS) algorithms is statistically analyzed when they are used to mitigate multipath effect in an Acoustic Local Positioning System (ALPS). The experiments are carried out with sets of two hundred real signals acquired in positions where there exists a strong multipath interference, showing that the proposed methods have a better performance than the classical correlation + thresholding-based detection method. Especially, in the SIC/MP method case, its corresponding Error Cummulative Distribution Function (ECDF) shows that practically 100% of the Time of Flight (TOF) measurements affected by multipath interference are recovered, obtaining positioning errors below 10 cm for 60% of the measurements.