Reverberation noise in active sonar leads to a very complicated situation for targetdetection. Reverberation is often modeled as the autoregressive model. In this paper, theautoregressive model is considered for reverberation and the Principal Component Inverse (PCI)algorithm is used to separate target echo signal from reverberation. This consideration helps us topropose a new method to improve computational complexity for the rank determination of theobservation matrix via singular value decomposition. It is shown that this new method is efficienton real data to separate target echo signal from reverberation.