Reverberation noise in active sonar leads to a very complicated situation for target detection. Reverberation is often modeled as the autoregressive model. In this paper, the autoregressive 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 to propose a new method to improve computational complexity for the rank determination of the observation matrix via singular value decomposition. It is shown that this new method is efficient on real data to separate target echo signal from reverberation.