Abstract: The theoretical model and signal processing of correlation measurements to estimate the velocity of a vessel relative to the bottom are discussed. With the random component of velocity considered, the sonar array space-time correlation function of bottom reverberations within Fraunhofer zone is derived. It is the theoretical model of acoustic correlation measurements, which is composed of zero order, first order and second order Bessel function. By the model,'wave invariance' can be well described. Localized Least Mean Squares (LLMS) criterion is put forward for velocity estimation. Sequential Quadratic Programming (SQP) method is adopted as the optimization method. So the systematic signal processing method for acoustic correlation measurements is established. A prototype Correlation Velocity Log (CVL) underwent several deep sea trials, the results show that theoretical model approximately coincides with experimental data. Square loop tracklines of the ship in 3560 m deep area were adopted to inspect its velocity estimate error. Varying velocity cruise test and drifting test were also carried out. The CVL performed well in these tests. A least squares linear regression analysis shows a significant correlation between the speeds of CVL and those of GPS. The Root-Mean-Square (RMS) error of the velocities of CVL is less than (l.4%v + 3)cm/s, where v is the velocity of vessel.