Oceanic turbulence measurements made by an acoustic Doppler velocimeter (ADV) suffer from noise that potentially affects the estimates of turbulence statistics. This study examines the abilities of Kalman filtering and autoregressive moving average models to eliminate noise in ADV velocity datasets of laboratory experiments and offshore observations. Results show that the two methods have similar performance in ADV de-noising, and both effectively reduce noise in ADV velocities, even in cases of high noise. They eliminate the noise floor at high frequencies of the velocity spectra, leading to a longer range that effectively fits the Kolmogorov ?5/3 slope at mid- range frequencies. After de-noising adopting the two methods, the values of the mean velocity are almost unchanged, while the root-mean-square horizontal velocities and thus turbulent kinetic energy decrease appreciably in these experiments. The Reynolds stress is also affected by high noise levels, and de-noising thus reduces uncertainties in estimating the Reynolds stress.