A new signal-processing method to realize blind source separation (BSS) in an underwater lidar-radar system based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and independent component analysis (ICA) is presented in this paper. The new statistical signal processing approach can recover weak target reflections from strong backward scattering clutters in turbid water, thus greatly improve the ranging accuracy. The proposed method can overcome the common problem of ICA, i.e. the number of observations must be equal to or larger than the number of sources to be separated, therefore multiple independent observations are required, which normally is realized by repeating the measurements in identical circumstances. In the new approach, the observation matrix for ICA is constructed by CEEMDAN from a single measurement. BSS can be performed on a single measurement of the mixed source signals. The CEEMDAN-ICA method avoid the uncertainty induced by the change of measurement circumstances and reduce the errors in ICA algorithm. In addition, the new approach can also improve the detection efficiency because the number of measurement is reduced. The new approach was tested in an underwater lidar-radar system. A mirror and a white Polyvinyl chloride (PVC) plate were used as target, respectively. Without using the CEEMDAN- Fast ICA, the ranging error with the mirror was 12.5 cm at 2 m distance when the attenuation coefficient of the water was 7.1 m-1. After applying the algorithm, under the same experimental conditions, the ranging accuracy was improved to 4.33 cm. For the PVC plate, the ranging errors were 5.01 cm and 21.54 cm at 3.75 attenuation length with and without the algorithm respectively. In both cases, applying this algorithm can significantly improve the ranging accuracy.