The statistical properties of the noise in the Mie lidar signal are analyzed by the statistical hypotheses testing method. Based on this, an adaptive filter is proposed to eliminate the noise. The least mean square error algorithm is used to achieve optimal filtering, in which the mean square error is minimized by adjusting the filter's weight matrix. The validity of the adaptive filter is verified by numerical simulation and experimental data retrieving. In the numerical simulation, the signal-to-noise ratio of the adaptive filter is larger than that of the wavelet transform filter, and the mean square error of the output of the adaptive filter is less than the wavelet transform filter. In experimental data retrieving, the filtered lidar signals of the adaptive filter and wavelet transform filter are used to retrieve the extinction coefficient respectively in different weather conditions. The amplitude of the ripples in the extinction coefficient profile of the adaptive filter is less than that of the wavelet transform filter. Additionally, the adaptive filter's extinction coefficient profile is smoother than that of the wavelet transform filter. The detail of the extinction coefficient is displayed more clearly in the profile of the adaptive filter. The research result is of great importance for improving the accuracy of lidar data retrieving.
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