Optimal method of linear regression in laser remote sensing

Remote lidar sensing in the photon-counting mode is now the commonly accepted method for studying atmospheric processes in the lower and free atmosphere. However, when processing signals obtained from lidar measurements, investigators necessarily face the problem of achieving accuracy in reconstructing the atmospheric parameters despite the presence of inhomogeneous noise in the measured signals. We propose an optimal method of linear regression (OMLR) of signals. The accuracy of the the method for the reconstructed signal is estimated. An example of application of the OMLR to the reconstruction of the temperature profile from the data obtained with a Raman lidar at the Siberian Lidar Station of the Institute of Atmospheric Optics (Tomsk, Russia) is given. The proposed method is distinguished by simplicity of interpretation of the criteria used, based on careful adherence to statistical principles. This method is shown to be an efficient auxiliary tool for the processing of measured data.