Comparison between the Kalman and the Non-Linear Least-Squares Estimators in Low Signal-to-Noise Ratio Lidar Inversion

This works departs from previously published results of the authors and focus on joint estimation and time evolution of the atmospheric backscatter profile and a range-independent lidar ratio by means of 1) adaptive extended Kalman filtering (EKF) and 2) non-linear least-squares (NLSQ), under moderate-to-low signal-to-noise ratios (SNR<100 at the starting sounding range). A Rayleigh/Mie atmosphere and a calibrated lidar system are considered. Performance parameters studied are data sufficiency, tracking of the optical parameter time fluctuations, inversion errors, power estimation, and noise impact. The EKF inversion solution is, in turn, compared with Klett´s method as a reference. Finally, it is shown that the EKF outweighs the NSLQ in noisy environments.