Joint estimation of extinction and backscatter simulated profiles from elastic-backscatter lidar return signals is tackled by means of an extended Kalman filter (EKF). First, we introduced the issue from a theoretical point of view by using both an EKF formulation and an appropriate atmospheric stochastic model; second, it is tested through extensive simulation and under simplified conditions; and, finally, a first real application is discussed. An atmospheric model including both temporal and spatial correlation features is introduced to describe approximate fluctuation statistics in the sought-after atmospheric optical parameters and hence to include a priori information in the algorithm. Provided that reasonable models are given for the filter, inversion errors are shown to depend strongly on the atmospheric condition (i.e., the visibility) and the signal-to-noise ratio along the exploration path in spite of modeling errors in the assumed statistical properties of the atmospheric optical parameters. This is of advantage in the performance of the Kalman filter because they are often the point of most concern in identification problems. In light of the adaptive behavior of the filter and the inversion results, the EKF approach promises a successful alternative to present-day nonmemory algorithms based on exponential-curve fitting or differential equation formulations such as Klett’s method.
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