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In this work we discuss inclusion of a priori information about the smoothness ofatmospheric profiles in inversion algorithms. The smoothness requirement canbe formulated in the form of Tikhonov-type regularization, where thesmoothness of atmospheric profiles is considered as a constraint or in theform of Bayesian optimal estimation (maximum a posteriori method, MAP), wherethe smoothness of profiles can be included as a priori information. Wedevelop further two recently proposed retrieval methods. One of them -Tikhonov-type regularization according to the target resolution - developsthe classical Tikhonov regularization. The second method - maximum aposteriori method with smoothness a priori - effectively combines the ideasof the classical MAP method and Tikhonov-type regularization.We discuss a grid-independent formulation for the proposed inversion methods, thusisolating the choice of calculation grid from the question of how strong thesmoothing should be.<P  style="line-height: 20px;">The discussed approaches are applied to the problem of ozone profileretrieval from stellar occultation measurements by the GOMOS instrument onboard the Envisat satellite. Realistic simulations for the typicalmeasurement conditions with smoothness a priori information created from10-years analysis of ozone sounding at Sodankyl\ue4 and analysis of the totalretrieval error illustrate the advantages of the proposed methods.<P  style="line-height: 20px;">The proposed methods are equally applicable to other profile retrievalproblems from remote sensing measurements

Ozone profile smoothness as a priori information in the inversion of limb measurements