Hyper-spectral Atmospheric Infrared Sounder (AIRS) mainly covers the CO₂ and H₂O absorption bands. Different from CO₂ channels, the brightness temperature bias of water vapor channel follows non-Gaussian statistics. In order to use AIRS channel spectral information effectively, new algorithm research is needed, two methods are presented in this paper: (1)Different from the observation error of the given spectral channel remains unchanged during the classical variational assimilation minimization iteration, the paper based on the posterior estimate of variational assimilation, namely, observation error re-estimation, re-estimating the channel observation error, which is then regarded as the weight of observation to the objective function of classical variational assimilation; Observation error re-estimation can be used to identify the reasonable observation errors which can fit variational assimilation model better. By using the weight function of M-estimators (L2-estimator, Huber-estimator, Fair-estimator and Cauchy-estimator) to couple the classical variational assimilation, and then obtain the generalized variational assimilation, make it Non-Gaussian. Re-estimated the contribution rate of observation terms to the objective function during each minimization iteration. The simulated brightness temperatures of AIRS are used to conduct ideal experiments. It is show that two methods of observation error re-estimation and Huber-estimator can provide better results than the classical method. We diagnose the impact of observations on the analysis with degrees of freedom for signal (DFS). The result of diagnosis shows that two methods can increase the available information of brightness temperatures of water vapour channels during the assimilation process. Furthermore, the analysis field obtained by using the algorithm (observation error re-estimation and Huber-estimator) in this paper is compared with the temperature field of sounding data, and it is obtained that the Huber-estimator, which generalized scale is set as 1.345 K with the best effect, which is set as 2.5 K latter, and the observation error re-estimation is better than classical variational assimilation. The effect of 200~750 hPa was relatively significant. The retrieval temperature at the surface and around the tropopause (80~200 hPa)is less than 2 K based on Huber-estimator variational assimilation. The results of this paper can lay the theoretical foundation and provide the algorithm reference for the variational assimilation of hyper-spectral data of Feng-Yun 4A and Feng-Yun 3D satellite.