Kalman filtering and smoothing of radiation belt observations on the basis of model and measurement error identification

Data assimilation by Kalman filter of the radiation belts observations requires specification of poorly known relevant error statistics that need to be identified to provide the accurate reconstruction of the radiation belt dynamics. Identification of error statistics in data assimilation is of particular importance for radiation belt models, since large uncertainties of the observations and the model may cause the failure of data assimilation solution and lead to false conclusions about the state and evolution of radiation belts. In this study, we develop the identification technique of unknown model and observation errors for the successive assimilation of multiple-satellite observations characterized by large variety of observation error statistics. Further improvement and the accuracy increase of PSD reconstruction is demonstrated by the implementation of the backward smoothing procedure applied to the forward Kalman filter estimates.