Noise statistics identification for Kalman filtering of the electron radiation belt observations: 2. Filtration and smoothing

In this study we present the further improvement of data assimilation using the 1-D radial diffusion model for relativistic electron phase space density (PSD) and observations of CRRES satellite. The main purpose of our study is estimation of the radiation belt dynamics for the prediction and mitigation of space weather effects in the hazardous space environment. We develop further noise statistics identification technique presented in the companion paper to estimate the observation error statistics that are crucially important for optimal performance of data assimilation. Assimilation of satellite observations into first-principles physics model of radiation belts, when both model and observation error statistics are poorly known, may cause large errors in the PSD estimation and lead to failure of a data assimilation algorithm. We identify the coefficients of proportionality characterizing the dependence of observation errors on satellite observations. The effectiveness of the proposed identification technique is illustrated by applying the Kalman filter with optimal identified and nonoptimal observation errors statistics to the sparse CRRES observations over a period of 441 days, from 28 July 1990 to 11 October 1991. 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.