Estimation of a Source Parameter in Radiation Belt Electron Data using a Kalman Filter

The highly energetic electrons in Earth's radiation belts form an extremely hazardous environment to both manned and unmanned space missions; mitigating the related risks requires a full understanding of the dynamics of the system. However, determining the relative contribution of local acceleration, loss, and radial diffusion terms is a complicated task. A sequential algorithm, such as a Kalman filter, is capable of estimating electron phase space density (PSD) and parameters for the source, loss, and radial transport terms. We report the results of applying an Extended Kalman Filter to energetic electron data using a 1-D Fokker-Planck equation for radial diffusion with a parameterized free term added for local acceleration. The dataset provides sparse observations of electron PSD from L = 4 to L = 10 for first and second adiabatic invariants M = 2083 MeV/G and K = 0.1 G^1/2 R_E (corresponding to about 1.1 MeV at geosynchronous orbit). This data assimilation technique fills in gaps in the dataset in both space and time, allowing for the estimation of PSD for the full radial range (L=3 to L=10). Additionally, the inclusion of the source term in the state vector causes the filter to estimate the source parameters. We present the results of simultaneous estimation for PSD and parameters for local heating.