UPC-RapidNetwork: Kalman Filter Tomography TOMION technique

From the input ionospheric combination of carrier phases (difference of simultaneous transmitter-receiver carrier phases, L1-L2 in GPS, in length units after correcting the transmitter and receiver phase center deviations), expressed in terms of the Jacobian of the voxel-based model, the estimations of the mean electron density of illuminated voxels, as far as the carrier phase ambiguities, is done by means of the Kalman filter. It can be consider equivalent to a Least Squares estimation with memory of the previous values of the unknown under a relative weight in the inverse problem given by a time increasing uncertainty (or process noise). This memory capability is very useful working in a Sun-fixed or solar-geomagnetic reference system, where the electron density values remains quite stationary in agreement with the stationarity of the voxel-Sun distance, the main typical ionization driver. The output of this Kalman filter computation is used for subsequent slant TEC computation as the ambiguity term.