The Sun-Earth's interaction is characterized by a highly dynamic electromagnetic environment, in which the magnetic field produced in the Earth's core plays an important role. One of the striking characteristics of the present geomagnetic field is denoted the South Atlantic Anomaly (SAA) where the total field intensity is unusually low and the flux of charged particles, trapped in the inner Van Allen radiation belts, is maximum. Here, we use, on one hand, a recent geomagnetic field model, CHAOS-6, and on the other hand, data provided by different platforms (satellites orbiting the Earth -POES NOAA for 1998 and CALIPSO for 2006. Evolution of the SAA particle flux can be seen as the result of two main effects, the secular variation of the Earth's core magnetic field and the modulation of the density of the inner radiation belts during the solar cycle, as a function of the L value that characterises the drift shell, where charged particles are trapped. To study the evolution of the particle flux anomaly, we rely on a Principal Component Analysis (PCA) of either POES particle flux or CALIOP dark noise. Analysed data are distributed on a geographical grid at satellite altitude, based on a L-shell reference frame constructed from the moving eccentric dipole. Changes in the main magnetic field are responsible for the observed westward drift. Three PCA modes account for the time evolution related to solar effects. Both the first and second modes have a good correlation with the thermospheric density, which varies in response to the solar cycle. The first mode represents the total intensity variation of the particle flux in the SAA, and the second the movement of the anomaly between different L-shells. The proposed analysis allows us to well recover the westward drift rate, as well as the latitudinal and longitudinal solar cycle oscillations, although the analysed data do not cover a complete (Hale) magnetic solar cycle (around 22 yr). Moreover, the developments made here would enable us to forecast the impact of the South Atlantic Anomaly on space weather. A model of the evolution of the eccentric dipole field (magnitude, offset and tilt) would suffice, together with a model for the solar cycle evolution.