Predicting radiation belt electron flux with adaptive multi-input linear filters
The broad goal of the research and results described in this thesis is to improve our ability to make short-term space weather forecasts, and in particular, to predict relativistic electron flux variations over a broad range of altitudes based on measured solar wind inputs. Previous efforts using single-input time-stationary finite impulse response (FIR) linear prediction filters have enjoyed limited success, but generally fail to account for various non-stationary (statistically speaking), and ultimately non-linear dynamical behavior. Two different methods designed to account for the non-stationary radiation belt behavior are studied.
The first assumes poor predictions result from failing to account for all relevant system inputs. Designing linear filters that operate on multiple simultaneous inputs eliminates much bias caused by single-input filters due to simple time-correlations of unmodeled solar wind inputs. FIR profiles (as functions of geomagnetic equatorial altitude, or L-shell) subsequently transition from somewhat smeared functions of space and time-lag, to a set of more specific and impulsive responses that can distinguish between different types of input events. An added benefit is the improvement in prediction efficiencies (PEs) over single-input filters at all altitudes.
The second method for accounting for non-stationary radiation belt behavior involves the adaptive identification of the linear prediction filter coefficients. The well-known Kalman Filter is used to recursively update filter coefficients and minimize prediction error on the fly. This gives a simple linear filter the flexibility to track considerably NON-linear dynamics with time. Not surprisingly, prediction efficiencies improve dramatically at nearly all altitudes for both single-input and multi-input filters. This improvement is not uniform across all L-shells, but rather tends to scale with regions of the radiation belts that exhibit increasingly persistent behavior. This is expected since persistence allows the Kalman Filter more time to adjust the FIR coefficients to match the current conditions.
One drawback is that the Kalman Filter adapts at different rates for different inputs based on their magnitude and dynamic variability. Vsw response functions are therefore able to adapt more quickly to changing conditions, and generally experience more improved PEs than either of the other inputs, when used in a single-input configuration. When adaptive multi-input filter coefficients are calculated, the fact that Vsw filter coefficients adapt more quickly causes it to account for an undue share of the electron flux variability. Very good predictions are still provided across a broad range L-shells, but definitive statements regarding the physical cause of the various responses are ill-advised. Modifications to the standard Kalman Filter identification algorithm are suggested in the thesis that address this problem, but they have not been implemented for the studies discussed in this thesis.