Prior studies have examined the time-stationary (and quasi-stationary) dynamic response of relativistic electrons in the Earth's outer radiation belt to changes in solar wind bulk speed using linear prediction filters <Baker et al., 1990; Vassiliadis et al., 2002>. For this study, we have implemented an adaptive system identification scheme, based on the Kalman filter with process noise, to determine optimal time-dependent electron response functions. The nonlinear dynamic response of the radiation belts can then be tracked in time by recursively updating the optimal linear filter coefficients as new observations become available. We demonstrate a significant improvement in zero-time-lag electron log-flux predictions relative to models that are based on time-stationary linear prediction filters, while incurring only a slight increase in computational complexity. We conclude by discussing modifications necessary for an operational specification and forecast model, including the assimilation of real-time data, more sophisticated model structures, and a more practical gridded description of the radiation belt state.