  The classic Hodgkin-Huxley model is widely used for understanding the
electrophysiological dynamics of a single neuron. While applying a constant
current to the system results in a single voltage spike, it is possible to
produce more interesting dynamics by applying time-varying currents, which may
not be experimentally measurable. The aim of this work is to estimate
time-varying applied currents of different deterministic forms given noisy
voltage data. In particular, we utilize an augmented ensemble Kalman filter
with parameter tracking to estimate four different deterministic applied
currents, analyzing how the model dynamics change in each case. We test the
efficiency of the parameter tracking algorithm in this setting by exploring the
effects of changing the standard deviation of the parameter drift and the
frequency of data available on the resulting time-varying applied current
estimates and related uncertainty.
