  In this paper, the parameter estimation problem for a multi-timescale
adaptive threshold (MAT) neuronal model is investigated. By manipulating the
system dynamics, which comprise of a non-resetting leaky integrator coupled
with an adaptive threshold, the threshold voltage can be obtained as a
realizable model that is linear in the unknown parameters. This linearly
parametrized realizable model is then utilized inside a prediction error based
framework to identify the threshold parameters with the purpose of predicting
single neuron precise firing times. The iterative linear least squares
estimation scheme is evaluated using both synthetic data obtained from an exact
model as well as experimental data obtained from in vitro rat somatosensory
cortical neurons. Results show the ability of this approach to fit the MAT
model to different types of fluctuating reference data. The performance of the
proposed approach is seen to be superior when comparing with existing
identification approaches used by the neuronal community.
