Weighted Least-Squares Approach for Identification of a Reduced-Order Adaptive Neuronal Model

This brief is focused on the parameter estimation problem of a second-order adaptive quadratic neuronal model. First, it is shown that the model discontinuities at the spiking instants can be recast as an impulse train driving the system dynamics. Through manipulation of the system dynamics, the membrane voltage can be obtained as a realizable model that is linear in the unknown parameters. This linearly parameterized realizable model is then utilized inside a prediction error-based framework to design a dynamic estimator that allows for rapid estimation of model parameters under a persistently exciting input current injection. Simulation results show the feasibility of this approach to predict multiple neuronal firing patterns. Results using both synthetic data (obtained from a detailed ion-channel-based model) and experimental data (obtained from in vitro embryonic rat motoneurons) suggest directions for further work.