Parameter estimation of slow potassium dynamics in a neuron model for seizure-like activity via adaptive lag synchronization and unscented Kalman filter

We introduce a method that combines the unscented Kalman filter (UKF) and the adaptive lag synchronization (ALS) to estimate the unknown parameters of a neuron model with seizure-like activity using only the heavily noise-corrupted time series of membrane potentials. Although both UKF and ALS are able to estimate the parameters, UKF performs worse when the number of unknown parameters increases, while ALS requires system states that cannot be measured in practice. Therefore, we incorporate UKF as an observer of the unmeasured states into ALS method to estimate multiple parameters. The effectiveness of the combined method is guaranteed by Lyapunov stability theorem and Barbalat's lemma in theory. Numerical simulations demonstrate that, when two parameters are estimated simultaneously, the combined approach has better performance and higher accuracy than only using UKF or ALS method. This exploration of the proposed approach may play an important role in studying new treatments in seizure control.