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An expectation-maximization algorithm based Kalman smoother approach for single-trial estimation of event-related potentials

This paper applies an expectation-maximization (EM) based Kalman smoother (KS) approach for single-trial event-related potential (ERP) estimation. Existing studies assume a Markov diffusion process for the dynamics of ERP parameters which is recursively estimated by optimal filtering approaches such as Kalman filter (KF). However, these studies only consider estimation of ERP state parameters while the model parameters are pre-specified using manual tuning, which is time-consuming for practical usage besides giving suboptimal estimates. We extend the KF approach by adding EM based maximum likelihood estimation of the model parameters to obtain more accurate ERP estimates automatically. We also introduce different model variants by allowing flexibility in the covariance structure of model noises. Optimal model selection is performed based on Akaike Information Criterion (AIC). The method is applied to estimation of chirp-evoked auditory brainstem responses (ABRs) for detection of wave V critical for assessment of hearing loss. Results shows that use of more complex covariances are better estimating inter-trial variability.