Successful epilepsy surgery hinges on accurately identifying the epileptogenic zone in the brain. This identification can be achieved through source reconstruction from surface electroencephalography (EEG), necessitating a solution to the EEG inverse problem. This problem can be reframed as a state estimation challenge, which is addressed using Kalman filtering. The dynamics of the brain and the measurement process are modeled with suitable state-space models. This work advances the spatiotemporal Kalman filter, a modified version designed for the complex EEG inverse problem, applying it to epileptology. It explores the impact of brain discretization and the Laplacian operator on the Kalman filter's accuracy. The filter is utilized for reconstructing sources of epileptiform discharges and the onset of focal seizures, with performance assessed in low-density EEG scenarios. For high-density EEG, a dimensionality reduction technique is incorporated to enhance localization accuracy and computational efficiency. Additionally, a model for multimodal fusion of magneto- and electroencephalography is introduced within the source reconstruction framework. Finally, the regional spatiotemporal Kalman filter enables the localization of activity from subcortical brain structures. This dynamic approach to the EEG inverse problem via Kalman filtering potentially enhances the accuracy and spatial resolution of brain source reconstruction from
