Localization of the brain neural generators that create Electroencephalographs (EEGs) has been an important problem in clinical, research and technological applications related to the brain. The active regions in the brain are modeled as equivalent current dipoles, and the positions and moments of these dipoles or brain sources are estimated. So far, the brain dipoles are assumed to be fixed or time-invariant. However, recent neurological studies are showing that brain sources are not static but vary (in terms of location and moment) depending on various internal and external stimuli. This paper presents a shift in the current paradigm of brain source localization by considering dynamic sources in the brain. We formulate the brain source estimation problem from EEG measurements as a (nonlinear) state-space model. We use the Particle Filter (PF), essentially a sequential Monte Carlo method, to track the trajectory of the moving dipoles in the brain. We further address the "curse of dimensionality," issue of the PF by taking advantage of the structure of the EEG state-space model, and marginalizing out the linearly evolving states. A Kalman Filter is used to optimally estimate the linear elements, whereas the PF is used to track only the non-linear components. This technique reduces the dimension of the problem; thus exponentially reducing the computational cost. Our simulation results show that, where the PF fails, the Marginalized PF is able to successfully track two dipoles in the brain with only 500 particles.