Electroencephalography (EEG)-based brain computer interface (BCI) is the most studied noninvasive interface to build a direct communication pathway between the brain and an external device. However, correlated noises in EEG measurements still constitute a significant challenge. Alternatively, building BCIs based on filtered brain activity source signals instead of using their surface projections, obtained from the noisy EEG signals, is a promising and not well-explored direction. In this context, finding the locations and waveforms of inner brain sources represents a crucial task for advancing source-based noninvasive BCI technologies. In this paper, we propose a novel multicore beamformer particle filter (multicore BPF) to estimate the EEG brain source spatial locations and their corresponding waveforms. In contrast to conventional (single-core) beamforming spatial filters, the developed multicore BPF considers explicitly temporal correlation among the estimated brain sources by suppressing activation from regions with interfering coherent sources. The hybrid multicore BPF brings together the advantages of both deterministic and Bayesian inverse problem algorithms in order to improve the estimation accuracy. It solves the brain activity localization problem without prior information about approximate areas of source locations. Moreover, the multicore BPF reduces the dimensionality of the problem to half compared with the PF solution, thus alleviating the curse of dimensionality problem. The results, based on generated and real EEG data, show that the proposed framework recovers correctly the dominant sources of brain activity.