Tracking and estimating dynamic magnetoencephalography (MEG) dipole source based on nonlinear Kalman Filters

Localization of magnetoencephalography (MEG) dipole sources has critical applications in biomedical measurements. In this thesis, we have developed a series of Kalman filter-based methods to track and estimate dynamic MEG dipole sources. Using the Gauss-Markov modeling of the dipole source and the dipole components on the x-, y-, and z-directions of the dipole source, the Kalman Filter based method has the significant advantage of fast computational speed. We have also modeled a multicomponent vector sensor array to receive MEG signals to avoid the ambiguity associated with MEG measurements. We have developed tracking and estimating algorithms based on both the Extended Kalman Filter (EKF) and Sigma-Point Kalman Filter (SPKF). We have also combined the regular EKF and SPKF with a projector obtained from the signal subspace method. These modified EKF and SPKF algorithm successfully project out the interference corresponding to spontaneous brain activities. The modified EKF- and SPKF-based algorithms can tolerate difficult simulated environments involving strong temporally nonstationary background noise. Combining Generalized Least Square (GLS) estimation with the Kalman filter can adapt the Kalman filtering method to the case where the dipole components on the x-, y-, z-directions of the SOI dipole source do not satisfy the prerequisites of applying the Kalman filter. Smoothing has also been applied to improve the tracking and estimating performances.