Nonlinear state and parameter estimation of the hemodynamic model using fMRI bold signal

The joint estimation of the parameters and the states of the hemodynamic model from the blood oxygen level dependent (BOLD) signal is a challenging problem. In the functional magnetic resonance imaging (fMRI) literature, quite interestingly, many proposed algorithms work only as a filtering method. In the fMRI state estimation literature, extended Kalman filter (EKF) is asserted to be not robust and worse than standard particle filters (PF). We compared EKF with PF and observed that the contrary is true. We also implemented particle filter that approximates the proposal function by the extended Kalman filter. We compared Gaussian type approximated estimation techniques like extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF) as well as stochastic inference techniques like standard particle filters (PF) and auxiliary particle filter (APF). Filtering makes the estimation of the hidden states and the parameters less reliable compared with the algorithms that use smoothing. We improved the EKF performance by adding smoother. The joint state and parameter estimation is improved substantially by performing the iterative EKS (IEKS) algorithm. We compared IEKS performance with the square-root cubature Kalman smoother (SCKS) algorithm. We show that its accuracy for the state and the parameter estimation is better and much faster than iterative SCKS. SCKS was found to be a better estimator than the dynamic expectation maximization (DEM), EKF, local linearization filter (LLF) and PF methods. We show in this thesis that IEKS is a better estimator than iterative SCKS under different process and measurement noise conditions.