Comparison of the hemodynamic filtering methods and particle filter with extended Kalman filter approximated proposal function as an efficient hemodynamic state estimation method

Estimating the hidden hemodynamic states that underlie measured blood oxygen level dependent (BOLD) signals is an important model inversion challenge in functional neuroimaging. Various filtering techniques are proposed in the literature. Those are 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). In this technical note, we compare particle filter type algorithms and Gaussian approximated inference methods. We also implement a particular type of particle filter that approximates the optimal proposal function by the Extended Kalman filter (PF-EKF). We show that the allegation that Extended Kalman type approximated methods are poor in performance is not true. On the contrary, they are better. We tested this assertion under different parameter sets, inputs, a wide range of noise conditions and unknown initial condition. This finding is important for developing fast and accurate alternative model inversion schemes, which is the topic of our subsequent paper.