Joint state and parameter estimation of the hemodynamic model by particle smoother expectation maximization method

Abstract

Objective. In this paper, we aimed for the robust estimation of the parameters and states of the hemodynamic model by using blood oxygen level dependent signal. Approach. In the fMRI literature, there are only a few successful methods that are able to make a joint estimation of the states and parameters of the hemodynamic model. In this paper, we implemented a maximum likelihood based method called the particle smoother expectation maximization (PSEM) algorithm for the joint state and parameter estimation. Main results. Former sequential Monte Carlo methods were only reliable in the hemodynamic state estimates. They were claimed to outperform the local linearization (LL) filter and the extended Kalman filter (EKF). The PSEM algorithm is compared with the most successful method called square-root cubature Kalman smoother (SCKS) for both state and parameter estimation. SCKS was found to be better than the dynamic expectation maximization (DEM) algorithm, which was shown to be a better estimator than EKF, LL and particle filters. Significance. PSEM was more accurate than SCKS for both the state and the parameter estimation. Hence, PSEM seems to be the most accurate method for the system identification and state estimation for the hemodynamic model inversion literature. This paper do not compare its results with Tikhonov-regularized Newton—CKF (TNF-CKF), a recent robust method which works in filtering sense.