On-line optimal design of process noise covariance in nonlinear Kalman Filters: A hemodynamic model application

Abstract

The Kalman Filter (KF) is a powerful state estimation technique developed for linear time-varying systems and has recently extended for estimating nonlinear time varying dynamical systems. However, a major challenge for this technique is the choice of the tuning filter parameters that often necessitates a long and tedious process, particularly for large nonlinear systems. In the present work, we propose a new method based on Adaptive Design Optimization (ADO) method in which the tuning parameters are autonomous designed, within the forward Kalman pass, based on sensitivity analysis of the model. The method is applied for the model inversion in a hemodynamic model for which the hidden states (hemodynamic variables) along with unknown neuronal activity (NA) input are estimated based on simulated noisy BOLD signal observations. The proposed approach is demonstrated to produce more confident estimates and better convergence without the need of an iterative tuning process from the designer.