Continuous Venous Oxygen Saturation Estimation: A Robust Population-Informed-Personalized Gaussian Sum-Extended Kalman Filtering Approach

Abstract This article investigates the robustification of the population-informed-personalized Gaussian sum-extended Kalman filter (PI-P-GSEKF) developed in our prior work and its application to continuous venous oxygen saturation (SvO2) estimation. The PI-P-GSEKF was developed to enable state estimation in systems with extremely large variability. It includes a bank of extended Kalman filters (EKFs), whose operating points (i.e., nominal parameter vectors) are selected via generative sampling followed by Markov Chain Monte Carlo (MCMC) sampling with one-time partial state measurement. The state is estimated as the weighted sum of state estimates from all of the EKFs, with the weight for each EKF calculated based on the likelihood of its prediction at every measurement instant. Despite its adequate performance in general, its state estimate can suffer from high-sensitivity operating points whose inaccuracy with respect to the ground truth operating point results in large EKF errors and adversely impacts the PI-P-GSEKF. We explored two ideas to robustify the PI-P-GSEKF against this challenge: (i) penalizing high-sensitivity operating points in MCMC sampling (called robust MCMC sampling) and (ii) calculating the weights for the EKFs based on the likelihood of their predictions in a measurement horizon (called robust Gaussian summing). We examined the efficacy of these ideas in the context of continuous venous oxygen saturation (SvO2) estimation from arterial oxygen saturation measurement, which is important in critical care and cardiopulmonary medicine but is highly invasive and challenging. The results suggested that both ideas could reduce SvO2 estimation error compared with the standard PI-P-GSEKF ((i): 4%; (ii): 13%; (i) + (ii): 16%, on average). However, how to set the length of the sampling interval for weight calculation remains an open challenge.