Nonlinear state estimation for complex immune responses

The inflammatory response is a complex, highly nonlinear biological process, for which complete measurements of all variables are not usually available. Since it is desirable to find therapeutic inputs that enable the response to be controlled toward a favorable outcome, it is crucial to estimate the states that are impossible to measure, and use them for the appropriate control strategy. This article begins with a study of nonlinear observability of a reduced mathematical model of the acute inflammatory response. This will provide theoretical support for employing various state estimation approaches, including the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and the particle filter (PF). A comparison of these techniques is presented with respect to the reduced model of inflammation and the performance of each filter is evaluated in terms of accuracy and consistency.