Parameter identification for nonlinear state-space models of a biological network via linearization and robust state estimation

Developing mathematical models of biological systems and estimating their parameters hold a key to understanding and predicting the dynamic behaviors of biological systems which contain gene regulatory networks, signal transduction pathways, etc. A widely adopted way to model dynamic biological systems is to employ nonlinear state-space models, in which the extended Kalman filter (EKF) is sometimes used for estimating both their states and parameters. However, first-order linearization usually results in modeling errors, but the EKF based method does not take either unmodeled or parametric uncertainty into account. As a result, the estimation performance of the EKF based method may not be satisfactory, such as slow convergence speed and low estimation accuracy. To overcome these problems, a sensitivity penalization based robust state estimator is suggested for estimating parameters of nonlinear biological systems. Simulation results show that the estimation accuracy of the proposed method can be significantly higher than that of the EKF based method.