Adaptive Unscented Kalman Filter for Estimation of Parameters in Kinetic Metabolic Models

Parameter estimation is considered to be one of the greatest challenges in computational systems biology. Biological experiments can measure only a fraction of the kinetic parameters and the rest has to be estimated in silico. Recently parameter estimation problems have been addressed in the framework of control theory. One of the most successful and widely used methods in control theory for estimation of states and parameters is the Kalman filter and its various non linear extension like Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Lillacci et. al. [3] successfully applied EKF whereas Baker et. al. [1] applied UKF for parameter estimation in biological models. Though UKF has shown promising results in estimating unknown parameter value in biological models where the system is defined by nonlinear ODEs, it still inherits some of the limitations of Kalman Filter which means, it can achieve good results under prior assumptions of proper information of the noise distribution and proper initial conditions. But this a priori information is not always available in practice and so assumptions have to be made. If the assumptions are not correct, it might lead the filter to diverge from the solution. One way to solve the problem would be to introduce adaptive mechanism into normal UKF which will also estimate the parameters to match the real statistics and which are not known a priory. Zhe Jiang et. al. [2] proposed a novel adaptive UKF (AUKF) which could make nonlinear joint estimation of both time-varying states and error covariance statistics.