Comparison of Bayesian estimation methods for modeling flow transients in gas pipelines

The aim of this work was to investigate the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and sequential importance resampling (SIR) filter for real-time estimation of a hyperbolic partial differential equation (PDE) system describing the gas flow transients in pipelines. The numerical method of lines was used for solving the system of PDEs. The spatial discretization was based on a five-point, fourth-order finite difference approximation and the time integrations were done using the fourth-order Runge-Kutta scheme (RK4). The resulting nonlinear state-space model was used by the Bayesian filtering algorithms for estimation of the system states. Numerical experiments were conducted to compare the accuracy, robustness and computation time. The results indicated that the difference in terms of accuracy between the EKF and UKF was small and considering the computation time of the UKF and numerically robustness of calculating the Jacobian matrix, the use of EKF might be a better choice when fast solutions are required. The UKF outperformed the EKF and SIR filter when steep variations in the mass flow rate boundary conditions occurred together with low model uncertainty.