One of the most significant systems that can be expressed by partial differential equations (PDEs) is the transmission pipeline system. To avoid the accidents that originated from oil and gas pipeline leakage, the exact location and quantity of leakage are required to be recognized. The designed goal is a leakage diagnosis based on the system model and the use of real data provided by transmission line systems. Nonlinear equations of the system have been extracted employing continuity and momentum equations. In this paper, the extended Kalman filter (EKF) is used to detect and locate the leakage and to attenuate the negative effects of measurement and process noises. Besides, a robust extended Kalman filter (REKF) is applied to compensate for the effect of parameter uncertainty. The quantity and the location of the occurred leakage are estimated along the pipeline. Simulation results show that REKF has better estimations of the leak and its location as compared with that of EKF. This filter is robust against process noise, measurement noise, parameter uncertainties, and guarantees a higher limit for the covariance of state estimation error as well. It is remarkable that simulation results are evaluated by OLGA software.
