In this work, a non-isothermal model of natural gas in pipelines including mass, momentum and energy balance equations are used as model equations for modeling and state estimation in gas pipeline systems. An algorithm is proposed to handle the discontinuities that appear in the dynamic model of a GTN. The states of GTN are estimated using the continuous/discrete form of the extended Kalman filter for two benchmarks and some heuristic rules for sensor placement in a GTN are concluded. Also, a framework for distributed and decentralized state estimation in high-pressure and long-distance gas transmission networks (GTNs) is proposed. Some heuristic rules are suggested for system decomposition...