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We formulate two estimation problems for pipeline systems in which measurements of compressible gas flow through a network of pipes is affected by time-varying injections, withdrawals, and compression. We consider a state estimation problem that is then extended to a joint state and parameter estimation problem that can be used for data assimilation. In both formulations, the flow dynamics are described on each pipe by space- and time-dependent density and mass flux that evolve according to adoi:10.1109/tcst.2018.2851507 fatcat:q42iu7ixfvbernct4h4y5ouwgy