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 a system of coupled partial differential equations, in which momentum dissipation is modeled using the Darcy-Wiesbach friction approximation. These dynamics are first spatially discretized to obtain a system of nonlinear ordinary differential equations on which state and parameter estimation formulations are given as nonlinear least squares problems. A rapid, scalable computational method for performing a nonlinear least squares estimation is developed. Extensive simulations and computational experiments on multiple pipeline test networks demonstrate the effectiveness of the formulations in obtaining state and parameter estimates in the presence of measurement and process noise.