  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
modelled 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.
