  We present a method for joint state and parameter estimation for natural gas
networks where gas pressures and flows through a network of pipes depend on
time-varying injections, withdrawals, and compression controls. The estimation
is posed as an optimal control problem constrained by coupled partial
differential equations on each pipe that describe space- and time-dependent
density and mass flux. These are discretized and combined with nodal conditions
to give dynamic constraints for posing the estimation as nonlinear least
squares problems. We develop a rapid, scalable computational method for
performing the estimation in the presence of measurement and process noise.
Finally, we evaluate its effectiveness using a data set from a capacity
planning model for an actual pipeline system and a month of time-series data
from its supervisory control and data acquisition (SCADA) system.
