Combined state-parameter estimation for shallow water equations

In this article, a method for assimilating data into the shallow water equations when some of the model parameters are unknown is presented. The one dimensional Saint-Venant equations are used as a model of water flow in open channels. Using these equations, a nonlinear state space model is obtained. Lagrangian measurements of the flow velocity field are used as observations or measurements. These measurements may be obtained from a group of drifters equipped with GPS receivers and communication capabilities which move with the flow and report their position at every time step. Using the derived state-space model, the extended Kalman filter is used to estimate the state and the unknown model parameters given the latest measurements. The performance of the method is evaluated using data collected from an experiment performed at the USDA-ARS Hydraulic Engineering Research Unit (HERU) in Stillwater, Oklahoma in November 2009.