Kalman filter based estimation of flow states in open channels using Lagrangian sensing

In this article, we investigate real-time estimation of flow state in open channels using the measurements obtained from Lagrangian sensors (drifters). One-dimensional Shallow Water Equations (SWE), also known as Saint-Venant equations, are used as the mathematical model for the flow. After linearizing and discretizing the PDEs using an explicit linear scheme, we construct a linear state-space model of the flow. The Kalman filter is then used to estimate the states by incorporating the measurements obtained from passive drifters. Drifters which are equipped with GPS receivers move with the flow and report their position at every time step. The position of the drifters at every time step are used to approximate the average velocity of the flow at the corresponding locations and time step. The method is implemented in simulation on a section of the Sacramento river in California using real data and the results are validated with a two-dimensional simulation of the river. Finally, the performance of the method using Lagrangian sensors is compared to the case of using Eulerian sensors.