Moving Horizon vs. Unscented Kalman Filter for State Estimation in Streamflow Prediction

In this paper, a Moving Horizon Estimator (MHE) and an Unscented Kalman Filter (UKF) are applied and compared for state estimation in flood forecasting. The investigations are based on a conceptual rainfall-runoff model proposed by Lorent/Gevers for streamflow forecasting. Data for the investigations was collected from the region Trusetal in Germany. Streamflow prediction, especially for watersheds with fast response to intense rain, require the knowledge of the current state of the system (e.g., soil moisture content). Firstly, a Moving Horizon Estimator (MHE) was applied for the state estimation, due to our good experience with it in other applications, its ability to deal with non-Gaussian disturbances and the fact that the hydrologic model is nonlinear, and its states satisfy equality and inequality constraints. Due to computational intensity of the MHE, an UKF was also implemented for comparison. Even though theory and most literature conclude the superiority of MHE to UKF, in this application example the results show that the UKF and the MHE produce almost similar results with UKF slightly better, which might be due to several reasons such as problems with the initialization of the hessian matrix, choice of prediction horizon and existence of local optima in MHE. Therefore, comprehensive investigations were performed in this respect.