Filtragem estocástica não linear aplicada ao problema de monitoramento e estimativa de enchentes

Abstract

In the last decade, there has been an increase in the awareness about flood prevention, creating an impulse to improve flood monitoring and forecasting techniques, of which water level prediction is a crucial part. The purpose of this study is the implementation of non-linear stochastic filters applied to a system of flood level estimation and monitoring, for which the mathematical model is also non-linear. For this reason, a study on the stochastic filtering theory is carried, from the Kalman Filter (KF) to the Extended Kalman Filter (EKF), the Unscented Kalman Filter (UKF), and the Particle Filter (PF). The states to be monitored on a flood level estimation and monitoring system are defined in three different mathematical models found in the literature. The three stochastic filters are implemented using MATLAB and, for all mathematical models, the measurements are generated via simulation. The performance of each filter is quantified through error analysis, from MSE and RMSE, and through the analysis of the stochastic filters’ estimates trajectories, and a comparative between the filters and mathematical models takes place. The application of these non-linear stochastic filters for a non-linear mathematical model is quantified in the results for the mathematical models found in the literature, allowing a comparative of the filters and of the impact of their particularities for each mathematical model to be held. The PF presented superior results for the implementation applied to the first mathematical model, presenting smaller errors when compared to the KF derivatives. For the other mathematical models, however, the KF derivatives had better performances, especially the FKU, which presented the best estimates.