Application of a Distributed Parameter Filter to Predict Simulated Tidal Induced Shallow Water Flow

Abstract

The theory of distributed parameter filtering is used to construct a filter for the estimation of the state variables of a physical system mathematically modelled by one-dimensional linear shallow water flow equations. These equations consist of the momentum and the continuity equations and the state variables of the system are the water level and velocities. The stochasticities of the system are modelled by white Gaussian noise. The filter uses random generated data corrupted by a white Gaussian noise to update its prediction process. The estimation process contains two steps: a predictor and an update of both state variables and error covariances of the estimates of these variables. The optimality criterion for the filter equations is the minimization of the variance. The relevance of the distributed parameter filter is demonstrated in an application involving a simulation of tidal induced flow in rivers or estuaries. The results exhibited excellent filter performance and a considerable improvement with respect to the deterministic prediction.KeywordsWater LevelWhite Gaussian NoiseWater VelocitySystem NoiseDistribute Parameter SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.