Efficient algorithms for Kalman filtering

	Three dimensional shallow water models are important for the prediction of water levels and currents in the coastal zone. During stormy weather the quality of the predictions is strongly affected by the uncertainty in the model. It is possible to improve tracking and prediction errors by assimilation of measurements. One of the applications in this project is the on-line tracking of currents in three dimensions for shipping in the Eurochannel and the Meuse channel. Here HF-radar measurements of surface currents can be used for improvement of the model results.
	For on-line data assimilation in principle the Kalman filtering algorithm can be used to find the 'optimal' estimate that is consistent with both model and measurements. Direct application of the equations derived by Kalman results in severe computational problems, therefore approximation of these equations are needed. Square Root formulations of the Kalman filter equations are for various reasons more suitable for approximation. Focus of the project will be finding efficient algorithms based on approximation of Square Root Filter equations that can be used for the large models that are used in practical applications.
	Focus of the project will be finding efficient algorithms based on approximation of square Root Filter equations that can be used for the large models that are used in practical applications.

Data assimilation for nonlinear models

	Non-linear model dynamics seriously complicates the application of data assimilation. Although several theoretical solutions exist, practical solution of non-linear data assimilation problems is only possible approximately, except for very small systems. In apparent contradiction with these theoretical difficulties many near-linear approximations, such as the extended Kalman filter perform often very well also for highly non-linear models.
	In this project an attempt is made to compare several available approximate methods, such as the first and second order versions of the RRSQRT filter, the ensemble Kalman filter and the SEEK/SEIK algorithms.
	Aim of the project is the development of a method of analysis for comparing these algorithms.