Sparsity-Based Kalman Filters for Data Assimilation

Several variations of the Kalman filter algorithm, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are widely used in science and engineering applications. In this paper, we introduce two algorithms of sparsity-based Kalman filters, namely the sparse UKF and the progressive EKF. The filters are designed specifically for problems with very high dimensions. Different from various types of ensemble Kalman filters (EnKFs) in which the error covariance is approximated using a set of dense ensemble vectors, the algorithms developed in this paper are based on sparse matrix approximations of error covariance. The new algorithms enjoy several advantages. The error covariance has full rank without being limited by a set of ensembles. In addition to the estimated states, the algorithms provide updated error covariance for the next assimilation cycle. The sparsity of error covariance significantly reduces the required memory size for the numerical computation. In addition, the granularity of the sparse error covariance can be adjusted to optimize the parallelization of the algorithms

Wind Energy Potential Estimation via a Hybrid Data Assimilation Method

This research proposes a 4D-Var ensemble-based data assimilation framework for wind energy potentialestimation. In this formulation, in the 4D-Var context, the intrinsic need of adjoint models is avoided via the use of an ensemble of model realizations. These ensembles are employed to build control spaces onto which analysis increments are estimated. Control spaces are built via a modified Cholesky decomposition. The particular structure of this estimator allows for a matrix-free implementation of the proposed filter formulation. Experimental tests are performed,making use of wind turbines catalogs and the Atmospheric General Circulation Model Speedy. The results reveal that our proposed framework can properly estimate wind energy potential capacities within reasonable accuracies in terms of Root-Mean-Square-Error, and even more,these estimations are better than those of traditional 4D-Var ensemble-based methods. Besides, Wind Turbine Generators(WTGs) with low rate-capacity are the ones which provide homogeneous behavior of error estimations around the globe. As the rate-capacity increases,the potential energy increases as well, but the error dispersion of ensemble members grow, which can difficult decision-makingprocesses. Of course, rate-capacity is just a single parameter of many in the WTG context, and we do not consider, for instance, economic aspects in our study, which can be crucial for deciding whether or not to employ green sources of energy.DoctoradoDoctor en Ingeniería de Sistemas y Computació