A dynamic likelihood approach to filtering. (13th October 2017) - Restrepo, J. M.
Abstract : A Bayesian data assimilation scheme is formulated for advection‐dominated or hyperbolic evolutionary problems, and observations. It uses the physics to dynamically update the likelihood in order to extend the impact of the likelihood on the posterior, a strategy that would be particularly useful when the observation network is sparse in space and time and the associated measurement uncertainties are low. The filter is applied to a problem with linear dynamics and Gaussian statistics, and compared to the exact estimate, a model outcome, and the Kalman filter estimate. By comparing to the exact estimate the dynamic likelihood filter is shown to be superior to model outcomes and to the Kalman estimate, when the observation system is sparse. The added computational expense of the method is linear in the number of observations and thus computationally efficient, suggesting that the method is practical even if the space dimensions of the physical problem are large. Abstract : A data assimilation scheme is formulated which is applicable to hyperbolic and advection‐dominated problems. It addresses sparsity of observations and can be used in forecasting mode. From top to bottom, the panels show: an exact solution, a model outcome, the assimilated Kalman Fitler result, and an assimilated Dynamic Likelihood Filter outcome.