An Ensemble Bayesian Filter for State Estimation

Data assimilation and parameter estimation problems arise when simulators, such as climate or weather simulators are available. Simulators require an initial state of variables and parameters. Variables can evolve, and parameters by definition do not change. The system model also involves models of any measurement systems. Uncertainty is characterised by probability densities over the initial variables and the parameters. The problem is to compute an approximation to the probability density as observations arrive and the system evolves. Current approaches use a mixture of variational methods and ensemble methods. These tend to be either robust and inconsistent with the principles of Bayesian statistics or principled but prone to numerical instability or collapse of the ensemble into, essentially a single realisation. The following describes attempts to develop a principled ensemble method that remains robust. This ‘Ensemble Bayesian Filter’ (eBf) stays close to fundamental principles but exploits the successful heuristics that have been used in the Ensemble Kalman Filter [1]. The paper demonstrates some improvement in robustness, largely through re-organisation of the linear algebra. However, as discussed in the concluding section, an algorithm that is both robust and principled, and also sufficiently accurate is still to be demonstrated.