Ensemble data assimilation using optimal control in the Wasserstein metric

An ensemble data assimilation method is proposed that based on optimal control minimizing the cost of mismatch in Wasserstein metric observation space. The new achieved state without calculating posterior distribution particle and states are evolved deterministically, which easy to be implemented. appropriate for systems multiple, noisy, partial observations available (e.g. citizen weather stations or smart phones). demonstrated for: (i) deterministic dynamics with uncertain initial conditions, (ii) multiple noisy a randomly forced ordinary differential equation (ODE), (iii) from sample paths stochastic (SDE). A bi-modal measure supported strange attractor tested. numerical results show our performs relatively small distance measures approximation performance. But implementation bit expensive due complexity computation, especially large set particles.