Multiresolution stochastic models for the efficient solution of large-scale space-time estimation problems

The successful application of a previously developed tree-based multiscale estimation framework to large-scale static estimation problems has proven the statistical flexibility and the computational efficiency of the framework. However, the estimation of processes evolving in time remains a considerable challenge. We address this challenge by investigating multiscale models for the steady-state estimation of dynamic systems. In particular, we build such models for 1-D and 2-D heat diffusion processes, making use of a canonical correlations realization technique. The problem of the assimilation of satellite altimetric measurements of the dynamic ocean surface over time is also addressed.