A random map implementation of implicit filters
  Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined equation be solved for each particle and at each time an observation becomes available. We present a new implementation of implicit filters in which we find the solution of the equation via a random map. As examples, we assimilate data for a stochastically driven Lorenz system with sparse observations and for a stochastic Kuramoto-Sivashinski equation with observations that are sparse in both space and time. 
Matthias Morzfeld, Xuemin Tu, Ethan Atkins and Alexandre J. Chorin
math.NA math-ph math.MP math.PR