A random map implementation of implicit filters
This work provides a new computational approach for implicit particle filters, addressing a key bottleneck in data assimilation for high-dimensional dynamical systems.
The paper introduces a random map implementation of implicit particle filters for data assimilation, solving an underdetermined equation for each particle. It demonstrates the method on Lorenz and Kuramoto-Sivashinski systems with sparse observations, achieving efficient high-probability sampling.
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.