A random map implementation of implicit filters

TL;DR

This paper introduces a novel implementation of implicit particle filters using a random map approach, enabling efficient data assimilation for complex stochastic systems with sparse observations.

Contribution

It presents a new method for solving the implicit filter equations via random maps, improving computational efficiency and applicability.

Findings

Successfully assimilated data for Lorenz system with sparse observations.

Applied to stochastic Kuramoto-Sivashinski equation with sparse space-time data.

Demonstrated effectiveness of the random map implementation in complex stochastic models.

Abstract

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.