Recent Trends on Nonlinear Filtering for Inverse Problems

TL;DR

This paper reviews recent developments in nonlinear filtering, especially the Ensemble Kalman Filter, highlighting theoretical advances and practical performance in solving inverse problems.

Contribution

It provides a comprehensive review of EnKF, including stability analysis, infinite particle limits, and multi-objective extensions, with empirical illustrations.

Findings

EnKF performance is effective for inverse problems.

Recent theoretical advances improve understanding of EnKF stability.

Extensions enable multi-objective optimization in inverse problems.

Abstract

Among the class of nonlinear particle filtering methods, the Ensemble Kalman Filter (EnKF) has gained recent attention for its use in solving inverse problems. We review the original method and discuss recent developments in particular in view of the limit for infinitely particles and extensions towards stability analysis and multi--objective optimization. We illustrate the performance of the method by using test inverse problems from the literature.