# Ensemble transform algorithms for nonlinear smoothing problems

## TL;DR

This paper explores ensemble transform algorithms for nonlinear smoothing, introducing a new ensemble transform particle smoother that is consistent and flexible, with practical techniques tested on complex problems.

## Contribution

It introduces the ensemble transform particle smoother, a novel method that is consistent in the particle limit and adaptable for complex nonlinear smoothing tasks.

## Key findings

- The ensemble transform particle smoother is consistent in the particle limit.
- Adaptive spread corrections improve smoothing accuracy.
- Localization techniques facilitate application to complex problems.

## Abstract

Several numerical tools designed to overcome the challenges of smoothing in a nonlinear and non-Gaussian setting are investigated for a class of particle smoothers. The considered family of smoothers is induced by the class of linear ensemble transform filters which contains classical filters such as the stochastic ensemble Kalman filter, the ensemble square root filter and the recently introduced nonlinear ensemble transform filter. Further the ensemble transform particle smoother is introduced and particularly highlighted as it is consistent in the particle limit and does not require assumptions with respect to the family of the posterior distribution. The linear update pattern of the considered class of linear ensemble transform smoothers allows one to implement important supplementary techniques such as adaptive spread corrections, hybrid formulations, and localization in order to facilitate their application to complex estimation problems. These additional features are derived and numerically investigated for a sequence of increasingly challenging test problems.