  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.
