Algorithms for high-dimensional non-linear filtering and smoothing problems
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Several numerical tools designed to overcome the challenges of smoothing in a high dimensional nonlinear 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 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 localisation, adaptive spread corrections and hybrid formulations which combine smoothers with complementary properties. These additional features are derived and numerically investigated for the proposed family of smoothers.
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