This work is about a slow-fast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Second, we prove that the low dimensional filter on the slow manifold approximates the original filter in a suitable metric. Finally, we illustrate this approximate filter numerically in an example.
@article{arxiv.1711.05377,
title = {Effective Filtering on a Random Slow Manifold},
author = {Huijie Qiao and Yanjie Zhang and Jinqiao Duan},
journal= {arXiv preprint arXiv:1711.05377},
year = {2018}
}