Abstract
The demand for tractable non-Gaussian Bayesian estimation has increased the popularity of kernel and mixture density representations. Here, using Gaussian Mixture Models (GMM), we posit that the reduction of total variance also remains an important objective in non-linear filtering, particularly in the presence of bias. We propose multi-objective estimation as an essential ingredient in data assimilation.
Using Ensemble Learning, two relatively weak estimators, namely the EnKF and Mixture Ensemble Filter (MEnF), are combined to produce a strong one. The Boosted-MEnF (B-MEnF) stacks MEnF and EnKF to mitigate bias and uses cascade generalization to reduce variance. In the Lorenz-63 model, it lowers mixture complexity without resampling and reduces posterior variance without increasing estimation error.
Our MEnF is a purely ensemble-based GMM filter with a reduced dimensionality burden and without ad-hoc ensemble-mixture member associations. It is expressed as a compact ensemble transform which enables efficient fixed-interval and fixed-lag smoothers (MEnS) as well as the B-MEnF/S.
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Notes
- 1.
MAP problem can also be solved.
- 2.
Note that this problem is not the same as a Wiener filtering problem.
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Seybold, H., Ravela, S., Tagade, P. (2015). Ensemble Learning in Non-Gaussian Data Assimilation. In: Ravela, S., Sandu, A. (eds) Dynamic Data-Driven Environmental Systems Science. DyDESS 2014. Lecture Notes in Computer Science(), vol 8964. Springer, Cham. https://doi.org/10.1007/978-3-319-25138-7_21
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DOI: https://doi.org/10.1007/978-3-319-25138-7_21
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