Mixture-Weighted Ensemble Kalman Filter with Quasi-Monte Carlo Transport
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Klebanov, Ilja Schillings, Claudia Wrischnig, Dana |
| author_facet | Klebanov, Ilja Schillings, Claudia Wrischnig, Dana |
| contents | The Bootstrap Particle Filter (BPF) and the Ensemble Kalman Filter (EnKF) are two widely used methods for sequential Bayesian filtering: the BPF is asymptotically exact but can suffer from weight degeneracy, while the EnKF scales well in high dimension yet is exact only in the linear-Gaussian case. We combine these approaches by retaining the EnKF transport step and adding a principled importance-sampling correction. Our first contribution is a general importance-sampling theory for mixture targets and proposals, including variance comparisons between individual- and mixture-based estimators. We then interpret the stochastic EnKF analysis as sampling from explicit Gaussian-mixture proposals obtained by conditioning on the current or previous ensemble, which leads to six self-normalized IS-EnKF schemes. We embed these updates into a broader class of ensemble-based filters and prove consistency and error bounds, including weight-variance comparisons and sufficient conditions ensuring finite-variance importance weights. As a second contribution, we construct transported quasi-Monte Carlo (TQMC) point sets for the Gaussian-mixture laws arising in prediction and analysis, yielding TQMC-enhanced variants that can substantially reduce sampling error without changing the filtering pipeline. Numerical experiments on benchmark models compare the proposed mixture-weighted and TQMC-enhanced filters, showing improved filtering accuracy relative to BPF, EnKF, and the standard weighted EnKF, and that the weighted schemes eliminate the EnKF error plateau often caused by analysis-target mismatch. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18992 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mixture-Weighted Ensemble Kalman Filter with Quasi-Monte Carlo Transport Klebanov, Ilja Schillings, Claudia Wrischnig, Dana Methodology Numerical Analysis 60G35, 62M05, 65C35, 65C05, 62F15 The Bootstrap Particle Filter (BPF) and the Ensemble Kalman Filter (EnKF) are two widely used methods for sequential Bayesian filtering: the BPF is asymptotically exact but can suffer from weight degeneracy, while the EnKF scales well in high dimension yet is exact only in the linear-Gaussian case. We combine these approaches by retaining the EnKF transport step and adding a principled importance-sampling correction. Our first contribution is a general importance-sampling theory for mixture targets and proposals, including variance comparisons between individual- and mixture-based estimators. We then interpret the stochastic EnKF analysis as sampling from explicit Gaussian-mixture proposals obtained by conditioning on the current or previous ensemble, which leads to six self-normalized IS-EnKF schemes. We embed these updates into a broader class of ensemble-based filters and prove consistency and error bounds, including weight-variance comparisons and sufficient conditions ensuring finite-variance importance weights. As a second contribution, we construct transported quasi-Monte Carlo (TQMC) point sets for the Gaussian-mixture laws arising in prediction and analysis, yielding TQMC-enhanced variants that can substantially reduce sampling error without changing the filtering pipeline. Numerical experiments on benchmark models compare the proposed mixture-weighted and TQMC-enhanced filters, showing improved filtering accuracy relative to BPF, EnKF, and the standard weighted EnKF, and that the weighted schemes eliminate the EnKF error plateau often caused by analysis-target mismatch. |
| title | Mixture-Weighted Ensemble Kalman Filter with Quasi-Monte Carlo Transport |
| topic | Methodology Numerical Analysis 60G35, 62M05, 65C35, 65C05, 62F15 |
| url | https://arxiv.org/abs/2601.18992 |