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Peer-reviewedCC BY 4.0Statistics and Computing

Data assimilation using a global Girsanov nudged particle filter

  • Maneesh Kumar Singh1,2
  • Joshua Hope-Collins1
  • Colin J. Cotter1
  • Dan Crisan1
  1. 1Department of Mathematics, Imperial College London, London, UK
  2. 2Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai India
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Abstract

We present a particle filtering algorithm for stochastic models on infinite dimensional state space, making use of Girsanov perturbations to nudge the ensemble of particles into regions of higher likelihood. We argue that the optimal control problem needs to couple control variables for all of the particles to maintain an ensemble with good effective sample size (ESS). We provide an optimisation formulation that separates the problem into three stages, separating the nonlinearity in the ESS term in the functional with the nonlinearity due to the forward problem, and allowing independent parallel computation for each particle when calculations are performed over control variable space. The particle filter is applied to the stochastic Kuramoto-Sivashinsky equation, and compared with the temper-jitter particle filter approach. We observe that whilst the nudging filter produces an ensemble with a larger spread than the temper-jitter filter, it responds to extreme events in the assimilated data more quickly and robustly.

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Cite

BibTeXRIS
BibTeX
@article{singh2026data,
  title = {{Data assimilation using a global Girsanov nudged particle filter}},
  author = {Maneesh Kumar Singh and Joshua Hope-Collins and Colin J. Cotter and Dan Crisan},
  journal = {Statistics and Computing},
  year = {2026},
  month = nov,
  doi = {10.1007/s11222-026-11019-z},
  url = {https://doi.org/10.1007/s11222-026-11019-z},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Data assimilation using a global Girsanov nudged particle filter
AU  - Maneesh Kumar Singh
AU  - Joshua Hope-Collins
AU  - Colin J. Cotter
AU  - Dan Crisan
PY  - 2026
DA  - 2026/11/01
JO  - Statistics and Computing
DO  - 10.1007/s11222-026-11019-z
UR  - https://doi.org/10.1007/s11222-026-11019-z
AB  - We present a particle filtering algorithm for stochastic models on infinite dimensional state space, making use of Girsanov perturbations to nudge the ensemble of particles into regions of higher likelihood. We argue that the optimal control problem needs to couple control variables for all of the particles to maintain an ensemble with good effective sample size (ESS). We provide an optimisation formulation that separates the problem into three stages, separating the nonlinearity in the ESS term in the functional with the nonlinearity due to the forward problem, and allowing independent parallel computation for each particle when calculations are performed over control variable space. The particle filter is applied to the stochastic Kuramoto-Sivashinsky equation, and compared with the temper-jitter particle filter approach. We observe that whilst the nudging filter produces an ensemble with a larger spread than the temper-jitter filter, it responds to extreme events in the assimilated data more quickly and robustly.
SN  - 0960-3174
ER  -