What the collapse of the ensemble Kalman filter tells us about particle filters

Abstract

The ensemble Kalman filter (EnKF) is a reliable data assimilation tool for high-dimensional meteorological problems. On the other hand, the EnKF can be interpreted as a particle filter, and particle filters (PF) collapse in high-dimensional problems. We explain that these seemingly contradictory statements offer insights about how PF function in certain high-dimensional problems, and in particular support recent efforts in meteorology to ‘localize’ particle filters, i.e. to restrict the influence of an observation to its neighbourhood.

Keywords:

• ensemble Kalman filter
• particle filter
• collapse of particle filters

Acknowledgements

We thank Prof. Alexandre J. Chorin of UC Berkeley and Berkeley National Laboratory for interesting discussion and encouragement.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

MM was supported by the Office of Naval Research [grant number N00173-17-2-C003]; by an Alfred P. Sloan Research Fellowship, and by the National Science Foundation [grant number DMS-1619630]. DH gratefully acknowledges support from the Office of Naval Research [PE-0601153N]. The work upon which this material is based upon was started while MM was a postdoc, supported by the US Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program [contract number DE-AC02005CH11231]; and by the National Science Foundation [grant number DMS-1419044].