Convergence analysis of ensemble Kalman inversion: the linear, noisy case

Abstract

We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed ensemble size. We will build on recent results on the convergence in the noise-free case and generalise them to the case of noisy observational data, in particular the influence of the noise on the convergence will be investigated, both theoretically and numerically. We focus on linear inverse problems where a very complete theoretical analysis is possible.

Keywords:

• Bayesian inverse problems
• ensemble Kalman filter
• parameter identification

AMS Subject Classifications:

• 65N21
• 62F15
• 65N75

Acknowledgements

Both authors are grateful to the careful reading, and suggestions, of two referees. AMS is also thanks DARPA and ONR for funding parts of this research.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the EPSRC Programme Grant EQUIP; DARPA [grant number W911NF-15-2-0121]; ONR [grant number N00014-17-1-2079].