Sequential State and Parameter Estimation within the Ensemble Kalman Filter

Jonathan Stroud* (1) and Matthias Katzfuss (2), Christopher K. Wikle (3)
(1) McDonough School of Business, Georgetown University
(2) Department of Statistics, Texas A&M University
(3) Department of Statistics, University of Missouri

We propose a new methodology for sequential state and parameter estimation in high-dimensional spatio-temporal dynamic models. We first show empirically that standard sequential Monte Carlo methods such as the auxiliary particle filter fail in high-dimensional systems. We then propose a new combined filtering and parameter learning algorithm based on the ensemble Kalman filter that does not degenerate as the state dimension increases. The method can be used for Gaussian systems with nonlinear observation and/or evolution operators. We illustrate the methodology using a space-time advection-diffusion model observed with noise, first using simulated data and then on a real example of radar reflectivity images.

*Preference: Poster