Particle Filters and Data Assimilation

Abstract

State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state relates to partial and noisy observations that have been made. Inference and prediction then involves solving a challenging inverse problem: calculating the conditional distribution of quantities of interest given the observations. This article reviews Monte Carlo algorithms for solving this inverse problem, covering methods based on the particle filter and the ensemble Kalman filter. We discuss the challenges posed by models with high-dimensional states, joint estimation of parameters and the state, and inference for the history of the state process. We also point out some potential new developments which will be important for tackling cutting-edge filtering applications.

To appear in `Annual Review of Statistics and Its Application'

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• Identification of Tissue Optical Properties During Thermal Laser-Tissue Interactions: An Ensemble Kalman Filter-Based Approach
• Analyzing the Effects of Observation Function Selection in Ensemble Kalman Filtering for Epidemic Models
• When Artificial Parameter Evolution Gets Real: Particle Filtering for Time-Varying Parameter Estimation in Deterministic Dynamical Systems