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Abstract:
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Particle filters based on importance sampling cannot avoid the curse of dimensionality and will suffer from weight collapse in high-dimensional systems, meaning that one particle gets most weight, and the others close to weight zero. Instead, particle filters have been developed that enforce equal weights, either in one step or a few step(s), or by solving a differential equation for each particle at observation time. The former rely heavily on regularization, or can be shown to be biased. The latter, so-called particle flows, are increasingly popular, especially when combined with kernel embedding. We will discuss the application of such a particle filter to a high-dimensional quasi-geostrophic model that mimics atmospheric or oceanic circulation. It is shown that the method is robust without the need for localization (a technique in which the full problem is subdivided into smaller subproblems), and discuss convergence and actual performance. Furthermore, we will discuss other variants that perform the embedding in different ways, leading to different particle flows and hence different convergence properties, moving towards optimal settings for geoscience applications.
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