Acevedo, W. and de Wiljes, J. and Reich, S. (2017) Secondorder accurate ensemble transform particle filters. SFB 1114 Preprint . (Submitted)

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Abstract
Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble trans form particle filter (ETPF) (S. Reich, A nonparametric ensemble transform method for Bayesian inference, SIAM J. Sci. Comput., 35, (2013), pp. A2013–A2014) replaces the resampling step of a standard particle filter by a linear transformation which allows for a hybridization of particle filters with ensemble Kalman filters and renders the resulting hybrid filters applicable to spatially extended systems. However, the linear transformation step is computationally expensive and leads to an underestimation of the ensemble spread for small and moderate ensemble sizes. Here we address both of these shortcomings by developing secondorder accurate extensions of the ETPF. These extensions allow one in particular to replace the exact solution of a linear transport problem by its Sinkhorn approximation. It is also demonstrated that the nonlinear ensemble transform filter (NETF) arises as a special case of our general framework. We illustrate the performance of the secondorder accurate filters for the chaotic Lorenz63 and Lorenz96 models and a dynamic scene viewing model. The numerical results for the Lorenz63 and Lorenz96 models demonstrate that significant accuracy improvements can be achieved in comparison to a standard ensemble Kalman filter and the ETPF for small to moderate ensemble sizes. The numerical results for the sceneviewing model reveal, on the other hand, that secondorder corrections can lead to statistically inconsistent samples from the posterior parameter distribution.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group 
ID Code:  2073 
Deposited By:  Silvia Hoemke 
Deposited On:  24 Apr 2017 08:38 
Last Modified:  25 Apr 2017 11:24 
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