TY  - JOUR
A1  - Acevedo, Walter
A1  - De Wiljes, Jana
A1  - Reich, Sebastian
T1  - Second-order accurate ensemble transform particle filters
JF  - SIAM journal on scientific computing
N2  - 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 transform particle filter (ETPF) [S. Reich, SIAM T. 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 second order 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 arises as a special case of our general framework. We illustrate the performance of the second-order accurate filters for the chaotic Lorenz-63 and Lorenz-96 models and a dynamic scene-viewing model. The numerical results for the Lorenz-63 and Lorenz-96 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 scene-viewing model reveal, on the other hand, that second-order corrections can lead to statistically inconsistent samples from the posterior parameter distribution.
KW  - Bayesian inference
KW  - data assimilation
KW  - particle filter
KW  - ensemble Kalman filter
KW  - Sinkhorn approximation
Y1  - 2017
U6  - https://doi.org/10.1137/16M1095184
SN  - 1064-8275
SN  - 1095-7197
SN  - 2168-3417
VL  - 39
IS  - 5
SP  - A1834
EP  - A1850
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  -