A particle flow filter for high‐dimensional system applications

Abstract A novel particle filter proposed recently, the flow (PFF), avoids long‐existing weight degeneracy problem in filters and, therefore, has great potential to be applied high‐dimensional systems. The PFF adopts idea of a flow, which sequentially pushes particles from prior posterior distribution, without changing each particle. essence is that it assumes embedded reproducing kernel Hilbert space, so practical solution for obtained. independent choice limit an infinite number particles. Given finite particles, we have found scalar fails and sparsely observed settings. new matrix‐valued prevents collapse marginal distribution variables system. performance tested compared with well‐tuned local ensemble transform Kalman (LETKF) using 1,000‐dimensional Lorenz 96 model. It shown comparable LETKF linear observations, except explicit covariance inflation not necessary PFF. For nonlinear outperforms able capture multimodal likelihood behavior, demonstrating viable path fully geophysical data assimilation.