Regularized Particle Filter with Langevin Resampling Step

The solution of an inverse problem involves the estimation of variables and parameters values given by the state‐space system. While a general (infinite‐dimensional) optimal filter theory [1, 2] exists for nonlinear systems with Gaussian or non‐Gaussian noise, applications rely on (finite‐dimensional) suboptimal approximations to the optimal filter for practical implementations. The most widely‐studied filters of this kind include the Regularized Particle Filter (RPF) [3, 4] and the Ensemble Square Root Filter (EnSRF) [5]. The latter is an ad‐hoc approximation to the Bayes Filter, while the former is rigorously formulated, based upon the Glivenko‐Cantelli theorem. By introducing a new global resampling step to the RPF, the EnSRF is proved to approximate the RPF in a special case.