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) . 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.
|Original language||English (US)|
|Title of host publication||International Conference on Numerical Analysis and Applied Mathematics|
|Publisher||AMER INST PHYSICS|
|Number of pages||1079|
|State||Published - 2010|