Abstract: |
State and parameter estimation in high dimensional systems is one of the most problematic parts in both monitoring and control. The Ensemble Kalman filter (ENKF) was proposed for dealing with this problem by using a very small number of samples. We are restricted in the number of samples because of the computation time and online implementation. It works well for systems with a distribution close to the Gaussian, but when the Gaussian approximation is not accurate the ENKF can diverge. We proposed a robustified Gaussian mixture Monte Carlo filter (RGMMC) with a tuning parameter in order to deal with general systems. The method shrinks the particles towards their mean values, and it has more flexibility than the EnKF. In this paper we extend this previous work for dealing with correlated samples. Its performance is almost equal to the ENKF when we have correlated predicted samples because all Gaussian mixtures tend to collapse, behaving like a Gaussian distribution. In the current work we remove the collinearity between samples to separate the Gaussian mixtures in the predictive distribution. The method studies some dimension reduction techniques such as ridge regression, principal component regression, and localization. We implement the proposed method on a couple of examples, including a petroleum reservoir simulator. |
