An Iterative Version of the Adaptive Gaussian Mixture Filter

The adaptive Gaussian mixture filter (AGM) was introduced as a robust filter technique for large scale applications and an alternative to the well known ensemble Kalman filter (EnKF). The bias of AGM is determined by two parameters, one adaptive weight parameter and one predetermined bandwidth parameter which decides the size of the linear update. The bandwidth parameter must often be selected significantly different from zero in order to make large enough linear updates to match the data, at the expense of bias in the estimates. In the iterative AGM we introduce here we take advantage of the fact that the history matching problem is usually estimation of parameters. If the prior distribution of parameters is close to the posterior distribution, it is possible to match the observations with a small bandwidth parameter. Hence the bias of the filter solution is small. In order to obtain this scenario we iteratively run the AGM throughout the data history with a very small bandwidth to create a new prior distribution from the updated samples after each iteration. After a few iterations, nearly all samples from the previous iteration match the data and the above scenario is achieved.