The application of fuzzy adaptive Kalman filtering and smoother Kalman for well logging tool

Abstract

In this article, the application of fuzzy adaptive Kalman filter for estimation of well-log data problems is presented The adaptive technics has been an approach to avoid the divergence problem in Kalman filter when the detailed knowledge about a system models are not completed Natural gamma-ray tool (NGT) is a natural gamma ray sonde, which detects the emitted gamma-ray during the formation of thorium, uranium and potassium at different energy levels. A computer is used to measure the concentrations of Th (Thorium), U (Uranium) and K (potassium) in different depths. Regular techniques have some uncertainties in the estimation of reservoir evaluation, regarding to the perturbation. In this paper, it is shown that there may be an adaptive Kalman filter with the fuzzy inference system and Rauch-Tung-Striebel smoother, based on a model with less information, has a better estimation of the concentrations of Th, U and K in vertical variations.

New estimation methodologies for well logging problems via a combination of fuzzy Kalman filter and different smoothers

“…Thus, they are not exact and have uncertainty and they change over time in some applications. The Fuzzy Kalman filter has been considered in [16,32] to address this problem. The aim of the fuzzy Kalman filter is to adapt measurement noise covariance matrix, , or process noise covariance matrix, .…”

“…The reliability of process model depends on matrix and is determined by this matrix [16]. With respect to Eqs.…”

“…There are many methods in the literature for improvement of the estimations of the elements , and , such as Guy Ruckebusch, 1982 and1983 [2, 14] and Murray, 1987 [4]. Most of the recent activities in the field of well logging were similar to the article [15].A smoother based on the fuzzy adaptive Kalman filter was introduced in [16] for estimation of well-log data problems. Although the suggested filter can estimate, the well-log data, but there is still a large amount of noise on in the data.…”