Improved Estimation for Well-Logging Problems Based on Fusion of Four Types of Kalman Filters

The concept of information fusion has gained a widespread interest in many fields due to its complementary properties. It makes systems more robust against uncertainty. This paper presents a new approach for the well-logging estimation problem by using a fusion methodology. The natural gamma-ray tool (NGT) is considered as an important instrument in the well logging. The NGT detects changes in natural radioactivity emerging from the variations in concentrations of micronutrients as uranium (U), thorium (Th), and potassium (K). The main goal of this paper is to have precise estimation of the concentrations of
$U$
,
$Th$
, and
$K$
. Four types of Kalman filters are designed to estimate the elements using the NGT sensor. Then, a fusion of the Kalman filters is utilized into an integrated framework by an ordered weighted averaging (OWA) operator to enhance the quality of the estimations. A real covariance of the output error based on the innovation matrix is utilized to design weighting factors for the OWA operator. The simulation studies indicate not only a reliable performance of the proposed method compared with the individual Kalman filters but also a better response in contrast with previous fusion methodologies.