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Kalman Filter Approach for Inversion of Airborne Electromagnetic Data
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, Engineering and Mining Geophysics 2018, Apr 2018, Volume 2018, p.1 - 7
Abstract
Kalman filter is a well-proven tool in the theory of optimal estimation. It minimizes variance of the estimation error in terms of probabilistic approach. Despite the special terminology, the Kalman filter algorithm minimizes the objective function, representing the squared difference between the measured vector and the calculated one for the parameters of selected model. In a certain sense, it is equivalent to the least squares method - a conventional airborne electromagnetic data inversion method. In this paper I describe the essence of the Kalman approach to solving inverse problems. The example of one-dimensional inverse problem shows that setting an a-priori value of the estimation error covariance matrix in a certain way one can get the solution for both vertical and lateral constraints. The Kalman filter algorithm takes into account the measurement noise, which is specified as the dispersion of signals in the corresponding measurement channels at high altitude. Special covariance matrix representation allow to use corresponding Kalman filter calculation methods to provide the computational stability of the algorithm. The Kalman approach makes it possible to combine modern techniques used in airborne survey data processing. I give an example of the Kalman filter use in the frequency-domain airborne data processing.