In extremum seeking control, the gradient estimation is the key enabler for a successful online optimization. For this purpose, the classical algorithm uses a combination of high- and low-pass filters. In this investigation extended Kalman filters (EKF) are used instead. The approach is explained in detail and advantages of Kalman filtering will become apparent. A novel approach for the gradient estimation for dual-input single-output systems is presented. The proposed EKF incorporates the coupling of the output to both inputs, thus, enabling a superior gradient estimate. A simulation study shows that faster convergence of the extremum-seeking controller can be achieved using this estimator. The feasibility of the proposed algorithm in an experimental setup is demonstrated by control of thermoacoustic instabilities in an atmospheric combustor test rig. (C) 2012 Elsevier Ltd. All rights reserved.