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In this paper, we apply the information-theoretic learning (ITL) technique to the extended Luenberger observer. Instead of prespecifying the globally stable observer gains for nonlinear dynamic systems, we propose minimizing the entropy of the error between the measurement and the estimated output to update the observer gains. A stochastic gradient-based algorithm is presented and the performance of the entropy observer is demonstrated on linear and nonlinear dynamic systems. We also point out that this approach leads to the introduction of kernel methods into state estimation.