• Geophysics and Geophysical Exploration
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• v.22 no.4
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• pp.195-201
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• 2019

The logarithmic objective function used in waveform inversion minimizes the logarithmic differences between the observed and modeled data. Laplace-domain waveform inversions usually adopt the logarithmic objective function and the diagonal elements of the pseudo-Hessian for optimization. In this case, we apply the Levenberg-Marquardt algorithm to prevent the diagonal elements of the pseudo-Hessian from being zero or near-zero values. In this study, we analyzed the diagonal elements of the pseudo-Hessian of the logarithmic objective function and showed that there is no zero or near-zero value in the diagonal elements of the pseudo-Hessian for acoustic waveform inversion in the Laplace domain. Accordingly, we do not need to apply the Levenberg-Marquardt algorithm when we regularize the gradient direction using the pseudo-Hessian of the logarithmic objective function. Numerical examples using synthetic and field datasets demonstrate that we can obtain inversion results without applying the Levenberg-Marquardt method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.47 no.7
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• pp.499-507
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• 2019

Despite the well-known mathematical model of fixed-wing aircraft, there are various studies to meet desired performances by considering the modeling errors in the extended flight envelope. This paper proposes a new adaptation mechanism of model-reference adaptive control, which applies the Levenberg-Marquardt algorithm to the pitch attitude control of fixed-wing UAV. In addition, reference model in the adaptation law is set by referring to the dynamic properties of the plant model. The performance of the proposed adaptive control law is verified through simulations and flight tests.