• Journal of IKEEE
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• v.19 no.2
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• pp.219-224
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• 2015

Electrical impedance tomography is an imaging technique to reconstruct the internal conductivity distribution based on applied currents and measured voltages in a domain of interest. In this paper, a modified Gauss-Newton method is proposed for conductivity image reconstruction. In the proposed method, the dimension of the inverse term is reduced by replacing the number of elements with the number of measurement data in the conductivity updating equation of the conventional Gauss-Newton method. Therefore, the computation time is greatly reduced as compared to the conventional Gauss-Newton method. Moreover, the regularization parameter is selected by computing the minimum-maximum from the diagonal components of the Jacobian matrix at every iteration. The numerical experiments with several scenarios were carried out to evaluate the reconstruction performance of the proposed method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.9
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• pp.1141-1145
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• 2016

In general, a variable forgetting factor is applied to the RLS algorithm for the time-varying parameter estimation in the non-stationary environments. The introduction of a variable forgetting factor to RLS needs heavy additional calculation complexity. We propose a new Gauss Newton variable forgetting factor RLS algorithm which needs small amount of calculation as well as estimates the better parameters in time-varying nonstationary environment. The algorithm performs as good as the conventional Gauss Newton variable forgetting factor RLS and the required additional calculation complexity reduces from $O(N^2)$ to O(N).

• Proceedings of the Acoustical Society of Korea Conference
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• spring
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• pp.173-176
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• 2000

시변 신호 추적 특성을 향상시키기 위하여, Gauss-Newton Variable Forgetting Factor RLS (GN-VFF-RLS) Algorithm을 제안한다. 최적화된 망각인자를 가정한 기존의 RLS 알고리듬과 비교하여, 제안된 방법은 특히 신호의 변화가 급격히 일어날 경우 주목할만한 추정 성능의 향상을 보여준다. 제안된 알고리듬의 시변 추정 특성을 신호 대 잡음비와 시변 정도에 대하여 모의 실험하고 기존의 추정 알고리듬들과 비교한다.

• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.955-970
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• 2014

We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also included in this study.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.7
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• pp.683-687
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• 2007

In last decades, several linearization methods for the AOA measurements have been proposed, for example, Gauss-Newton method and Closed-Form solution. Gauss-Newton method can achieve high accuracy, but the convergence of the iterative process is not always ensured if the initial guess is not accurate enough. Closed-Form solution provides a non-iterative solution and it is less computational. It does not suffer from convergence problem, but estimation error is somewhat larger. This paper proposes a Self-Tuning Weighted Least Square AOA algorithm that is a modified version of the conventional Closed-Form solution. In order to estimate the error covariance matrix as a weight, a two-step estimation technique is used. Simulation results show that the proposed method has smaller positioning error compared to the existing methods.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2480-2484
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• 2005

Electrical resistance tomograpy (ERT) maps resistivity values of the soil subsurface and characterizes buried objects. The characterization includes location, size, and resistivity of buried objects. In this paper, truncated least squares (TLS) is presented for the solution of the ERT image reconstruction. Results of numerical experiments in ERT solved by the TLS approach is presented and compared to that obtained by the Gauss-Newton method.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.739-751
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• 1994

• Journal of IKEEE
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• v.22 no.1
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• pp.149-155
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• 2018

In this paper, we used ET(Electrical Tomography) for earth resistivity image reconstruction of vertical multi layer underground model. The earth resistivity is analyzed generally as the parallel multi-layer model, however possibly there happens vertical layer model. Here to find the best electrode array in case of vertical layer underground model, Wenner, Schlumberger, and Dipole-dipole electrode arrays, which are well known electrode arrays used in ET, have been tested. And Gauss-Newton algorithm is used in ET inversion. RMS error analysis shows that Wenner electrode array is best in imaging.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.4
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• pp.83-90
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• 2017

Electrical impedance tomography is a relatively new nondestructive imaging modality in which the internal conductivity distribution is reconstructed based on the injected currents and measured voltages through electrodes placed on the surface of a domain. In this paper, a fast iterative Gauss-Newton method is proposed to increase the spatial resolution as well as reduce the inverse computational time in the inverse problem, which could be applied to online binary mixture flow applications. To evaluate the reconstruction performance of the proposed method, numerical experiments have been carried out and the results are analyzed.

• Geophysics and Geophysical Exploration
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• v.7 no.3
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• pp.207-212
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• 2004

This article reviews recent developments in three-dimensional (3-D) magntotelluric (MT) imaging. The inversion of MT data is fundamentally ill-posed, and therefore the resultant solution is non-unique. A regularizing scheme must be involved to reduce the non-uniqueness while retaining certain a priori information in the solution. The standard approach to nonlinear inversion in geophysis has been the Gauss-Newton method, which solves a sequence of linearized inverse problems. When running to convergence, the algorithm minimizes an objective function over the space of models and in the sense produces an optimal solution of the inverse problem. The general usefulness of iterative, linearized inversion algorithms, however is greatly limited in 3-D MT applications by the requirement of computing the Jacobian(partial derivative, sensitivity) matrix of the forward problem. The difficulty may be relaxed using conjugate gradients(CG) methods. A linear CG technique is used to solve each step of Gauss-Newton iterations incompletely, while the method of nonlinear CG is applied directly to the minimization of the objective function. These CG techniques replace computation of jacobian matrix and solution of a large linear system with computations equivalent to only three forward problems per inversion iteration. Consequently, the algorithms are efficient in computational speed and memory requirement, making 3-D inversion feasible.