• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.875-881
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• 2011

This paper describes a new method of estimating the gradient of a function with perturbation and correlation. We impose a known periodic perturbation to the input variable and observe the output of the function in order to obtain much richer and more reliable information. By taking the correlation between the input perturbation and the resultant function outputs, we can determine the gradient of the function. The computation of the correlation does not require derivatives; therefore the gradient can be estimated reliably. Robust estimation of the gradient using perturbation/correlation, which is very effective when an analytical solution is not available, is described. To verify the effectiveness of perturbation/correlation based estimation, the results of gradient estimation are compared with the analytical solutions of an example function. The effects of amplitude of the perturbation and number of samplings in a period are investigated. A minimization of a function with the gradient estimation method is performed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.1-22
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• 2020

An accurate and efficient gradient estimation method on unstructured grid is presented by proposing a switching process between two Least-Square methods. Diverse test cases show that the gradient estimation by Least-Square methods exhibit better characteristics compared to Green-Gauss approach. Based on the investigation, switching between the two Least-Square methods, whose merit complements each other, is pursued. The condition number of the Least-Square matrix is adopted as the switching criterion, because it shows clear correlation with the gradient error, and it can be easily calculated from the geometric information of the grid. To illustrate switching process on general grid, condition number is analyzed using stencil vectors and trigonometric relations. Then, the threshold of switching criterion is established. Finally, the capability of Switching Weighted Least-Square method is demonstrated through various two- and three-dimensional applications.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.9C
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• pp.882-888
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• 2006

Multiuser detection can significantly increase system capacity and improve service quality compared with the existing matched filter. In this paper, we introduce an method which efficiently calculates the maximum likelihood (ML) metric based on the gradient search (GS). The ML detection needs user powers as well as their spreading codes. A method is also proposed that allows us to detect data bits with the estimation of user powers when they are unknown. Computer simulation shows that the proposed method can nearly achieve the same performance as the GS with perfectly hewn user powers.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.8
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• pp.126-135
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• 2014

The Euclidean distance between error probability density functions (EDEP) has been used as a performance criterion for supervised adaptive signal processing in impulsive noise environments. One of the drawbacks of the EDEP algorithm is a heavy computational complexity due to the double summation operations at each iteration time. In this paper, a recursive method to reduce its computational burden in the estimation of the EDEP and its gradient is proposed. For the data block size N, the computational complexity for the estimation of the EDEP and its gradient can be reduced to O(N) by the proposed method, while the conventional estimation method has $O(N^2)$. In the performance test, the proposed EDEP and its gradient estimation yield the same estimation results in the steady state as the conventional block-processing method. The simulation results indicates that the proposed method can be effective in practical adaptive signal processing.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.49 no.2
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• pp.130-136
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• 2012

In this paper, we propose a near-field range estimation method for a uniform linear array that can calibrate bearing estimation error which give a bad influence on a range estimation process. When a range is fixed, the bearing error is calibrated to maximize the beamformer output by the proposed algorithm based on the gradient method. Simulation results show that the proposed algorithm can compensate the bearing error which is less than the mainlobe beamwidth so that reduce the range estimation error as similar as the case of no bearing error.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.2
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• pp.59-68
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• 1993

The motion vector estimation and motion boundary detection have been briskly studied since they are an important clue for analysis of object structure and 3-d motion. The purpose of this researches is more exact estimation, but there are two main causes to make inaccurate. The one is the erroneous measurement of gradients in brightness values and the other is the blurring of motion boundries which is caused by the smoothness constraint. In this paper, we analyze the gradient measurement error of conventional methods and propose new technique based on it. When the proposed method is applied to the motion boundary detection in Schunck and motion vector estimation in Horn & Schunck, it is shown to have much better performance than conventional method is some artificial and real image sequences.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.1288-1293
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• 2004

Inverse radiation problems are solved for estimating the boundary conditions such as temperature distribution and wall emissivity in axisymmetric absorbing, emitting and scattering medium, given the measured incident radiative heat fluxes. Various regularization methods, such as hybrid genetic algorithm, conjugate-gradient method and Newton method, were adopted to solve the inverse problem, while discussing their features in terms of estimation accuracy and computational efficiency. Additionally, we propose a new combined approach of adopting the genetic algorithm as an initial value selector, whereas using the conjugate-gradient method and Newton method to reduce their dependence on the initial value.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1715-1725
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• 1998

A two-dimensional transient inverse heat conduction problem involving the estimation of the unknown location, ($X^*$, $Y^*$), and timewise varying unknown strength, $G({\tau})$, of a line heat source embedded inside a rectangular bar with insulated boundaries has been solved simultaneously. The regular conjugate gradient method, RCGM and the modified conjugate gradient method, MCGM with adjoint equation, are used alternately to estimate the unknown strength $G({\tau})$ of the source term, while the parameter estimation approach is used to estimate the unknown location ($X^*$, $Y^*$) of the line heat source. The alternate use of the regular and the modified conjugate gradient methods alleviates the convergence difficulties encountered at the initial and final times (i.e ${\tau}=0$ and ${\tau}={\tau}_f$), hence stabilizes the computation and fastens the convergence of the solution. In order to examine the effectiveness of this approach under severe test conditions, the unknown strength $G({\tau})$ is chosen in the form of rectangular, triangular and sinusoidal functions.

• The Journal of Korea Robotics Society
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• v.14 no.4
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• pp.258-263
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• 2019

Some animals have special sensing functions in order to find foods, home and mates. Instead of passively sensing, they discharge signals and then extract necessary information from the response. More importantly, they utilize the gradients of the sensed signal in order to find the destination or objects. In this paper this special strategy is formulated mathematically, i.e., the perturbation and the correlation based gradient estimation is developed. A stereo sensor system using temperature sensors mounted on motors is developed for verification. The proposed method can estimate the gradient of the measured value accurately. Using this method, the direction in the maximum measured value can be estimated accurately, and the position of the heat source can be estimated from the intersection of the directions estimated from both sensors.

• Journal of Korean Society of Transportation
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• v.27 no.4
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• pp.145-154
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• 2009

The main goal of this paper is to develop a methodology for increasing the reliability of truck OD matrices in Seoul Metropolitan Area. We propose a Hybrid Method made up of five processes by using Non-Traffic Assignment and Gradient Method. A Hybrid Method and Gradient Method have applied for comparison and estimation in Seoul Metropolitan Area. Mean Error and Root Mean Square Error of a Hybrid Method present lower than Gradient Method. The findings of this paper show that the new truck OD matrices created by a Hybrid Method are more reliable than the existing truck OD matrices in the Seoul Metropolitan Area.