The Use of Mathematical-Statistics Methods in the Solution of Incorrectly Posed Problems

Turchin, Valentin F.; Kozlov, V. P.; Malkevich, M. S.

doi:10.1070/pu1971v013n06abeh004273

Cited by 186 publications

(71 citation statements)

References 35 publications

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“…Though the point of view of this work is quite different, the results are very similar to those of Turchin et al (5) (also reported in this volume). This method has also been used in a quantum mechanical context as a tool to find the correct theory (6,7).…”

Section: Introductionsupporting

confidence: 92%

The maximum entropy method

Seligman

Advanced Methods in the Evaluation of Nuclear Scattering Data

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Section: Introductionsupporting

confidence: 92%

The maximum entropy method

Seligman

Advanced Methods in the Evaluation of Nuclear Scattering Data

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“…astronomy, mechanics, geophysics, wave propagation, etc) the decision of which problem is forward or inverse is not as arbitrary. Turchin et al (1971) define forward problems in the physics domain as a process that is oriented along a cause -effect sequence. A corresponding inverse problem is associated with the reversed, effect -cause sequence.…”

Section: Methodsmentioning

confidence: 99%

Inverse Diffraction Parabolic Wave Equation Localisation System (IDPELS)

Spencer

Walker²,

Hawkes³

2005

J. of GPS

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Abstract. While GPS is a relatively mature technology, its susceptibility to radio frequency interference (RFI) is substantial. Various investigations, including the Volpe Report (Volpe, 2001) which was the result of a US Presidential Decision Directive (PDD-63) assigned to the Department of Transportation (DOT), have recommended that methods should be developed to monitor, report and locate interference sources for applications where loss of GPS is not tolerable. With GPS becoming an integral utility for developed society, the significance of research projects that enhance and expand the capabilities of GPS RFI localisation is highly important.In response to this requirement for GPS interference localisation, a novel technique called "Inverse Diffraction Parabolic Equation Localisation System" (IDPELS) has been developed.This technique exploits detailed knowledge of the local terrain and an inverse diffraction propagation model based on the Parabolic Equation method (PEM). In wave-propagation theory, an inverse problem may involve the determination of characteristics concerning the source, from field values measured at a certain point or certain regions in space. PEM is an electromagnetic propagation modelling tool that has been extensively used for many applications. This paper will present simulation and field trial results of IDPELS. Simulation results show that this technique has good promise to be useful in locating GPS jamming sources in highly-complex environments, based on networks of GPS sensing antennas. Results also show that the method is capable of locating multiple interference sources. Trials concerning the practical application of IDPELS are also provided. With measured lateral field profiles recorded with a single moving sensor platform in a van, results indicate IDPELS to be a pragmatic localisation technique.

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“…(1) For the regularization parameter α itself one can introduce the posterior probability density function [4,5] and choose α with a maximum probability density. It can be done either using the most probable value of noise or assuming the standard deviation σ of the noise of the absorption coefficient to be known (for our spectrum σ = 9 · 10 −4 , as determined from the FT following [6]).…”

Section: The Choice Of Optimal Deconvolutionmentioning

confidence: 99%

“…In early work [4], for the solution of ill-posed problems the statistical approach was proposed. Following that work, in the present paper we shall consider the deconvolution problem in the framework of Bayesian method, detailed formalism of which was described in [5].…”

Section: Introductionmentioning

confidence: 99%

Deconvolution problems in x-ray absorption fine structure spectroscopy

Klementev¹

2001

J. Phys. D: Appl. Phys.

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A Bayesian method application to the deconvolution of EXAFS spectra is considered. It is shown that for purposes of EXAFS spectroscopy, from the infinitely large number of Bayesian solutions it is possible to determine an optimal range of solutions, any one from which is appropriate. Since this removes the requirement for the uniqueness of solution, it becomes possible to exclude the instrumental broadening and the lifetime broadening from EXAFS spectra. In addition, we propose several approaches to the determination of optimal Bayesian regularization parameter. The Bayesian deconvolution is compared with the deconvolution which uses the Fourier transform and optimal Wiener filtering. It is shown that XPS spectra could be in principle used for extraction of a oneelectron absorptance. The amplitude correction factors obtained after deconvolution are considered and discussed. 61.10.Ht

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The Use of Mathematical-Statistics Methods in the Solution of Incorrectly Posed Problems

Cited by 186 publications

References 35 publications

The maximum entropy method

The maximum entropy method

Inverse Diffraction Parabolic Wave Equation Localisation System (IDPELS)

Deconvolution problems in x-ray absorption fine structure spectroscopy

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