Stieltjes moment problem via fractional moments

Inverardi, Pierluigi Novi; Petri, Alberto; Pontuale, Giorgio; Tagliani, Aldo

doi:10.1016/j.amc.2004.06.060

Cited by 38 publications

(18 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, fractional moments have been already proposed in [19][20][21] in the framework of the maximum entropy principle. Yet, we want just to highlight that the FSMs used in the proposed representations are defined along a complex line parallel to the imaginary axis.…”

Section: Remarkmentioning

confidence: 99%

A new representation of power spectral density and correlation function by means of fractional spectral moments

Cottone

Paola

2010

Probabilistic Engineering Mechanics

View full text Add to dashboard Cite

Section: Remarkmentioning

confidence: 99%

A new representation of power spectral density and correlation function by means of fractional spectral moments

Cottone

Paola

2010

Probabilistic Engineering Mechanics

View full text Add to dashboard Cite

“…x has the same moments as those of ( ) f x , and it can be fairly close to ( ) f x as shown by Inverardi et al [8]. When i μ is unknown, which is common in practice, it can be estimated…”

Section: Detection Algorithm Based On Maxent Pdf Estimationmentioning

confidence: 70%

“…In this paper, we employ the MaxEnt PDF estimation, which is widely concerned in recent years [7][8][9], for the realization of the PDF estimation module, and the deduced algorithm is described in the next subsection.…”

Section: Basic Rationale For the Blind-cfar Detectormentioning

confidence: 99%

A new CFAR detector based on PDF estimation of clutter using maximum entropy method

Wang

2011

SPIE Proceedings

View full text Add to dashboard Cite

A new CFAR (constant false alarm rate) algorithm is proposed for the Blind-CFAR detector which is proposed for CFAR detection in various types of clutter. The new algorithm employs the maximum entropy (MaxEnt) method to estimate the PDF (probability density function) of clutter and thus the CFAR detection thresholds based on the samples of reference cells and some moment constraints. Performance of the new algorithm is proved to converge to the performance of the ideal detector as the numbers of the reference cells and the moment constraints approach to infinity. With finite reference cells and moment constraints, performance of the new algorithm is compared with that of the maximum likelihood (ML) CFAR detector in uniform Weibull clutter with known and mismatched shape parameters. The results show that, the Blind-CFAR detector employing the new algorithm performs as well as the ML-CFAR detector in case of known shape parameters and it outperforms the ML-CFAR detector in case of mismatched shape parameters.

show abstract

“…Specially, these constraints for this method apply on the function moments which can be integer or fractional. The use of integer moments has been considered widely because of the ability of characterizing the most distribution functions, good convergence behavior and including the physical information in a few low integer moments [5]. However, in most proposed methods using integer moments, the model is restricted to a certain number of low-order moments.…”

Section: Introductionmentioning

confidence: 99%

“…So, the use of fractional moments for estimation seems to be a better choice. Since the fractional moments with positive order can be expressed as a weighted sum of all integer moments, a few number of fractional moments also contain the most information exist in the integer moments [5]. Recently, development of wireless communication systems makes it necessary to use the frequency resources more efficiently.…”

Section: Introductionmentioning

confidence: 99%

Model order selection based on different information criteria for PDF estimation using maximum entropy method and application in cognitive radio systems

Hosseini

Saberali

Sabahi

2014

7'th International Symposium on Telecommunications (IST'2014)

View full text Add to dashboard Cite

In this paper, we propose two new information criteria to select the desired model order for probability density function (PDF) estimation using the maximum entropy method (MEM). These two proposed information criteria are based on Akaike information criterion (AIC) and Bayesian information criterion (BIC), respectively. The PDF estimation using MEM can be presented using integer and fractional moments. We use two proposed information criteria by considering trade-off between the goodness of fit of the model and the complexity of the model which result in obtaining the appropriate model order. In underlay cognitive radio (CR) systems, the primary user makes a powerful interference for the secondary user which changes the system noise PDF to a non-Gaussian one. The MEM can estimate this non-Gaussian PDF which in turn can be used in nonlinear detection schemes to suppress the degrading effect of the primary user. The simulation results show the high accuracy of the proposed model order selection criteria.

show abstract

Stieltjes moment problem via fractional moments

Cited by 38 publications

References 7 publications

A new representation of power spectral density and correlation function by means of fractional spectral moments

A new representation of power spectral density and correlation function by means of fractional spectral moments

A new CFAR detector based on PDF estimation of clutter using maximum entropy method

Model order selection based on different information criteria for PDF estimation using maximum entropy method and application in cognitive radio systems

Contact Info

Product

Resources

About