Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613563
A. Zoubir, C.L. Brown, B. Boashash
A modification to a previously developed characteristic function based Gaussianity test is proposed. The power of the test is consequently improved. This test is then extended to the multivariate case, allowing it to be applied to correlated data. Monte Carlo simulations are performed to compare power with two other tests for multivariate Gaussianity, with encouraging results.
{"title":"Testing multivariate Gaussianity with the characteristic function","authors":"A. Zoubir, C.L. Brown, B. Boashash","doi":"10.1109/HOST.1997.613563","DOIUrl":"https://doi.org/10.1109/HOST.1997.613563","url":null,"abstract":"A modification to a previously developed characteristic function based Gaussianity test is proposed. The power of the test is consequently improved. This test is then extended to the multivariate case, allowing it to be applied to correlated data. Monte Carlo simulations are performed to compare power with two other tests for multivariate Gaussianity, with encouraging results.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115987846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613523
Jitendra Tugnait
The problem considered is that of identification of unknown parameters of multivariable, linear "errors-in-variables" models, i.e., linear systems where measurements of both input and output of the system are noise contaminated. Attention is focused on frequency-domain approaches where the integrated polyspectrum (bispectrum or trispectrum) of the input and the integrated cross-polyspectrum, respectively, of the given time-domain input-output data are exploited. We first develop (computable) expressions for the covariance matrix of the system transfer function estimate and show that the system transfer function matrix estimate is asymptotically complex Gaussian. Then we propose and analyze a pseudo-maximum likelihood (PML) estimator of system parameters using the developed statistics of the system transfer function estimate. Finally two simulation examples are presented.
{"title":"Identification of multivariable stochastic linear systems using integrated polyspectrum given noisy input-output data","authors":"Jitendra Tugnait","doi":"10.1109/HOST.1997.613523","DOIUrl":"https://doi.org/10.1109/HOST.1997.613523","url":null,"abstract":"The problem considered is that of identification of unknown parameters of multivariable, linear \"errors-in-variables\" models, i.e., linear systems where measurements of both input and output of the system are noise contaminated. Attention is focused on frequency-domain approaches where the integrated polyspectrum (bispectrum or trispectrum) of the input and the integrated cross-polyspectrum, respectively, of the given time-domain input-output data are exploited. We first develop (computable) expressions for the covariance matrix of the system transfer function estimate and show that the system transfer function matrix estimate is asymptotically complex Gaussian. Then we propose and analyze a pseudo-maximum likelihood (PML) estimator of system parameters using the developed statistics of the system transfer function estimate. Finally two simulation examples are presented.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115726156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613542
Yifeng Zhou, H. Leung
In this paper, we present a minimum entropy fusion approach for multisensor data fusion in non-Gaussian environments. We represent the fused data in the form of the weighted sum of the multisensor outputs and use the varimax norm as the information measure. The optimum weights are obtained by maximizing the varimax norm of the fused data. The minimum entropy fusion solution only depends on the empirical distribution of the sensor data and makes no specific distribution assumptions about the sensor data. Numerical simulation results are provided to show the effectiveness of the proposed fusion approach.
{"title":"Minimum entropy approach for multisensor data fusion","authors":"Yifeng Zhou, H. Leung","doi":"10.1109/HOST.1997.613542","DOIUrl":"https://doi.org/10.1109/HOST.1997.613542","url":null,"abstract":"In this paper, we present a minimum entropy fusion approach for multisensor data fusion in non-Gaussian environments. We represent the fused data in the form of the weighted sum of the multisensor outputs and use the varimax norm as the information measure. The optimum weights are obtained by maximizing the varimax norm of the fused data. The minimum entropy fusion solution only depends on the empirical distribution of the sensor data and makes no specific distribution assumptions about the sensor data. Numerical simulation results are provided to show the effectiveness of the proposed fusion approach.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131069474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613567
B. Pesquet-Popescu, P. Larzabal
Self-similar processes have received increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena which exhibit "1/f" spectra and/or long-range dependence. On the other hand the wavelet decomposition became a very useful tool in describing nonstationary self-similar processes. In this paper we first investigate the existence and the properties of higher-order statistics of self-similar processes with finite variance. Then, we consider some self-similar processes with infinite variance and study the statistical properties of their wavelet coefficients.
{"title":"Higher and lower-order properties of the wavelet decomposition of self-similar processes","authors":"B. Pesquet-Popescu, P. Larzabal","doi":"10.1109/HOST.1997.613567","DOIUrl":"https://doi.org/10.1109/HOST.1997.613567","url":null,"abstract":"Self-similar processes have received increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena which exhibit \"1/f\" spectra and/or long-range dependence. On the other hand the wavelet decomposition became a very useful tool in describing nonstationary self-similar processes. In this paper we first investigate the existence and the properties of higher-order statistics of self-similar processes with finite variance. Then, we consider some self-similar processes with infinite variance and study the statistical properties of their wavelet coefficients.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"11 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124279060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613557
M. Coulon, J. Tourneret, M. Ghogho
The detection of two spectrally equivalent (SE) processes is addressed. The two SE processes are modeled using two SE parametric models: the noisy AR model and the ARMA model. Higher-order statistics are shown to be an efficient tool for the SE process detection problem. A new detector based on the higher-order Yule-Walker matrix singularity is studied. The detector performance is compared in supervised and unsupervised learning. The model order mismatch is then studied.
{"title":"Detection and classification of spectrally equivalent processes: a parametric approach","authors":"M. Coulon, J. Tourneret, M. Ghogho","doi":"10.1109/HOST.1997.613557","DOIUrl":"https://doi.org/10.1109/HOST.1997.613557","url":null,"abstract":"The detection of two spectrally equivalent (SE) processes is addressed. The two SE processes are modeled using two SE parametric models: the noisy AR model and the ARMA model. Higher-order statistics are shown to be an efficient tool for the SE process detection problem. A new detector based on the higher-order Yule-Walker matrix singularity is studied. The detector performance is compared in supervised and unsupervised learning. The model order mismatch is then studied.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116903204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613511
C. Bourin, P. Bondon
Bilinear systems are useful to model nonlinear time series. They can be described by a nonlinear recursive equation involving a finite number of parameters. Their analysis and particularly the estimation of the parameters is of central interest. In this paper we establish difference equations between lagged moments and cumulants up to third-order of a simple bilinear model, and show how to use these relations to estimate the parameters.
{"title":"On the identifiability of bilinear stochastic systems","authors":"C. Bourin, P. Bondon","doi":"10.1109/HOST.1997.613511","DOIUrl":"https://doi.org/10.1109/HOST.1997.613511","url":null,"abstract":"Bilinear systems are useful to model nonlinear time series. They can be described by a nonlinear recursive equation involving a finite number of parameters. Their analysis and particularly the estimation of the parameters is of central interest. In this paper we establish difference equations between lagged moments and cumulants up to third-order of a simple bilinear model, and show how to use these relations to estimate the parameters.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132451317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613559
Robert D. Pierce
Many physical phenomena are non-Gaussian and if the observed data have frequently occurring extreme values, then the phenomena may be modeled as a random process with an alpha-stable distribution. When positive and negative outcomes are equally likely, then the process would be symmetric alpha-stable (S/spl alpha/S); however when only positive outcomes are possible, then the process would be positive alpha-stable (P/spl alpha/S). Phenomena related to energy or power are examples. This paper presents the characteristics and potential applications for the P/spl alpha/S distribution. For this distribution all negative-order moments exist, and ratios of these moments are used to estimate alpha. Application areas that are examined include: seismic activity, ocean wave variability, and radar sea clutter modulation. The correlation properties of these data are examined.
{"title":"Application of the positive alpha-stable distribution","authors":"Robert D. Pierce","doi":"10.1109/HOST.1997.613559","DOIUrl":"https://doi.org/10.1109/HOST.1997.613559","url":null,"abstract":"Many physical phenomena are non-Gaussian and if the observed data have frequently occurring extreme values, then the phenomena may be modeled as a random process with an alpha-stable distribution. When positive and negative outcomes are equally likely, then the process would be symmetric alpha-stable (S/spl alpha/S); however when only positive outcomes are possible, then the process would be positive alpha-stable (P/spl alpha/S). Phenomena related to energy or power are examples. This paper presents the characteristics and potential applications for the P/spl alpha/S distribution. For this distribution all negative-order moments exist, and ratios of these moments are used to estimate alpha. Application areas that are examined include: seismic activity, ocean wave variability, and radar sea clutter modulation. The correlation properties of these data are examined.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129086852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613536
T. Kaiser, J. Mendel
In this paper we provide explicit formulas for the covariances of second-third-, and fourth-order sample cumulants as used in narrowband array processing. These covariances provide a basis for analysing the performance of cumulant based algorithms for finite-sample length, which is in contrast to usual asymptotic performance analyses. The use of these formulas, which consist of several thousand terms, will be demonstrated, and a rough idea of their applicability to a performance analysis for finite numbers of samples will be given.
{"title":"Covariance of finite-sample cumulants in array-processing","authors":"T. Kaiser, J. Mendel","doi":"10.1109/HOST.1997.613536","DOIUrl":"https://doi.org/10.1109/HOST.1997.613536","url":null,"abstract":"In this paper we provide explicit formulas for the covariances of second-third-, and fourth-order sample cumulants as used in narrowband array processing. These covariances provide a basis for analysing the performance of cumulant based algorithms for finite-sample length, which is in contrast to usual asymptotic performance analyses. The use of these formulas, which consist of several thousand terms, will be demonstrated, and a rough idea of their applicability to a performance analysis for finite numbers of samples will be given.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123392328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613532
A. Gershman, J. Bohme
A recently reported estimator bank approach (see IEEE SP Lett., vol.4, p.54, 1997) is extended below to the fourth-order direction finding algorithms. The essence of our approach is to exploit "parallel" underlying eigenstructure based estimators for removing the outliers and improving the direction finding performance in the threshold domain. The pseudorandomly generated weighted fourth-order MUSIC estimators are exploited as underlying techniques for estimator bank. Motivated by the superior performance and reduced computational complexity of beamspace and root modifications of the second-order eigenstructure techniques, beamspace root implementations of fourth-order MUSIC and fourth-order estimator bank are developed. Simulations show dramatical improvements of the threshold performance.
{"title":"Improving the threshold performance of higher-order direction finding methods via pseudorandomly generated estimator banks","authors":"A. Gershman, J. Bohme","doi":"10.1109/HOST.1997.613532","DOIUrl":"https://doi.org/10.1109/HOST.1997.613532","url":null,"abstract":"A recently reported estimator bank approach (see IEEE SP Lett., vol.4, p.54, 1997) is extended below to the fourth-order direction finding algorithms. The essence of our approach is to exploit \"parallel\" underlying eigenstructure based estimators for removing the outliers and improving the direction finding performance in the threshold domain. The pseudorandomly generated weighted fourth-order MUSIC estimators are exploited as underlying techniques for estimator bank. Motivated by the superior performance and reduced computational complexity of beamspace and root modifications of the second-order eigenstructure techniques, beamspace root implementations of fourth-order MUSIC and fourth-order estimator bank are developed. Simulations show dramatical improvements of the threshold performance.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124010020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613518
A. Yamani, K. F. U. P. M. Box, Dhahran, S. Arabia, M. Bettayeb, L. Ghouti
Pulse-echo reflection techniques are used for ultrasonic flaw detection in most commercial instruments. As the measured pulse echo signal is assumed to be the result of linearly convolving the defect impulse response (IR) with the measurement system response the objective is thus, to remove the effect of the measurement system through a deconvolution operation and extract the defect impulse response. The major drawback of conventional second-order statistics (SOS)-based deconvolution techniques are their inability to identify non-minimum phase systems, and their sensitivity to additive Gaussian noise. Our contribution is to show that higher-order statistics (HOS)-based deconvolution techniques are more suitable to unravel the effects of the measurement systems and the additive Gaussian noise. Synthetic as well as real ultrasonic signals are used to support this claim.
{"title":"Higher-order statistics-based deconvolution of ultrasonic nondestructive testing signals","authors":"A. Yamani, K. F. U. P. M. Box, Dhahran, S. Arabia, M. Bettayeb, L. Ghouti","doi":"10.1109/HOST.1997.613518","DOIUrl":"https://doi.org/10.1109/HOST.1997.613518","url":null,"abstract":"Pulse-echo reflection techniques are used for ultrasonic flaw detection in most commercial instruments. As the measured pulse echo signal is assumed to be the result of linearly convolving the defect impulse response (IR) with the measurement system response the objective is thus, to remove the effect of the measurement system through a deconvolution operation and extract the defect impulse response. The major drawback of conventional second-order statistics (SOS)-based deconvolution techniques are their inability to identify non-minimum phase systems, and their sensitivity to additive Gaussian noise. Our contribution is to show that higher-order statistics (HOS)-based deconvolution techniques are more suitable to unravel the effects of the measurement systems and the additive Gaussian noise. Synthetic as well as real ultrasonic signals are used to support this claim.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115317599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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