Sensor array processing based on subspace fitting
Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace...
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| Vydáno v: | IEEE transactions on signal processing Ročník 39; číslo 5; s. 1110 - 1121 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
IEEE
01.05.1991
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| Témata: | |
| ISSN: | 1053-587X, 1941-0476 |
| On-line přístup: | Získat plný text |
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| Abstract | Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace-fitting-based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method. The asymptotic distribution of the estimation error is derived for a general subspace weighting, and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals.< > |
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| AbstractList | Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace-fitting-based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method. The asymptotic distribution of the estimation error is derived for a general subspace weighting, and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals. A large number of signal processing problems are concerned with estimating unknown signal parameters from sensor array measurements. This area has drawn much interest and many methods for parameter estimation based on array data have appeared in the literature. This paper presents some of these algorithms as variations of the same subspace fitting problem. The methods considered herein are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace fitting based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as ML. The asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals. A simulation study is presented, indicating that the asymptotic variance expressions are valid for a wide range of scenarios. Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace-fitting- based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method. The asymptotic distribution of the estimation error is derived for a general subspace weighting, and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals. A simulation study indicating that the asymptotic variance expressions are valid for a wide range of scenarios is presented. (I.E.) Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem. The methods considered are the deterministic maximum likelihood method (ML), ESPRIT, and a recently proposed multidimensional signal subspace method. These methods are formulated in a subspace-fitting-based framework, which provides insight into their algebraic and asymptotic relations. It is shown that by introducing a specific weighting matrix, the multidimensional signal subspace method can achieve the same asymptotic properties as the ML method. The asymptotic distribution of the estimation error is derived for a general subspace weighting, and the weighting that provides minimum variance estimates is identified. The resulting optimal technique is termed the weighted subspace fitting (WSF) method. Numerical examples indicate that the asymptotic variance of the WSF estimates coincides with the Cramer-Rao bound. The performance improvement compared to the other techniques is found to be most prominent for highly correlated signals |
| Author | Viberg, M. Ottersten, B. |
| Author_xml | – sequence: 1 givenname: M. surname: Viberg fullname: Viberg, M. organization: Dept. of Electr. Eng., Linkoping Univ., Sweden – sequence: 2 givenname: B. surname: Ottersten fullname: Ottersten, B. |
| BackLink | https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-60036$$DView record from Swedish Publication Index (Kungliga Tekniska Högskolan) https://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-95627$$DView record from Swedish Publication Index (Linköpings universitet) |
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| CODEN | ITPRED |
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| References | stout (ref30) 1974 ref13 ref34 ref12 stoica (ref11a) 1988 ref37 ref15 ref14 roy (ref19) 1987 ref11b bangs (ref2) 1971 ref39 ref17 ref38 ref16 ref18 schmidt (ref1) 1981 mardia (ref36) 1979 stoica (ref10) 1988 ref24 ref23 ref26 ref25 ref20 ljung (ref35) 1987 ref22 ref21 wilkinson (ref31) 1965 ref28 ref27 golub (ref33) 1989 ref29 ref8 ref7 ref9 ref4 ref3 ref6 stewart (ref32) 1973; 15 wax (ref5) 1985 |
| References_xml | – start-page: 2296 year: 1988 ident: ref10 article-title: MUSIC, maximum likelihood and Cram r-Rao bound publication-title: Proc ICASSP 88 Conf – ident: ref7 doi: 10.1109/29.1552 – year: 1989 ident: ref33 publication-title: Matrix Computations – year: 1985 ident: ref5 publication-title: Detection and estimation of superimposed signals – ident: ref39 doi: 10.1109/ACSSC.1988.754609 – ident: ref16 doi: 10.1109/TASSP.1986.1164815 – ident: ref18 doi: 10.1109/29.46553 – ident: ref11b doi: 10.1109/29.61541 – ident: ref26 doi: 10.1109/29.31267 – ident: ref17 doi: 10.1109/29.1557 – ident: ref14 doi: 10.1109/ICASSP.1984.1172704 – year: 1987 ident: ref19 publication-title: ESPRIT Estimation of signal parameters via rotational invariance techniques – ident: ref6 doi: 10.1109/TASSP.1986.1164949 – year: 1988 ident: ref11a publication-title: MUSIC maximum likelihood and Cram r-Rao bound Further results and comparisons – ident: ref9 doi: 10.1109/SPECT.1988.206199 – year: 1987 ident: ref35 publication-title: System Identification Theory for the User – ident: ref37 doi: 10.1109/78.80967 – ident: ref28 doi: 10.1137/0717073 – ident: ref20 doi: 10.1109/29.1618 – year: 1965 ident: ref31 publication-title: The Algebraic Eigenvalue Problem – ident: ref15 doi: 10.1049/ip-f-1.1985.0110 – volume: 15 start-page: 727 year: 1973 ident: ref32 article-title: Error and perturbation bounds for subspaces associated with certain eigenvalue problems publication-title: SIAM Rev doi: 10.1137/1015095 – ident: ref29 doi: 10.1109/29.17564 – ident: ref21 doi: 10.1109/TASSP.1986.1164935 – year: 1971 ident: ref2 publication-title: Array Processing with Generalized Beamformers – year: 1974 ident: ref30 publication-title: Almost Sure Convergence – ident: ref38 doi: 10.1109/ICASSP.1989.266917 – ident: ref13 doi: 10.1109/ICASSP.1980.1171029 – ident: ref8 doi: 10.1109/29.7543 – ident: ref4 doi: 10.1109/ICASSP.1984.1172397 – ident: ref23 doi: 10.1109/29.32276 – ident: ref22 doi: 10.1109/29.45548 – ident: ref27 doi: 10.1137/0710036 – ident: ref25 doi: 10.1109/TASSP.1985.1164557 – year: 1979 ident: ref36 publication-title: Multivariate Analysis – ident: ref3 doi: 10.1016/0165-1684(86)90075-7 – ident: ref24 doi: 10.1109/29.32277 – ident: ref12 doi: 10.1109/ACSSC.1988.754666 – ident: ref34 doi: 10.1214/aoms/1177704248 – year: 1981 ident: ref1 publication-title: A Signal Subspace Approach to Multiple Emitter Location and Spectral Estimation |
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| Snippet | Algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem.... A large number of signal processing problems are concerned with estimating unknown signal parameters from sensor array measurements. This area has drawn much... |
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| SubjectTerms | Array signal processing Automatic control Direction of arrival estimation Fitting Geophysical measurements Information technology Informationsteknik Maximum likelihood estimation Multidimensional systems Parameter estimation Processing Reglerteknik Sensor array Sensor arrays Signal processing Signal processing algorithms TECHNOLOGY TEKNIKVETENSKAP |
| Title | Sensor array processing based on subspace fitting |
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