Error Propagation of Capon’s Minimum Variance Estimator
The error propagation of Capon’s minimum variance estimator resulting from measurement errors and position errors is derived within a linear approximation. It turns out, that Capon’s estimator provides the same error propagation as the conventionally used least square fit method. The shape matrix wh...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2021-06-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2021.684410/full |
| _version_ | 1818588134343966720 |
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| author | S. Toepfer Y. Narita Y. Narita D. Heyner U. Motschmann U. Motschmann |
| author_facet | S. Toepfer Y. Narita Y. Narita D. Heyner U. Motschmann U. Motschmann |
| author_sort | S. Toepfer |
| collection | DOAJ |
| description | The error propagation of Capon’s minimum variance estimator resulting from measurement errors and position errors is derived within a linear approximation. It turns out, that Capon’s estimator provides the same error propagation as the conventionally used least square fit method. The shape matrix which describes the location depence of the measurement positions is the key parameter for the error propagation, since the condition number of the shape matrix determines how the errors are amplified. Furthermore, the error resulting from a finite number of data samples is derived by regarding Capon’s estimator as a special case of the maximum likelihood estimator. |
| first_indexed | 2024-12-16T09:19:55Z |
| format | Article |
| id | doaj.art-ab382bd35d33426bbdc21fdf636dd75f |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-16T09:19:55Z |
| publishDate | 2021-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-ab382bd35d33426bbdc21fdf636dd75f2022-12-21T22:36:47ZengFrontiers Media S.A.Frontiers in Physics2296-424X2021-06-01910.3389/fphy.2021.684410684410Error Propagation of Capon’s Minimum Variance EstimatorS. Toepfer0Y. Narita1Y. Narita2D. Heyner3U. Motschmann4U. Motschmann5Institut für Theoretische Physik, Technische Universität Braunschweig, Braunschweig, GermanySpace Research Institute, Austrian Academy of Sciences, Graz, AustriaInstitut für Geophysik und Extraterrestrische Physik, Technische Universität Braunschweig, Braunschweig, GermanyInstitut für Geophysik und Extraterrestrische Physik, Technische Universität Braunschweig, Braunschweig, GermanyInstitut für Theoretische Physik, Technische Universität Braunschweig, Braunschweig, GermanyDLR Institute of Planetary Research, Berlin, GermanyThe error propagation of Capon’s minimum variance estimator resulting from measurement errors and position errors is derived within a linear approximation. It turns out, that Capon’s estimator provides the same error propagation as the conventionally used least square fit method. The shape matrix which describes the location depence of the measurement positions is the key parameter for the error propagation, since the condition number of the shape matrix determines how the errors are amplified. Furthermore, the error resulting from a finite number of data samples is derived by regarding Capon’s estimator as a special case of the maximum likelihood estimator.https://www.frontiersin.org/articles/10.3389/fphy.2021.684410/fullCapon’s methoderror propagationleast-squares methodmaximum likelihoodcondition number |
| spellingShingle | S. Toepfer Y. Narita Y. Narita D. Heyner U. Motschmann U. Motschmann Error Propagation of Capon’s Minimum Variance Estimator Frontiers in Physics Capon’s method error propagation least-squares method maximum likelihood condition number |
| title | Error Propagation of Capon’s Minimum Variance Estimator |
| title_full | Error Propagation of Capon’s Minimum Variance Estimator |
| title_fullStr | Error Propagation of Capon’s Minimum Variance Estimator |
| title_full_unstemmed | Error Propagation of Capon’s Minimum Variance Estimator |
| title_short | Error Propagation of Capon’s Minimum Variance Estimator |
| title_sort | error propagation of capon s minimum variance estimator |
| topic | Capon’s method error propagation least-squares method maximum likelihood condition number |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2021.684410/full |
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