On the Relative and Absolute Positioning Errors in Self-Localization Systems
This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The total parameter space is shown to have a natural decomposition into relative and centroid transformation components. A linear representation of the transformation parameter space is show...
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| Veröffentlicht in: | IEEE transactions on signal processing 2008-11, Vol.56 (11), p.5668-5679 |
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| creator | Ash, J.N. Moses, R.L. |
| description | This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The total parameter space is shown to have a natural decomposition into relative and centroid transformation components. A linear representation of the transformation parameter space is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). The centroid transformation subspace-which includes representations of rotation, translation, and scaling-is characterized for a number of measurement models including distance, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and angle-difference-of-arrival (ADOA) measurements. The error decomposition may be applied to any localization algorithm in order to better understand its performance characteristics, and it may be applied to the Cramer-Rao bound (CRB) to determine performance limits in the relative and transformation domains. A geometric interpretation of the constrained CRB is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples are presented to illustrate the utility of the proposed error decomposition into relative and transformation components. |
| doi_str_mv | 10.1109/TSP.2008.927072 |
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The total parameter space is shown to have a natural decomposition into relative and centroid transformation components. A linear representation of the transformation parameter space is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). The centroid transformation subspace-which includes representations of rotation, translation, and scaling-is characterized for a number of measurement models including distance, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and angle-difference-of-arrival (ADOA) measurements. The error decomposition may be applied to any localization algorithm in order to better understand its performance characteristics, and it may be applied to the Cramer-Rao bound (CRB) to determine performance limits in the relative and transformation domains. A geometric interpretation of the constrained CRB is provided based on the principal angles between the measurement subspace and the constraint subspace. 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(IEEE) 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-1cdb32688b04a248cc0d81607a03f62347e0f8de9fdeb92a1db1e323f0c16f1a3</citedby><cites>FETCH-LOGICAL-c382t-1cdb32688b04a248cc0d81607a03f62347e0f8de9fdeb92a1db1e323f0c16f1a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4542553$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4542553$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20778865$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Ash, J.N.</creatorcontrib><creatorcontrib>Moses, R.L.</creatorcontrib><title>On the Relative and Absolute Positioning Errors in Self-Localization Systems</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>This paper considers the accuracy of sensor node location estimates from self-calibration in sensor networks. The total parameter space is shown to have a natural decomposition into relative and centroid transformation components. A linear representation of the transformation parameter space is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). The centroid transformation subspace-which includes representations of rotation, translation, and scaling-is characterized for a number of measurement models including distance, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and angle-difference-of-arrival (ADOA) measurements. The error decomposition may be applied to any localization algorithm in order to better understand its performance characteristics, and it may be applied to the Cramer-Rao bound (CRB) to determine performance limits in the relative and transformation domains. A geometric interpretation of the constrained CRB is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples are presented to illustrate the utility of the proposed error decomposition into relative and transformation components.</description><subject>Applied sciences</subject><subject>Ash</subject><subject>Constrained estimation</subject><subject>Coordinate measuring machines</subject><subject>CramÉr-Rao bound (CRB)</subject><subject>Decomposition</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Errors</subject><subject>Exact sciences and technology</subject><subject>Goniometers</subject><subject>Information, signal and communications theory</subject><subject>localization</subject><subject>Mathematical models</subject><subject>Matrix decomposition</subject><subject>Miscellaneous</subject><subject>Monitoring</subject><subject>Position (location)</subject><subject>Position measurement</subject><subject>principal angles</subject><subject>Representations</subject><subject>Rotation measurement</subject><subject>sensor networks</subject><subject>Sensor systems</subject><subject>Sensors</subject><subject>Signal and communications theory</subject><subject>Signal processing</subject><subject>Signal, noise</subject><subject>singular fisher information</subject><subject>Studies</subject><subject>Subspace constraints</subject><subject>Subspaces</subject><subject>Telecommunications and information theory</subject><subject>Time difference of arrival</subject><subject>Transformations</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kb1rHDEQxZeQQBzbdYo0IpCQZs8zklbSlsY4H3Bgk7MhndBqR4nM3sqR9gL2Xx8dZ1ykSDUD83sP5r2meYuwQoT-7GZzveIAZtVzDZq_aI6wl9iC1Opl3aETbWf0j9fNm1LuAFDKXh0166uZLb-IfafJLfEPMTeP7HwoadotxK5TiUtMc5x_ssucUy4szmxDU2jXybspPrr9mW0eykLbctK8Cm4qdPo0j5vbz5c3F1_b9dWXbxfn69YLw5cW_TgIrowZQDoujfcwGlSgHYiguJCaIJiR-jDS0HOH44AkuAjgUQV04rj5ePC9z-n3jspit7F4miY3U9oVK2QPgqOs4Kf_gqg08hoE6oq-_we9S7s81zesUYJ3HA1U6OwA-ZxKyRTsfY5blx8sgt23YGsLdt-CPbRQFR-ebF2pgYXsZh_Ls4yD1saornLvDlwkouez7CTvOiH-AkWFjvY</recordid><startdate>20081101</startdate><enddate>20081101</enddate><creator>Ash, J.N.</creator><creator>Moses, R.L.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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The total parameter space is shown to have a natural decomposition into relative and centroid transformation components. A linear representation of the transformation parameter space is shown to coincide with the nullspace of the unconstrained Fisher information matrix (FIM). The centroid transformation subspace-which includes representations of rotation, translation, and scaling-is characterized for a number of measurement models including distance, time-of-arrival (TOA), time-difference-of-arrival (TDOA), angle-of-arrival (AOA), and angle-difference-of-arrival (ADOA) measurements. The error decomposition may be applied to any localization algorithm in order to better understand its performance characteristics, and it may be applied to the Cramer-Rao bound (CRB) to determine performance limits in the relative and transformation domains. A geometric interpretation of the constrained CRB is provided based on the principal angles between the measurement subspace and the constraint subspace. Examples are presented to illustrate the utility of the proposed error decomposition into relative and transformation components.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TSP.2008.927072</doi><tpages>12</tpages></addata></record> |
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| subjects | Applied sciences Ash Constrained estimation Coordinate measuring machines CramÉr-Rao bound (CRB) Decomposition Detection, estimation, filtering, equalization, prediction Errors Exact sciences and technology Goniometers Information, signal and communications theory localization Mathematical models Matrix decomposition Miscellaneous Monitoring Position (location) Position measurement principal angles Representations Rotation measurement sensor networks Sensor systems Sensors Signal and communications theory Signal processing Signal, noise singular fisher information Studies Subspace constraints Subspaces Telecommunications and information theory Time difference of arrival Transformations |
| title | On the Relative and Absolute Positioning Errors in Self-Localization Systems |
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