Geometric-Algebra LMS Adaptive Filter and Its Application to Rotation Estimation
This letter exploits geometric (Clifford) algebra (GA) theory to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from geometric calculus (GC), the extension of GA to handle differential and integral calculus. Th...
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| Veröffentlicht in: | IEEE signal processing letters 2016-06, Vol.23 (6), p.858-862 |
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| container_title | IEEE signal processing letters |
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| creator | Lopes, Wilder B. Al-Nuaimi, Anas Lopes, Cassio G. |
| description | This letter exploits geometric (Clifford) algebra (GA) theory to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from geometric calculus (GC), the extension of GA to handle differential and integral calculus. The novel GA least-mean-squares (GA-LMS) adaptive filter, which inherits properties from standard adaptive filters and from GA, is developed to recursively estimate a rotor (multivector), a hypercomplex quantity able to describe rotations in any dimension. The adaptive filter (AF) performance is assessed via a 3-D point-clouds registration problem, which contains a rotation estimation step. Calculating the AF computational complexity suggests that it can contribute to reduce the cost of a full-blown 3-D registration algorithm, especially when the number of points to be processed grows. Moreover, the employed GA/GC framework allows for easily applying the resulting filter to estimating rotors in higher dimensions. |
| doi_str_mv | 10.1109/LSP.2016.2558461 |
| format | Article |
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From a least-squares cost function, the gradient is calculated following results from geometric calculus (GC), the extension of GA to handle differential and integral calculus. The novel GA least-mean-squares (GA-LMS) adaptive filter, which inherits properties from standard adaptive filters and from GA, is developed to recursively estimate a rotor (multivector), a hypercomplex quantity able to describe rotations in any dimension. The adaptive filter (AF) performance is assessed via a 3-D point-clouds registration problem, which contains a rotation estimation step. Calculating the AF computational complexity suggests that it can contribute to reduce the cost of a full-blown 3-D registration algorithm, especially when the number of points to be processed grows. Moreover, the employed GA/GC framework allows for easily applying the resulting filter to estimating rotors in higher dimensions.</description><identifier>ISSN: 1070-9908</identifier><identifier>EISSN: 1558-2361</identifier><identifier>DOI: 10.1109/LSP.2016.2558461</identifier><identifier>CODEN: ISPLEM</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>3D Registration ; Adaptive Filters ; Algebra ; Algorithms ; Calculus ; Cost function ; Estimating ; Estimation ; Geometric Algebra ; Mathematical analysis ; Point Cloud Alignment ; Quaternions ; Rotors ; Three dimensional ; Three-dimensional displays</subject><ispartof>IEEE signal processing letters, 2016-06, Vol.23 (6), p.858-862</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2016</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c366t-ac9fc64ab5c70dbd30cad739c02a52e4c2cb6a6a92d624f360bf16da3d0d43d83</citedby><cites>FETCH-LOGICAL-c366t-ac9fc64ab5c70dbd30cad739c02a52e4c2cb6a6a92d624f360bf16da3d0d43d83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/7460183$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/7460183$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Lopes, Wilder B.</creatorcontrib><creatorcontrib>Al-Nuaimi, Anas</creatorcontrib><creatorcontrib>Lopes, Cassio G.</creatorcontrib><title>Geometric-Algebra LMS Adaptive Filter and Its Application to Rotation Estimation</title><title>IEEE signal processing letters</title><addtitle>LSP</addtitle><description>This letter exploits geometric (Clifford) algebra (GA) theory to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from geometric calculus (GC), the extension of GA to handle differential and integral calculus. The novel GA least-mean-squares (GA-LMS) adaptive filter, which inherits properties from standard adaptive filters and from GA, is developed to recursively estimate a rotor (multivector), a hypercomplex quantity able to describe rotations in any dimension. The adaptive filter (AF) performance is assessed via a 3-D point-clouds registration problem, which contains a rotation estimation step. Calculating the AF computational complexity suggests that it can contribute to reduce the cost of a full-blown 3-D registration algorithm, especially when the number of points to be processed grows. Moreover, the employed GA/GC framework allows for easily applying the resulting filter to estimating rotors in higher dimensions.</description><subject>3D Registration</subject><subject>Adaptive Filters</subject><subject>Algebra</subject><subject>Algorithms</subject><subject>Calculus</subject><subject>Cost function</subject><subject>Estimating</subject><subject>Estimation</subject><subject>Geometric Algebra</subject><subject>Mathematical analysis</subject><subject>Point Cloud Alignment</subject><subject>Quaternions</subject><subject>Rotors</subject><subject>Three dimensional</subject><subject>Three-dimensional displays</subject><issn>1070-9908</issn><issn>1558-2361</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkMFLwzAUh4MoOKd3wUvBi5fOl6ZN02MZ2xxUHE7PIU1SyejammSC_72ZHR48ve_w_R7v_RC6xTDDGIrHaruZJYDpLMkyllJ8hiY4UJwQis8DQw5xUQC7RFfO7QCAYZZN0Gal-7321si4bD90bUVUPW-jUonBmy8dLU3rtY1Ep6K1d1E5DK2Rwpu-i3wfvfZ-5IXzZv-L1-iiEa3TN6c5Re_Lxdv8Ka5eVut5WcWSUOpjIYtG0lTUmcxB1YqAFConhYREZIlOZSJrKqgoEkWTtCEU6gZTJYgClRLFyBQ9jHsH238etPN8b5zUbSs63R8cxwxTICnNsqDe_1N3_cF24TqOc8YIywvIgwWjJW3vnNUNH2z4yX5zDPxYMQ8V82PF_FRxiNyNEaO1_tPzlAJmhPwArUF3Gg</recordid><startdate>201606</startdate><enddate>201606</enddate><creator>Lopes, Wilder B.</creator><creator>Al-Nuaimi, Anas</creator><creator>Lopes, Cassio G.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>201606</creationdate><title>Geometric-Algebra LMS Adaptive Filter and Its Application to Rotation Estimation</title><author>Lopes, Wilder B. ; Al-Nuaimi, Anas ; Lopes, Cassio G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c366t-ac9fc64ab5c70dbd30cad739c02a52e4c2cb6a6a92d624f360bf16da3d0d43d83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>3D Registration</topic><topic>Adaptive Filters</topic><topic>Algebra</topic><topic>Algorithms</topic><topic>Calculus</topic><topic>Cost function</topic><topic>Estimating</topic><topic>Estimation</topic><topic>Geometric Algebra</topic><topic>Mathematical analysis</topic><topic>Point Cloud Alignment</topic><topic>Quaternions</topic><topic>Rotors</topic><topic>Three dimensional</topic><topic>Three-dimensional displays</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lopes, Wilder B.</creatorcontrib><creatorcontrib>Al-Nuaimi, Anas</creatorcontrib><creatorcontrib>Lopes, Cassio G.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE signal processing letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Lopes, Wilder B.</au><au>Al-Nuaimi, Anas</au><au>Lopes, Cassio G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Geometric-Algebra LMS Adaptive Filter and Its Application to Rotation Estimation</atitle><jtitle>IEEE signal processing letters</jtitle><stitle>LSP</stitle><date>2016-06</date><risdate>2016</risdate><volume>23</volume><issue>6</issue><spage>858</spage><epage>862</epage><pages>858-862</pages><issn>1070-9908</issn><eissn>1558-2361</eissn><coden>ISPLEM</coden><abstract>This letter exploits geometric (Clifford) algebra (GA) theory to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from geometric calculus (GC), the extension of GA to handle differential and integral calculus. The novel GA least-mean-squares (GA-LMS) adaptive filter, which inherits properties from standard adaptive filters and from GA, is developed to recursively estimate a rotor (multivector), a hypercomplex quantity able to describe rotations in any dimension. The adaptive filter (AF) performance is assessed via a 3-D point-clouds registration problem, which contains a rotation estimation step. Calculating the AF computational complexity suggests that it can contribute to reduce the cost of a full-blown 3-D registration algorithm, especially when the number of points to be processed grows. Moreover, the employed GA/GC framework allows for easily applying the resulting filter to estimating rotors in higher dimensions.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/LSP.2016.2558461</doi><tpages>5</tpages><oa>free_for_read</oa></addata></record> |
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| issn | 1070-9908 1558-2361 |
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| source | IEEE Electronic Library (IEL) |
| subjects | 3D Registration Adaptive Filters Algebra Algorithms Calculus Cost function Estimating Estimation Geometric Algebra Mathematical analysis Point Cloud Alignment Quaternions Rotors Three dimensional Three-dimensional displays |
| title | Geometric-Algebra LMS Adaptive Filter and Its Application to Rotation Estimation |
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