Givens rotation based least squares lattice and related algorithms
The author presents a general and systematic approach for deriving new LS (least squares) estimation algorithms that are based solely on Givens rotations. In particular, this approach is used to derive efficient Givens-rotation-based LS lattice algorithms-the Givens-lattice algorithms. By exploiting...
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| Veröffentlicht in: | IEEE transactions on signal processing 1991-07, Vol.39 (7), p.1541-1551 |
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| container_title | IEEE transactions on signal processing |
| container_volume | 39 |
| creator | Ling, F. |
| description | The author presents a general and systematic approach for deriving new LS (least squares) estimation algorithms that are based solely on Givens rotations. In particular, this approach is used to derive efficient Givens-rotation-based LS lattice algorithms-the Givens-lattice algorithms. By exploiting the relationship between the Givens algorithms and the recursive modified Gram-Schmidt algorithm, it is shown that the time and order update of any order-recursive LS estimation algorithm can be realized by employing only Givens rotations. Applying this general conclusion to LS estimation of time-series signals results in the Givens-lattice algorithms. Two Givens-lattice algorithms, one with square roots and the other without, are presented. It is shown that the Givens-lattice algorithms are computationally more efficient than the fast QR algorithm of Cioffi (1987). The derivation of other Givens rotation-based LS estimation algorithms and their systolic array implementations are discussed.< > |
| doi_str_mv | 10.1109/78.134393 |
| format | Article |
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In particular, this approach is used to derive efficient Givens-rotation-based LS lattice algorithms-the Givens-lattice algorithms. By exploiting the relationship between the Givens algorithms and the recursive modified Gram-Schmidt algorithm, it is shown that the time and order update of any order-recursive LS estimation algorithm can be realized by employing only Givens rotations. Applying this general conclusion to LS estimation of time-series signals results in the Givens-lattice algorithms. Two Givens-lattice algorithms, one with square roots and the other without, are presented. It is shown that the Givens-lattice algorithms are computationally more efficient than the fast QR algorithm of Cioffi (1987). The derivation of other Givens rotation-based LS estimation algorithms and their systolic array implementations are discussed.< ></description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/78.134393</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>IEEE</publisher><subject>Adaptive filters ; Estimation error ; Filtering algorithms ; Lattices ; Least squares approximation ; Least squares methods ; Numerical stability ; Recursive estimation ; Signal processing algorithms ; Systolic arrays</subject><ispartof>IEEE transactions on signal processing, 1991-07, Vol.39 (7), p.1541-1551</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c308t-95f0d2104ecba95ac0220ca1fc443188d99f5973b7a63f890ec514b00c68598b3</citedby><cites>FETCH-LOGICAL-c308t-95f0d2104ecba95ac0220ca1fc443188d99f5973b7a63f890ec514b00c68598b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/134393$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/134393$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Ling, F.</creatorcontrib><title>Givens rotation based least squares lattice and related algorithms</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>The author presents a general and systematic approach for deriving new LS (least squares) estimation algorithms that are based solely on Givens rotations. In particular, this approach is used to derive efficient Givens-rotation-based LS lattice algorithms-the Givens-lattice algorithms. By exploiting the relationship between the Givens algorithms and the recursive modified Gram-Schmidt algorithm, it is shown that the time and order update of any order-recursive LS estimation algorithm can be realized by employing only Givens rotations. Applying this general conclusion to LS estimation of time-series signals results in the Givens-lattice algorithms. Two Givens-lattice algorithms, one with square roots and the other without, are presented. It is shown that the Givens-lattice algorithms are computationally more efficient than the fast QR algorithm of Cioffi (1987). The derivation of other Givens rotation-based LS estimation algorithms and their systolic array implementations are discussed.< ></description><subject>Adaptive filters</subject><subject>Estimation error</subject><subject>Filtering algorithms</subject><subject>Lattices</subject><subject>Least squares approximation</subject><subject>Least squares methods</subject><subject>Numerical stability</subject><subject>Recursive estimation</subject><subject>Signal processing algorithms</subject><subject>Systolic arrays</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1991</creationdate><recordtype>article</recordtype><recordid>eNqF0LFLxDAUBvAgCp6ng6tTJsGh50uTNMmoh57CgYuCW0jTV4302rskJ_jfW6ng6PTe4_34ho-QcwYLxsBcK71gXHDDD8iMGcEKEKo6HHeQvJBavR6Tk5Q-AJgQppqR21X4xD7ROGSXw9DT2iVsaIcuZZp2excx0c7lHDxS1zc04niNwnVvQwz5fZNOyVHruoRnv3NOXu7vnpcPxfpp9bi8WReeg86FkS00JQOBvnZGOg9lCd6x1gvBmdaNMa00itfKVbzVBtBLJmoAX2lpdM3n5HLK3cZht8eU7SYkj13nehz2yZaagxmT_oeyLJUZO5qTqwn6OKQUsbXbGDYuflkG9qdOq7Sd6hztxWQDIv656fkNNxBvFQ</recordid><startdate>19910701</startdate><enddate>19910701</enddate><creator>Ling, F.</creator><general>IEEE</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7SC</scope><scope>JQ2</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19910701</creationdate><title>Givens rotation based least squares lattice and related algorithms</title><author>Ling, F.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c308t-95f0d2104ecba95ac0220ca1fc443188d99f5973b7a63f890ec514b00c68598b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1991</creationdate><topic>Adaptive filters</topic><topic>Estimation error</topic><topic>Filtering algorithms</topic><topic>Lattices</topic><topic>Least squares approximation</topic><topic>Least squares methods</topic><topic>Numerical stability</topic><topic>Recursive estimation</topic><topic>Signal processing algorithms</topic><topic>Systolic arrays</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ling, F.</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ling, F.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Givens rotation based least squares lattice and related algorithms</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>1991-07-01</date><risdate>1991</risdate><volume>39</volume><issue>7</issue><spage>1541</spage><epage>1551</epage><pages>1541-1551</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><abstract>The author presents a general and systematic approach for deriving new LS (least squares) estimation algorithms that are based solely on Givens rotations. In particular, this approach is used to derive efficient Givens-rotation-based LS lattice algorithms-the Givens-lattice algorithms. By exploiting the relationship between the Givens algorithms and the recursive modified Gram-Schmidt algorithm, it is shown that the time and order update of any order-recursive LS estimation algorithm can be realized by employing only Givens rotations. Applying this general conclusion to LS estimation of time-series signals results in the Givens-lattice algorithms. Two Givens-lattice algorithms, one with square roots and the other without, are presented. It is shown that the Givens-lattice algorithms are computationally more efficient than the fast QR algorithm of Cioffi (1987). The derivation of other Givens rotation-based LS estimation algorithms and their systolic array implementations are discussed.< ></abstract><pub>IEEE</pub><doi>10.1109/78.134393</doi><tpages>11</tpages></addata></record> |
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| ispartof | IEEE transactions on signal processing, 1991-07, Vol.39 (7), p.1541-1551 |
| issn | 1053-587X 1941-0476 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_25227939 |
| source | IEEE Electronic Library (IEL) |
| subjects | Adaptive filters Estimation error Filtering algorithms Lattices Least squares approximation Least squares methods Numerical stability Recursive estimation Signal processing algorithms Systolic arrays |
| title | Givens rotation based least squares lattice and related algorithms |
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