A Widely Linear Complex Unscented Kalman Filter
Conventional complex valued signal processing algorithms assume rotation invariant (circular) signal distributions, and are thus suboptimal for real world processes which exhibit rotation dependent distributions (noncircular). In nonlinear sequential state space estimation, noncircularity can arise...
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| Veröffentlicht in: | IEEE signal processing letters 2011-11, Vol.18 (11), p.623-626 |
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| container_title | IEEE signal processing letters |
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| creator | Dini, D. H. Mandic, D. P. Julier, S. J. |
| description | Conventional complex valued signal processing algorithms assume rotation invariant (circular) signal distributions, and are thus suboptimal for real world processes which exhibit rotation dependent distributions (noncircular). In nonlinear sequential state space estimation, noncircularity can arise from the data, state transition model, and state and observation noises. We provide further insight by revisiting the augmented complex unscented Kalman filter (ACUKF) and illuminating its operation in such scenarios. The analysis establishes a relationship between the estimation error and the degree of second order noncircularity (improperness) in the system for the conventional complex unscented Kalman filter (CUKF), and is supported by simulations on both synthetic and real world proper and improper signals. |
| doi_str_mv | 10.1109/LSP.2011.2166259 |
| format | Article |
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The analysis establishes a relationship between the estimation error and the degree of second order noncircularity (improperness) in the system for the conventional complex unscented Kalman filter (CUKF), and is supported by simulations on both synthetic and real world proper and improper signals.</description><identifier>ISSN: 1070-9908</identifier><identifier>EISSN: 1558-2361</identifier><identifier>DOI: 10.1109/LSP.2011.2166259</identifier><identifier>CODEN: ISPLEM</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Algorithms ; Analytical models ; Augmented complex UKF ; complex circularity ; Computer simulation ; Covariance matrix ; Data models ; Error analysis ; improperness ; Invariants ; Kalman filters ; Mathematical model ; Matrices ; Noise ; Nonlinearity ; Signal processing ; unscented Kalman filter ; Vectors ; widely linear Kalman filter ; widely linear model</subject><ispartof>IEEE signal processing letters, 2011-11, Vol.18 (11), p.623-626</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Nov 2011</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c412t-6fd6aa298eef7f9b151e213721dfdacdd3636bc2846a674b8d26f205fc61e7623</citedby><cites>FETCH-LOGICAL-c412t-6fd6aa298eef7f9b151e213721dfdacdd3636bc2846a674b8d26f205fc61e7623</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6003762$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/6003762$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Dini, D. H.</creatorcontrib><creatorcontrib>Mandic, D. P.</creatorcontrib><creatorcontrib>Julier, S. J.</creatorcontrib><title>A Widely Linear Complex Unscented Kalman Filter</title><title>IEEE signal processing letters</title><addtitle>LSP</addtitle><description>Conventional complex valued signal processing algorithms assume rotation invariant (circular) signal distributions, and are thus suboptimal for real world processes which exhibit rotation dependent distributions (noncircular). In nonlinear sequential state space estimation, noncircularity can arise from the data, state transition model, and state and observation noises. We provide further insight by revisiting the augmented complex unscented Kalman filter (ACUKF) and illuminating its operation in such scenarios. The analysis establishes a relationship between the estimation error and the degree of second order noncircularity (improperness) in the system for the conventional complex unscented Kalman filter (CUKF), and is supported by simulations on both synthetic and real world proper and improper signals.</description><subject>Algorithms</subject><subject>Analytical models</subject><subject>Augmented complex UKF</subject><subject>complex circularity</subject><subject>Computer simulation</subject><subject>Covariance matrix</subject><subject>Data models</subject><subject>Error analysis</subject><subject>improperness</subject><subject>Invariants</subject><subject>Kalman filters</subject><subject>Mathematical model</subject><subject>Matrices</subject><subject>Noise</subject><subject>Nonlinearity</subject><subject>Signal processing</subject><subject>unscented Kalman filter</subject><subject>Vectors</subject><subject>widely linear Kalman filter</subject><subject>widely linear model</subject><issn>1070-9908</issn><issn>1558-2361</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkM9LAzEQhYMoWKt3wcviycu2M0k3yR5LsSouKGjxGNLNBLbsj7rZgv3vTWnx4Gnm8L3H42PsFmGCCPm0-HifcECccJSSZ_kZG2GW6ZQLiefxBwVpnoO-ZFchbABAo85GbDpPvipH9T4pqpZsnyy6ZlvTT7JqQ0ntQC55tXVj22RZ1QP11-zC2zrQzemO2Wr5-Ll4Tou3p5fFvEjLGfIhld5Ja3muibzy-RozJI5CcXTe2dI5IYVcl1zPpJVqttaOS88h86VEUpKLMXs49m777ntHYTBNFQfVtW2p2wWDgKCVzJSK6P0_dNPt-jauMzoHoaUSECE4QmXfhdCTN9u-amy_j03mINBEgeYg0JwExsjdMVIR0R8uAcRh4C9hNmnT</recordid><startdate>20111101</startdate><enddate>20111101</enddate><creator>Dini, D. 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H.</creatorcontrib><creatorcontrib>Mandic, D. P.</creatorcontrib><creatorcontrib>Julier, S. 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H.</au><au>Mandic, D. P.</au><au>Julier, S. J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Widely Linear Complex Unscented Kalman Filter</atitle><jtitle>IEEE signal processing letters</jtitle><stitle>LSP</stitle><date>2011-11-01</date><risdate>2011</risdate><volume>18</volume><issue>11</issue><spage>623</spage><epage>626</epage><pages>623-626</pages><issn>1070-9908</issn><eissn>1558-2361</eissn><coden>ISPLEM</coden><abstract>Conventional complex valued signal processing algorithms assume rotation invariant (circular) signal distributions, and are thus suboptimal for real world processes which exhibit rotation dependent distributions (noncircular). In nonlinear sequential state space estimation, noncircularity can arise from the data, state transition model, and state and observation noises. We provide further insight by revisiting the augmented complex unscented Kalman filter (ACUKF) and illuminating its operation in such scenarios. 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| subjects | Algorithms Analytical models Augmented complex UKF complex circularity Computer simulation Covariance matrix Data models Error analysis improperness Invariants Kalman filters Mathematical model Matrices Noise Nonlinearity Signal processing unscented Kalman filter Vectors widely linear Kalman filter widely linear model |
| title | A Widely Linear Complex Unscented Kalman Filter |
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