Analysis of stochastic gradient tracking of time-varying polynomial Wiener systems
This paper presents analytical and Monte Carlo results for a stochastic gradient adaptive scheme that tracks a time-varying polynomial Wiener (1958) system [i.e., a linear time-invariant (LTI) filter with memory followed by a time-varying memoryless polynomial nonlinearity]. The adaptive scheme cons...
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| Veröffentlicht in: | IEEE transactions on signal processing 2000-06, Vol.48 (6), p.1676-1686 |
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| container_title | IEEE transactions on signal processing |
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| creator | Bershad, N.J. Celka, P. Vesin, J.-M. |
| description | This paper presents analytical and Monte Carlo results for a stochastic gradient adaptive scheme that tracks a time-varying polynomial Wiener (1958) system [i.e., a linear time-invariant (LTI) filter with memory followed by a time-varying memoryless polynomial nonlinearity]. The adaptive scheme consists of two phases: (1) estimation of the LTI memory using the LMS algorithm and (2) tracking the time-varying polynomial-type nonlinearity using a second coupled gradient search for the polynomial coefficients. The time-varying polynomial nonlinearity causes a time-varying scaling for the optimum Wiener filter for Phase 1. These time variations are removed for Phase 2 using a novel coupling scheme to Phase 1. The analysis for Gaussian data includes recursions for the mean behavior of the LMS algorithm for estimating and tracking the optimum Wiener filter for Phase 1 for several different time-varying polynomial nonlinearities and recursions for the mean behavior of the stochastic gradient algorithm for Phase 2. The polynomial coefficients are shown to be accurately tracked. Monte Carlo simulations confirm the theoretical predictions and support the underlying statistical assumptions. |
| doi_str_mv | 10.1109/78.845925 |
| format | Article |
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The adaptive scheme consists of two phases: (1) estimation of the LTI memory using the LMS algorithm and (2) tracking the time-varying polynomial-type nonlinearity using a second coupled gradient search for the polynomial coefficients. The time-varying polynomial nonlinearity causes a time-varying scaling for the optimum Wiener filter for Phase 1. These time variations are removed for Phase 2 using a novel coupling scheme to Phase 1. The analysis for Gaussian data includes recursions for the mean behavior of the LMS algorithm for estimating and tracking the optimum Wiener filter for Phase 1 for several different time-varying polynomial nonlinearities and recursions for the mean behavior of the stochastic gradient algorithm for Phase 2. The polynomial coefficients are shown to be accurately tracked. Monte Carlo simulations confirm the theoretical predictions and support the underlying statistical assumptions.</description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/78.845925</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Adaptive filters ; Algorithms ; Computer simulation ; Economic models ; Least squares approximation ; Monte Carlo methods ; Nonlinear filters ; Nonlinearity ; Optimization ; Phase estimation ; Polynomials ; Recursion ; Stochastic processes ; Stochastic systems ; Stochasticity ; Studies ; Time varying systems ; Tracking ; Wiener filter</subject><ispartof>IEEE transactions on signal processing, 2000-06, Vol.48 (6), p.1676-1686</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2000</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c403t-b2fdf714b38959187a0352c9c095292ec3c8bb51f914fd67e9f66ce333b26e7d3</citedby><cites>FETCH-LOGICAL-c403t-b2fdf714b38959187a0352c9c095292ec3c8bb51f914fd67e9f66ce333b26e7d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/845925$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54736</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/845925$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Bershad, N.J.</creatorcontrib><creatorcontrib>Celka, P.</creatorcontrib><creatorcontrib>Vesin, J.-M.</creatorcontrib><title>Analysis of stochastic gradient tracking of time-varying polynomial Wiener systems</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>This paper presents analytical and Monte Carlo results for a stochastic gradient adaptive scheme that tracks a time-varying polynomial Wiener (1958) system [i.e., a linear time-invariant (LTI) filter with memory followed by a time-varying memoryless polynomial nonlinearity]. The adaptive scheme consists of two phases: (1) estimation of the LTI memory using the LMS algorithm and (2) tracking the time-varying polynomial-type nonlinearity using a second coupled gradient search for the polynomial coefficients. The time-varying polynomial nonlinearity causes a time-varying scaling for the optimum Wiener filter for Phase 1. These time variations are removed for Phase 2 using a novel coupling scheme to Phase 1. The analysis for Gaussian data includes recursions for the mean behavior of the LMS algorithm for estimating and tracking the optimum Wiener filter for Phase 1 for several different time-varying polynomial nonlinearities and recursions for the mean behavior of the stochastic gradient algorithm for Phase 2. The polynomial coefficients are shown to be accurately tracked. Monte Carlo simulations confirm the theoretical predictions and support the underlying statistical assumptions.</description><subject>Adaptive filters</subject><subject>Algorithms</subject><subject>Computer simulation</subject><subject>Economic models</subject><subject>Least squares approximation</subject><subject>Monte Carlo methods</subject><subject>Nonlinear filters</subject><subject>Nonlinearity</subject><subject>Optimization</subject><subject>Phase estimation</subject><subject>Polynomials</subject><subject>Recursion</subject><subject>Stochastic processes</subject><subject>Stochastic systems</subject><subject>Stochasticity</subject><subject>Studies</subject><subject>Time varying systems</subject><subject>Tracking</subject><subject>Wiener filter</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2000</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqF0UtLxDAQAOAgCq6rB6-eigfRQ9ekSZrMcVl8wYIgit5KmqZr1j7WJCv039vSxYMHPc0M8zEDMwidEjwjBMO1kDPJOCR8D00IMBJjJtL9PsecxlyKt0N05P0aY8IYpBP0NG9U1Xnro7aMfGj1u_LB6mjlVGFNE6LglP6wzWroB1ub-Eu5bqg3bdU1bW1VFb320rjIdz6Y2h-jg1JV3pzs4hS93N48L-7j5ePdw2K-jDXDNMR5UhalICynEjgQKRSmPNGgMfAEEqOplnnOSQmElUUqDJRpqg2lNE9SIwo6RRfj3I1rP7fGh6y2XpuqUo1ptz5LJCMpZsn_UHCgkkIPL_-EJBWEMs5B9vT8F123W9ff0mdSMikB8LD4akTatd47U2YbZ-v-fhnB2fCuTMhsfFdvz0ZrjTE_btf8BrPUjzQ</recordid><startdate>20000601</startdate><enddate>20000601</enddate><creator>Bershad, N.J.</creator><creator>Celka, P.</creator><creator>Vesin, J.-M.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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The adaptive scheme consists of two phases: (1) estimation of the LTI memory using the LMS algorithm and (2) tracking the time-varying polynomial-type nonlinearity using a second coupled gradient search for the polynomial coefficients. The time-varying polynomial nonlinearity causes a time-varying scaling for the optimum Wiener filter for Phase 1. These time variations are removed for Phase 2 using a novel coupling scheme to Phase 1. The analysis for Gaussian data includes recursions for the mean behavior of the LMS algorithm for estimating and tracking the optimum Wiener filter for Phase 1 for several different time-varying polynomial nonlinearities and recursions for the mean behavior of the stochastic gradient algorithm for Phase 2. The polynomial coefficients are shown to be accurately tracked. Monte Carlo simulations confirm the theoretical predictions and support the underlying statistical assumptions.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/78.845925</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | IEEE transactions on signal processing, 2000-06, Vol.48 (6), p.1676-1686 |
| issn | 1053-587X 1941-0476 |
| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Adaptive filters Algorithms Computer simulation Economic models Least squares approximation Monte Carlo methods Nonlinear filters Nonlinearity Optimization Phase estimation Polynomials Recursion Stochastic processes Stochastic systems Stochasticity Studies Time varying systems Tracking Wiener filter |
| title | Analysis of stochastic gradient tracking of time-varying polynomial Wiener systems |
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