Estimation of the Parameters of Sinusoidal Signals in Non-Gaussian Noise
Accurate estimation of the amplitude and frequency parameters of sinusoidal signals from noisy observations is an important problem in many signal processing applications. In this paper, the problem is investigated under the assumption of non-Gaussian noise in general and Laplace noise in particular...
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| Veröffentlicht in: | IEEE transactions on signal processing 2009-01, Vol.57 (1), p.62-72 |
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| creator | LI, Ta-Hsin SONG, Kai-Sheng |
| description | Accurate estimation of the amplitude and frequency parameters of sinusoidal signals from noisy observations is an important problem in many signal processing applications. In this paper, the problem is investigated under the assumption of non-Gaussian noise in general and Laplace noise in particular. It is proven mathematically that the maximum likelihood estimator derived under the condition of Laplace white noise is able to attain an asymptotic Cramer-Rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares. It is also proven that when applied to non-Laplace situations, the Laplace maximum likelihood estimator, which may also be referred to as the nonlinear least-absolute-deviations estimator, can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails. A computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function. Simulation results are provided to validate the analytical findings. |
| doi_str_mv | 10.1109/TSP.2008.2007346 |
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In this paper, the problem is investigated under the assumption of non-Gaussian noise in general and Laplace noise in particular. It is proven mathematically that the maximum likelihood estimator derived under the condition of Laplace white noise is able to attain an asymptotic Cramer-Rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares. It is also proven that when applied to non-Laplace situations, the Laplace maximum likelihood estimator, which may also be referred to as the nonlinear least-absolute-deviations estimator, can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails. A computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function. Simulation results are provided to validate the analytical findings.</description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/TSP.2008.2007346</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Amplitude estimation ; Applied sciences ; Asymptotic properties ; Computational modeling ; Detection, estimation, filtering, equalization, prediction ; Exact sciences and technology ; Frequency estimation ; harmonic retrieval ; heavy tail ; impulsive noise ; Information, signal and communications theory ; Laplace distribution ; least absolute deviation ; Least squares approximation ; Mathematical analysis ; Maximization ; Maximum likelihood estimation ; Maximum likelihood estimators ; Miscellaneous ; Noise ; Noise level ; Non-Gaussian ; Nonlinearity ; Parameter estimation ; Probability distribution ; robust ; Signal and communications theory ; Signal processing ; Signal representation. 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In this paper, the problem is investigated under the assumption of non-Gaussian noise in general and Laplace noise in particular. It is proven mathematically that the maximum likelihood estimator derived under the condition of Laplace white noise is able to attain an asymptotic Cramer-Rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares. It is also proven that when applied to non-Laplace situations, the Laplace maximum likelihood estimator, which may also be referred to as the nonlinear least-absolute-deviations estimator, can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails. A computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function. Simulation results are provided to validate the analytical findings.</description><subject>Amplitude estimation</subject><subject>Applied sciences</subject><subject>Asymptotic properties</subject><subject>Computational modeling</subject><subject>Detection, estimation, filtering, equalization, prediction</subject><subject>Exact sciences and technology</subject><subject>Frequency estimation</subject><subject>harmonic retrieval</subject><subject>heavy tail</subject><subject>impulsive noise</subject><subject>Information, signal and communications theory</subject><subject>Laplace distribution</subject><subject>least absolute deviation</subject><subject>Least squares approximation</subject><subject>Mathematical analysis</subject><subject>Maximization</subject><subject>Maximum likelihood estimation</subject><subject>Maximum likelihood estimators</subject><subject>Miscellaneous</subject><subject>Noise</subject><subject>Noise level</subject><subject>Non-Gaussian</subject><subject>Nonlinearity</subject><subject>Parameter estimation</subject><subject>Probability distribution</subject><subject>robust</subject><subject>Signal and communications theory</subject><subject>Signal processing</subject><subject>Signal representation. Spectral analysis</subject><subject>Signal, noise</subject><subject>spectral analysis</subject><subject>Telecommunications and information theory</subject><subject>White noise</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kU1LxDAQhosouK7eBS9FUE9dJ59NjiLrB4gKruAtZNuJZum2mrQH_70pu3jw4CWZyTzvDJM3y44JzAgBfbl4eZ5RADUeJeNyJ5sQzUkBvJS7KQbBCqHKt_3sIMYVAOFcy0l2N4-9X9ved23eubz_wPzZBrvGHkMcX158O8TO17ZJ4Xtrm5j7Nn_s2uLWDjF6OyY-4mG251IRj7b3NHu9mS-u74qHp9v766uHomKK9YVEJ2jNlxpspQXWDB04IZa6BoaghQWOaqmso9RVTlipRKnrZWW1krVUjE2zi03fz9B9DRh7s_axwqaxLXZDNKoUwEHwMpHn_5KMa1qCIAk8_QOuuiGMqxolCWGUEpog2EBV6GIM6MxnSB8Xvg0BMzpgkgNmdMBsHUiSs21fGyvbuGDbysdfHSVAoVTj_JMN5xHxt8ylZBoY-wFmLo3b</recordid><startdate>200901</startdate><enddate>200901</enddate><creator>LI, Ta-Hsin</creator><creator>SONG, Kai-Sheng</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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Spectral analysis</topic><topic>Signal, noise</topic><topic>spectral analysis</topic><topic>Telecommunications and information theory</topic><topic>White noise</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>LI, Ta-Hsin</creatorcontrib><creatorcontrib>SONG, Kai-Sheng</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>Pascal-Francis</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 transactions on signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>LI, Ta-Hsin</au><au>SONG, Kai-Sheng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Estimation of the Parameters of Sinusoidal Signals in Non-Gaussian Noise</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>2009-01</date><risdate>2009</risdate><volume>57</volume><issue>1</issue><spage>62</spage><epage>72</epage><pages>62-72</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><abstract>Accurate estimation of the amplitude and frequency parameters of sinusoidal signals from noisy observations is an important problem in many signal processing applications. In this paper, the problem is investigated under the assumption of non-Gaussian noise in general and Laplace noise in particular. It is proven mathematically that the maximum likelihood estimator derived under the condition of Laplace white noise is able to attain an asymptotic Cramer-Rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares. It is also proven that when applied to non-Laplace situations, the Laplace maximum likelihood estimator, which may also be referred to as the nonlinear least-absolute-deviations estimator, can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails. A computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function. Simulation results are provided to validate the analytical findings.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TSP.2008.2007346</doi><tpages>11</tpages></addata></record> |
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| subjects | Amplitude estimation Applied sciences Asymptotic properties Computational modeling Detection, estimation, filtering, equalization, prediction Exact sciences and technology Frequency estimation harmonic retrieval heavy tail impulsive noise Information, signal and communications theory Laplace distribution least absolute deviation Least squares approximation Mathematical analysis Maximization Maximum likelihood estimation Maximum likelihood estimators Miscellaneous Noise Noise level Non-Gaussian Nonlinearity Parameter estimation Probability distribution robust Signal and communications theory Signal processing Signal representation. Spectral analysis Signal, noise spectral analysis Telecommunications and information theory White noise |
| title | Estimation of the Parameters of Sinusoidal Signals in Non-Gaussian Noise |
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