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Exploiting Prior Information in Parametric Estimation Problems for Multi-Channel Signal Processing Applications
KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-6615-6583
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis addresses a number of problems all related to parameter estimation in sensor array processing. The unifying theme is that some of these parameters are known before the measurements are acquired. We thus study how to improve the estimation of the unknown parameters by incorporating the knowledge of the known parameters; exploiting this knowledge successfully has the potential to dramatically improve the accuracy of the estimates.

For covariance matrix estimation, we exploit that the true covariance matrix is Kronecker and Toeplitz structured. We then devise a method to ascertain that the estimates possess this structure. Additionally, we can show that our proposed estimator has better performance than the state-of-art when the number of samples is low, and that it is also efficient in the sense that the estimates have Cram\'er-Rao lower Bound (CRB) equivalent variance.

In the direction of arrival (DOA) scenario, there are different types of prior information; first, we study the case when the location of some of the emitters in the scene is known. We then turn to cases with additional prior information, i.e.~when it is known that some (or all) of the source signals are uncorrelated. As it turns out, knowledge of some DOA combined with this latter form of prior knowledge is especially beneficial, giving estimators that are dramatically more accurate than the state-of-art. We also derive the corresponding CRBs, and show that under quite mild assumptions, the estimators are efficient.

Finally, we also investigate the frequency estimation scenario, where the data is a one-dimensional temporal sequence which we model as a spatial multi-sensor response. The line-frequency estimation problem is studied when some of the frequencies are known; through experimental data we show that our approach can be beneficial. The second frequency estimation paper explores the analysis of pulse spin-locking data sequences, which are encountered in nuclear resonance experiments. By introducing a novel modeling technique for such data, we develop a method for estimating the interesting parameters of the model. The technique is significantly faster than previously available methods, and provides accurate estimation results.

Abstract [sv]

Denna doktorsavhandling behandlar parameterestimeringsproblem inom flerkanals-signalbehandling. Den gemensamma förutsättningen för dessa problem är att det finns information om de sökta parametrarna redan innan data analyseras; tanken är att på ett så finurligt sätt som möjligt använda denna kunskap för att förbättra skattningarna av de okända parametrarna.

I en uppsats studeras kovariansmatrisskattning när det är känt att den sanna kovariansmatrisen har Kronecker- och Toeplitz-struktur. Baserat på denna kunskap utvecklar vi en metod som säkerställer att även skattningarna har denna struktur, och vi kan visa att den föreslagna skattaren har bättre prestanda än existerande metoder. Vi kan också visa att skattarens varians når Cram\'er-Rao-gränsen (CRB).

Vi studerar vidare olika sorters förhandskunskap i riktningsbestämningsscenariot: först i det fall då riktningarna till ett antal av sändarna är kända. Sedan undersöker vi fallet då vi även vet något om kovariansen mellan de mottagna signalerna, nämligen att vissa (eller alla) signaler är okorrelerade. Det visar sig att just kombinationen av förkunskap om både korrelation och riktning är speciellt betydelsefull, och genom att utnyttja denna kunskap på rätt sätt kan vi skapa skattare som är mycket noggrannare än tidigare möjligt. Vi härleder även CRB för fall med denna förhandskunskap, och vi kan visa att de föreslagna skattarna är effektiva.

Slutligen behandlar vi även frekvensskattning. I detta problem är data en en-dimensionell temporal sekvens som vi modellerar som en spatiell fler-kanalssignal. Fördelen med denna modelleringsstrategi är att vi kan använda liknande metoder i estimatorerna som vid sensor-signalbehandlingsproblemen. Vi utnyttjar återigen förhandskunskap om källsignalerna: i ett av bidragen är antagandet att vissa frekvenser är kända, och vi modifierar en existerande metod för att ta hänsyn till denna kunskap. Genom att tillämpa den föreslagna metoden på experimentell data visar vi metodens användbarhet. Det andra bidraget inom detta område studerar data som erhålls från exempelvis experiment inom kärnmagnetisk resonans. Vi introducerar en ny modelleringsmetod för sådan data och utvecklar en algoritm för att skatta de önskade parametrarna i denna modell. Vår algoritm är betydligt snabbare än existerande metoder, och skattningarna är tillräckligt noggranna för typiska tillämpningar.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , xiv, 37 p.
Series
Trita-EE, ISSN 1653-5146 ; 2013:040
Keyword [en]
Array signal processing, covariance matrix, damped sinusoids, direction of arrival estimation, frequency estimation, Kronecker, NQR, NMR, parameter estimation, persymmetric, signal processing algorithms, structured covariance estimation, Toeplitz
Keyword [sv]
Array, signalbehandling, kovariansmatris, dämpad sinus, riktningbestämning, frekvensskattning, Kronecker, NQR, NMR, parameterestimering, persymmetrisk, algoritm, strukturerad kovariansmatris, Toeplitz
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:kth:diva-134034ISBN: 978-91-7501-916-1 (print)OAI: oai:DiVA.org:kth-134034DiVA: diva2:664459
Public defence
2013-12-06, Q2, Osquldas väg 10, KTH, Stockholm, 13:15 (English)
Opponent
Supervisors
Funder
EU, FP7, Seventh Framework Programme, 228044Swedish Research Council, 621-2011-5847
Note

QC 20131115

Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2013-11-15Bibliographically approved
List of papers
1. Optimal prior knowledge-based direction of arrival estimation
Open this publication in new window or tab >>Optimal prior knowledge-based direction of arrival estimation
2012 (English)In: IET Signal Processing, ISSN 1751-9675, E-ISSN 1751-9683, Vol. 6, no 8, 731-742 p.Article in journal (Refereed) Published
Abstract [en]

In certain applications involving direction of arrival (DOA) estimation the operator may have a-priori information on some of the DOAs. This information could refer to a target known to be present at a certain position or to a reflection. In this study, the authors investigate a methodology for array processing that exploits the information on the known DOAs for estimating the unknown DOAs as accurately as possible. Algorithms are presented that can efficiently handle the case of both correlated and uncorrelated sources when the receiver is a uniform linear array. The authors find a major improvement in estimator accuracy in feasible scenarios, and they compare the estimator performance to the corresponding theoretical stochastic Cramer-Rao bounds as well as to the performance of other methods capable of exploiting such prior knowledge. In addition, real data from an ultra-sound array is applied to the investigated estimators.

Place, publisher, year, edition, pages
London: Institution of Engineering and Technology, 2012
Keyword
Antenna arrays, array signal processing, direction of arrival estimation, Cramer-Rao bound
National Category
Signal Processing
Identifiers
urn:nbn:se:kth:diva-109489 (URN)10.1049/iet-spr.2011.0453 (DOI)000318231200003 ()2-s2.0-84880004678 (Scopus ID)
Funder
EU, FP7, Seventh Framework Programme, 228044ICT - The Next Generation
Note

QC 20130107

Available from: 2013-01-07 Created: 2013-01-05 Last updated: 2017-12-06Bibliographically approved
2. Prior-exploiting Direction-of-Arrival algorithms for partially uncorrelated source signals
Open this publication in new window or tab >>Prior-exploiting Direction-of-Arrival algorithms for partially uncorrelated source signals
2015 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 109, 182-192 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we investigate the performance of the recently proposed Direction-Of-Arrival (DOA) estimator POWDER (Prior Orthogonally Weighted Direction EstimatoR). The method is exploiting a specific form of prior information, namely that some DOAs are known, as well as that the correlation state between some of the source signals is known. In such scenarios, it is desirable to exploit the prior information already in the estimator design such that the knowledge can benefit the estimation of the DOAs of the unknown sources. Through an asymptotical statistical analysis, we find closed form expressions for the accuracy of the method. We also derive the relevant Cramér-Rao Bound, and we show the algorithm to be efficient under mild assumptions. The realizable performance in the finite sample-case is studied through numerical Monte-Carlo simulations, from which one can conclude that the theoretically predicted accuracies are attained for modest sample sizes and comparatively low SNR. This has the implication that the algorithm is significantly more accurate than other, state-of-art, methods, in a wide range of scenarios.

National Category
Signal Processing
Identifiers
urn:nbn:se:kth:diva-134097 (URN)10.1016/j.sigpro.2014.08.047 (DOI)000349426100016 ()2-s2.0-84918810016 (Scopus ID)
Note

Updated from submitted to published.

QC 20150325

Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2017-12-06Bibliographically approved
3. Robust Prior-Based Direction of Arrival Estimation
Open this publication in new window or tab >>Robust Prior-Based Direction of Arrival Estimation
2012 (English)In: 2012 IEEE Statistical Signal Processing Workshop, SSP 2012, IEEE conference proceedings, 2012, 81-84 p.Conference paper, Published paper (Refereed)
Abstract [en]

In certain Direction of Arrival (DOA) scenarios some of the sources are approximately known a priori. It is then desirable to be able to exploit this prior knowledge when estimating the DOAs of the unknown sources. In this paper we modify an estimator utilizing exact angular prior knowledge of some sources such that the estimator is able to exploit prior knowledge with some uncertainty. We derive the corresponding Cramer-Rao lower bound and present numerical results showing that the estimator can benefit from prior information, even when it is inaccurate.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2012
Keyword
Direction of arrival estimation, array signal processing, Bayesian estimation
National Category
Signal Processing
Identifiers
urn:nbn:se:kth:diva-103716 (URN)10.1109/SSP.2012.6319831 (DOI)000309943200021 ()2-s2.0-84868240861 (Scopus ID)978-1-4673-0183-1 (ISBN)
Conference
2012 IEEE Statistical Signal Processing Workshop, SSP 2012;Ann Arbor, MI;5 August 2012 through 8 August 2012
Funder
EU, FP7, Seventh Framework Programme, 228044ICT - The Next Generation
Note

QC 20121116

Available from: 2012-11-19 Created: 2012-10-18 Last updated: 2013-11-15Bibliographically approved
4. Subspace-based frequency estimation utilizing prior information
Open this publication in new window or tab >>Subspace-based frequency estimation utilizing prior information
2011 (English)In: 2011 IEEE Statistical Signal Processing Workshop (SSP), IEEE , 2011, 533-536 p.Conference paper, Published paper (Refereed)
Abstract [en]

In certain frequency estimation applications one or more of the underlyingfrequencies are known. For example, in rotary machines the known frequencymay be a strong network frequency masking important closely spacedfrequencies. Being able to include this information in the design of the estimator can be expected to improve the performance when estimating such closely spaced frequencies. We present a framework to include such priorinformation in a class of subspace-based estimators. Through Monte Carlo simulations and real-data applications we show the usefulness of our approach.

Place, publisher, year, edition, pages
IEEE, 2011
Keyword
Frequency estimation, Parameter estimation, Rotating machines, Failure analysis
National Category
Signal Processing Reliability and Maintenance
Identifiers
urn:nbn:se:kth:diva-45017 (URN)10.1109/SSP.2011.5967751 (DOI)000298377500134 ()2-s2.0-80052256591 (Scopus ID)978-1-4577-0569-4 (ISBN)
Conference
2011 IEEE Statistical Signal Processing Workshop (SSP)
Projects
ACCESS
Funder
EU, FP7, Seventh Framework Programme, 228044ICT - The Next Generation
Note
© 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Available from: 2011-10-26 Created: 2011-10-26 Last updated: 2013-11-15Bibliographically approved
5. An esprit-based parameter estimator for spectroscopic data
Open this publication in new window or tab >>An esprit-based parameter estimator for spectroscopic data
2012 (English)In: 2012 IEEE Statistical Signal Processing Workshop, SSP 2012, IEEE conference proceedings, 2012, 77-80 p.Conference paper, Published paper (Refereed)
Abstract [en]

The pulse spin-locking sequence is a common excitation sequence for magnetic resonance and nuclear quadrupole resonance signals, with the resulting measurement data being well modeled as a train of exponentially damped sinusoidals. In this paper, we derive an ESPRIT-based estimator for such signals, together with the corresponding Cramer-Rao lower bound. The proposed estimator is computationally efficient and only requires prior knowledge of the number of spectral lines, which is in general available in the considered applications. Numerical simulations indicate that the proposed method is close to statistically efficient, and that it offers an attractive approach for initialization of existing statistically efficient gradient or search based techniques.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2012
Keyword
Damping, Data models, Estimation, Magnetic resonance, Signal processing algorithms, Signal to noise ratio, NMR, NQR
National Category
Signal Processing
Identifiers
urn:nbn:se:kth:diva-103750 (URN)10.1109/SSP.2012.6319820 (DOI)000309943200020 ()2-s2.0-84868231140 (Scopus ID)978-146730183-1 (ISBN)
Conference
2012 IEEE Statistical Signal Processing Workshop, SSP 2012;Ann Arbor, MI;5 August 2012 through 8 August 2012
Funder
EU, European Research Council, 228044EU, European Research Council, 261670ICT - The Next Generation
Note

QC 20121030

Available from: 2012-10-30 Created: 2012-10-19 Last updated: 2013-11-15Bibliographically approved
6. On Kronecker and Linearly Structured Covariance Matrix Estimation
Open this publication in new window or tab >>On Kronecker and Linearly Structured Covariance Matrix Estimation
2014 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 6, 1536-1547 p.Article in journal (Refereed) Published
Abstract [en]

The estimation of covariance matrices is an integral part of numerous signal processing applications. In many scenarios, there exists prior knowledge on the structure of the true covariance matrix; e. g., it might be known that the matrix is Toeplitz in addition to Hermitian. Given the available data and such prior structural knowledge, estimates using the known structure can be expected to be more accurate since more data per unknown parameter is available. In this work, we study the case when a covariance matrix is known to be the Kronecker product of two factor matrices, and in addition the factor matrices are Toeplitz. We devise a two-step estimator to accurately solve this problem: the first step is a maximum likelihood (ML) based closed form estimator, which has previously been shown to give asymptotically (in the number of samples) efficient estimates when the relevant factor matrices are Hermitian or persymmetric. The second step is a re-weighting of the estimates found in the first steps, such that the final estimate satisfies the desired Toeplitz structure. We derive the asymptotic distribution of the proposed two-step estimator and conclude that the estimator is asymptotically statistically efficient, and hence asymptotically ML. Through Monte Carlo simulations, we further show that the estimator converges to the relevant Cramer-Rao lower bound for fewer samples than existing methods.

Keyword
Kronecker model, parameter estimation, signal processing algorithms, structured covariance estimation
National Category
Signal Processing
Identifiers
urn:nbn:se:kth:diva-134096 (URN)10.1109/TSP.2014.2298834 (DOI)000333025000017 ()2-s2.0-84896455737 (Scopus ID)
Funder
EU, FP7, Seventh Framework Programme, 228044Swedish Research Council, 621-2011-5847
Note

QC 20140422. Updated from manuscript to article in journal.

Available from: 2013-11-15 Created: 2013-11-15 Last updated: 2017-12-06Bibliographically approved

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