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Optimal Detectors for Transient Signal Families and Nonlinear Sensors: Derivations and Applications
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Tekniska sektionen, Institutionen för teknikvetenskaper, Signaler och System.
2003 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

This thesis is concerned with detection of transient signal families and detectors in nonlinear static sensor systems. The detection problems are treated within the framework of likelihood ratio based binary hypothesis testing.

An analytical solution to the noncoherent detection problem is derived, which in contrast to the classical noncoherent detector, is optimal for wideband signals. An optimal detector for multiple transient signals with unknown arrival times is also derived and shown to yield higher detection performance compared to the classical approach based on the generalized likelihood ratio test.

An application that is treated in some detail is that of ultrasonic nondestructive testing, particularly pulse-echo detection of defects in elastic solids. The defect detection problem is cast as a composite hypothesis test and a methodology, based on physical models, for designing statistically optimal detectors for cracks in elastic solids is presented. Detectors for defects with low computational complexity are also formulated based on a simple phenomenological model of the defect echoes. The performance of these detectors are compared with the physical model-based optimal detector and is shown to yield moderate performance degradation.

Various aspects of optimal detection in static nonlinear sensor systems are also treated, in particular the stochastic resonance (SR) phenomenon which, in this context, implies noise enhanced detectability. Traditionally, SR has been quantified by means of the signal-to-noise ratio (SNR) and interpreted as an increase of a system's information processing capability. Instead of the SNR, rigorous information theoretic distance measures, which truly can support the claim of noise enhanced information processing capability, are proposed as quantifiers for SR. Optimal detectors are formulated for two static nonlinear sensor systems and shown to exhibit noise enhanced detectability.

Ort, förlag, år, upplaga, sidor
Uppsala: Acta Universitatis Upsaliensis , 2003. , s. 99
Nyckelord [en]
Signalbehandling, optimal detection, transient signals, noncoherent detection, unknown arrival time, ultrasonic nondestructive testing, nonlinear sensor, stochastic resonance
Nyckelord [sv]
Signalbehandling
Nationell ämneskategori
Signalbehandling
Forskningsämne
signalbehandling
Identifikatorer
URN: urn:nbn:se:uu:diva-3343ISBN: 91-506-1664-1 (tryckt)OAI: oai:DiVA.org:uu-3343DiVA, id: diva2:162442
Disputation
2003-04-11, K23, Magistern, Uppsala, 13:15
Opponent
Handledare
Tillgänglig från: 2003-03-17 Skapad: 2003-03-17Bibliografiskt granskad
Delarbeten
1. An analytical series expansion solution to the problem of noncoherent detection
Öppna denna publikation i ny flik eller fönster >>An analytical series expansion solution to the problem of noncoherent detection
2004 (Engelska)Ingår i: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 50, nr 12, s. 3369-3375Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

The well-known noncoherent detection problem concerns optimal detection of an amplitude-modulated sinusoid, with an unknown phase angle, corrupted by additive Gaussian noise. The classical solution to this problem is the noncoherent detector which is known to be optimal if the envelope belongs to a specific set of functions or satisfies the narrow-band approximation i.e., that the bandwidth of the envelope is narrow in comparison with the (carrier) frequency of the sinusoid. In this work, an analytical series expansion solution to the likelihood ratio for the noncoherent detection problem is derived. This solution offers a generalization of the noncoherent detector in which the conditions imposed on the envelope stated above have been relaxed. Analytical expressions for the joint probability density functions (pdfs) of the in-phase and quadrature components, jointly expressed in polar coordinates, are also derived under the signal-plus-noise and the noise-only hypotheses, respectively. Numerical simulations of the detector performance are presented in the form of receiver operating characteristics (ROC) and minimum probability of error curves. The results from a comparison of the general analytical solution with the classical noncoherent detector show significant differences between the two detectors when the narrow-band approximation does not hold.

Nationell ämneskategori
Teknik och teknologier
Identifikatorer
urn:nbn:se:uu:diva-90173 (URN)10.1109/TIT.2004.838396 (DOI)
Tillgänglig från: 2003-03-17 Skapad: 2003-03-17 Senast uppdaterad: 2017-12-14Bibliografiskt granskad
2. Detection of Multiple Transient Signals with Unknown Arrival Times
Öppna denna publikation i ny flik eller fönster >>Detection of Multiple Transient Signals with Unknown Arrival Times
2005 (Engelska)Ingår i: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 51, nr 5, s. 1856-1860Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

The problem of optimal detection of signal transients with unknown arrival times contaminated by additive Gaussian noise is considered. The transients are assumed to be time continuous and belong to a parameterized family with the uncertainty about the parameters described by means of an a priori distribution. Under the assumption of a negligible probability that the independent transient observations overlap in time, a likelihood ratio is derived for the problem of detecting an unknown number of transients from the family, each transient with unknown arrival time. The uncertainty about the arrival times is assumed to be equal for all transients and is also described by means of a distribution. Numerical simulations of the performance of detecting a particular transient signal family are presented in the form of receiver operating characteristics (ROCs) for both the optimal detector and the classical generalized likelihood ratio test (GLRT). The results show that the optimal detector yields noticeable performance improvements over the GLRT. Moreover, the results show that the optimal detector may still outperform the GLRT when the true and modeled uncertainties about arrival times no longer agree.

Nationell ämneskategori
Teknik och teknologier
Identifikatorer
urn:nbn:se:uu:diva-90174 (URN)10.1109/TIT.2005.846445 (DOI)
Tillgänglig från: 2003-03-17 Skapad: 2003-03-17 Senast uppdaterad: 2017-12-14Bibliografiskt granskad
3. Optimal Detection of Crack Echo Families in Elastic Solids
Öppna denna publikation i ny flik eller fönster >>Optimal Detection of Crack Echo Families in Elastic Solids
2003 (Engelska)Ingår i: The Journal of the Acoustical Society of America, Vol. 113, nr 5, s. 2732-2741Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

Optimal detection of a striplike crack residing in an isotropic elastic solid with coarse microstructure by means of ultrasonic nondestructive evaluation (NDE) is considered. A physics-based approach to derive an optimal detector, which achieves the theoretical limitations constrained by the underlying physics, is presented. State-of-the-art physical models of crack echoes and of stochastic backscattering from the material structure in elastic solids are introduced and unified with the theory of optimal detection to yield a practically useful nonlinear filter bank implementation of the optimal detector. Monte Carlo simulations of the detection performance for the special case of a striplike crack with uncertain angular orientation are presented in the form of receiver operating characteristics (ROCs). These new results represent the physical limitations for detecting a crack under the stated conditions and serve as performance bounds to which other detectors should be compared. A physics-based generalized likelihood ratio (GLR) detector, which relies on the same nonlinear filter bank as the optimal detector, is also presented for the special case of a striplike crack. A comparison between the optimal and the GLR detectors shows that the GLR detector only slightly reduces the performance.

Nationell ämneskategori
Teknik och teknologier
Identifikatorer
urn:nbn:se:uu:diva-90175 (URN)12765391 (PubMedID)
Tillgänglig från: 2003-03-17 Skapad: 2003-03-17 Senast uppdaterad: 2013-06-14Bibliografiskt granskad
4. Phenomenological detectors for crack echo families in elastic solids
Öppna denna publikation i ny flik eller fönster >>Phenomenological detectors for crack echo families in elastic solids
2004 (Engelska)Ingår i: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 116, nr 1, s. 379-388Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

The potential performance of low-complexity phenomenological detectors for crack echo families in elastic solids is evaluated. Ultrasonic echoes from a strip-like crack residing in an isotropic elastic solid with coarse microstructure are considered and the achieved detector performance is compared to the theoretical upper bounds (constrained only by the underlying physics) obtained by means of a recently presented physics-based optimal detector. A phenomenological signal model for the scattering process is formulated based on the time-domain impulse-response method and used to derive detectors of low numerical complexity which are dependent on a small number of parameters. The proposed detectors are compared in terms of receiver operating characteristic curves, which are computed by means of Monte Carlo simulations for the case of a strip-like crack with uncertain angular orientation. The minimum probability of error criterion is used to optimize the detector parameters for the simulation study and shown to be useful even for small training data sets. These results show that the proposed detectors have close to optimal performance in particular for the case of high signal-to-noise ratios.

Nationell ämneskategori
Teknik och teknologier
Identifikatorer
urn:nbn:se:uu:diva-90176 (URN)
Tillgänglig från: 2003-03-17 Skapad: 2003-03-17 Senast uppdaterad: 2017-12-14Bibliografiskt granskad
5. Information-Theoretic Distance Measures and a Generalization of Stochastic Resonance
Öppna denna publikation i ny flik eller fönster >>Information-Theoretic Distance Measures and a Generalization of Stochastic Resonance
1998 Ingår i: Physical Review Letters, Vol. 81, nr 14, s. 2850-2853Artikel i tidskrift (Refereegranskat) Published
Identifikatorer
urn:nbn:se:uu:diva-90177 (URN)
Tillgänglig från: 2003-03-17 Skapad: 2003-03-17Bibliografiskt granskad
6. Information-Theoretic Characterization of System Performance for a Nonlinear Magneto-Resistive Sensor
Öppna denna publikation i ny flik eller fönster >>Information-Theoretic Characterization of System Performance for a Nonlinear Magneto-Resistive Sensor
Visa övriga...
2000 Ingår i: Stochastic and Chaotic Dynamics in the Lakes, AIP Conference Proceedings 502, 2000, s. 603-608Kapitel i bok, del av antologi (Övrigt vetenskapligt) Published
Identifikatorer
urn:nbn:se:uu:diva-90178 (URN)1-56396-915-7 (ISBN)
Tillgänglig från: 2003-03-17 Skapad: 2003-03-17Bibliografiskt granskad

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