Single tone parameter estimation from discrete-time observations

Rife, D. C.; Boorstyn, R.

doi:10.1109/tit.1974.1055282

Cited by 1,669 publications

(871 citation statements)

References 7 publications

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“…Since Larmor precession has no inertia, a magnetometer based on such precession responds instantaneously to a change in the field. Our knowledge of the new value of the frequency will be at first very uncertain, but will improve with time as T 3/2 (the best scaling for the uncertainty of a single-tone-frequency determination from a noisy signal [54]). This is discussed in the context of a practical self-oscillating magnetometer in Ref.…”

Section: Additional Characteristics Of a Magnetometermentioning

confidence: 99%

Optical magnetometry

2007

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Some of the most sensitive methods of measuring magnetic fields utilize interactions of resonant light with atomic vapor. Recent developments in this vibrant field are improving magnetometers in many traditional areas such as measurement of geomagnetic anomalies and magnetic fields in space, and are opening the door to new ones, including, dynamical measurements of bio-magnetic fields, detection of nuclear magnetic resonance (NMR), magnetic-resonance imaging (MRI), inertialrotation sensing, magnetic microscopy with cold atoms, and tests of fundamental symmetries of Nature.

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Section: Additional Characteristics Of a Magnetometermentioning

confidence: 99%

Optical magnetometry

2007

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“…More importantly, selected sparse solver is expected to be a minimum variance unbiased estimator (MVUE) of the parameters for a sparsity level so that the proposed framework achieves the Cramér-Rao lower bound in the estimation variance. OMP with dense discretization has this property at K 1 [11].…”

Section: B Sparse Solvermentioning

confidence: 89%

“…In the regular sampling, this is a well studied problem [11]. However, to best of our knowledge there is no reported study on the CRLB of the single tone frequency estimation under random sampling.…”

Section: A Base Case Of the Recursionmentioning

confidence: 99%

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A recursive way for sparse reconstruction of parametric spaces

Teke

Gürbüz

Arıkan

2014

2014 48th Asilomar Conference on Signals, Systems and Computers

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Abstract-A novel recursive framework for sparse reconstruction of continuous parameter spaces is proposed by adaptive partitioning and discretization of the parameter space together with expectation maximization type iterations. Any sparse solver or reconstruction technique can be used within the proposed recursive framework. Experimental results show that proposed technique improves the parameter estimation performance of classical sparse solvers while achieving Cramér-Rao lower bound on the tested frequency estimation problem.

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“…Since, under assumption of Gaussian noise, maximum likelihood (ML) principle [2] leads to nonlinear least squares (LS) problem, most of algorithms for computing ML estimates are iterative search routines in their nature [3][4][5]. As such, they are usually two-stage procedures, the first stage being a coarse initial estimation that provides seed values for the second stage, which iteratively approaches maximum likelihood solution.…”

Section: Introductionmentioning

confidence: 99%

Computational Aspects of Efficient Estimation of Harmonically Related Sine-Waves

2015

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Original scientific paperThis paper proposes an actual implementation of a well-known method [1] for spectral analysis of signals composed of harmonically related sine waves. The method itself requires computations which carried out directly according to the theoretical formulas do not yield computationally efficient implementation. Thus, utilizing matrix factorizations and mathematical "shortcuts", several algorithms have been developed, which perform computations efficiently and make the method suitable for large-scale applications. Implementation details are clearly explained both theoretically and from computational point of view, and the achieved improvements have been proven by extensive simulations. Particular calculations applied will be equally efficient in all similar problems, which renders the proposed routines into widely useful building blocks.Key words: signal analysis, algorithm, computation speed Analiza harmoničkog signala s gledišta računske učinkovitosti. Učlanku se opisuje nekoliko računski učinkovitih algoritama za primjenu dobro poznate i prihvaćene metode za analizu spektra signala sastavljenog od harmoničkih valova [1]. Metoda zahtijeva proračunečija provedba izravno po formulama koje opisuju teorijsku pozadinu postupka vodi u računski neučinkovite algoritme, stoga se koristeći faktorizacije matrica i neke matematičke "prečice" postupno razvijaju učinkoviti algoritmi primjenjivi i u analizama s velikim brojem uzoraka i sastavnica signala. Poboljšanja su jasno objašnjena i teorijski i s gledišta primjene, a dokazuju se opsežnim simulacijama. Posebni načini izračunavanja pojedinih matematičkih izraza primjenjivi su i u drugim sličnim problemima, što ihčini zanimljivim i važnim u raznim područjima znanosti.

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Single tone parameter estimation from discrete-time observations

Cited by 1,669 publications

References 7 publications

Optical magnetometry

Optical magnetometry

A recursive way for sparse reconstruction of parametric spaces

Computational Aspects of Efficient Estimation of Harmonically Related Sine-Waves

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