Three- and six-point estimators of sinusoidal signal characteristics

Sienkowski, S.; Krajewski, M.

doi:10.1080/21681724.2016.1209570

Cited by 2 publications

(4 citation statements)

References 10 publications

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“…Formula ( 15) was derived based on [12,27,28]. Unlike formulas known from the literature, it allows determining the expected value and variance of the estimator R[y, 0](mean squared value) taking into account the component (9) influence. The presented properties of the R[y, k] estimator were employed while evaluating the developed RC-HLA frequency estimator.…”

Section: Signal Autocorrelation Function and Its Propertiesmentioning

confidence: 99%

“…This class of signal with noise is measured in radar [1] and sonar [2] technologies, wireless communications [3], and speech signal analysis [4]. For this reason, this paper concerns the study of frequency estimators carried out for a model of a sinusoidal signal disturbed by Gaussian noise, like in [5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…The most well-known member of this group of estimators is the modified covariance (MC) [5] estimator which can be calculated based on any number of consecutive sinusoidal signal samples. A special case of the MC estimator is the aforementioned three-point estimator [5][6][7][8][9][10][11][12]. Such an estimator follows from the equation of linear signal sample prediction [17].…”

Section: Introductionmentioning

confidence: 99%

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Metrology and Measurement Systems

Sienkowski

Krajewski

2020

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This paper presents a new simple and accurate frequency estimator of a sinusoidal signal based on the signal autocorrelation function (ACF). Such an estimator was termed as the reformed covariance for half-length autocorrelation (RC-HLA). The designed estimator was compared with frequency estimators well-known from the literature, such as the modified covariance for half-length autocorrelation (MC-HLA), reformed Pisarenko harmonic decomposition for half-length autocorrelation(RPHD-HLA), modified Pisarenko harmonic decomposition for half-length autocorrelation (MPHD-HLA), zero-crossing (ZC), and iterative interpolated DFT (IpDFT-IR) estimators. We determined the samples of the ACF of a sinusoidal signal disturbed by Gaussian noise (simulations studies) and the samples of the ACF of a sinusoidal voltage(experimental studies), calculated estimators based on the obtained samples, and computed the mean squared error(MSE) to compare the estimators. The errors were juxtaposed with the Cramér-Rao lower bound (CRLB). The research results have shown that the proposed estimator is one of the most accurate, especially for SNR > 25 dB. Then the RC-HLA estimator errors are comparable to the MPHD-HLA estimator errors. However, the biggest advantage of the developed estimator is the ability to quickly and accurately determine the frequency based on samples collected from no more than five signal periods. In this case, the RC-HLA estimator is the most accurate of the estimators tested.

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Section: Signal Autocorrelation Function and Its Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Metrology and Measurement Systems

Sienkowski

Krajewski

2020

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“…The methods are the three-and four-point estimators proposed by Vizireanu [9,10]. Works concerning these methods and their modifications were also conducted by Sienkowski et al, and published in [11,12]. Works concerning related iteration methods are being carried out as well [13].…”

Section: Introductionmentioning

confidence: 99%

Metrology and Measurement Systems

Zygarlicki,

Zygarlicka,

Mroczka

2020

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The paper presents an algorithm for determining parameters of single sinusoidal components contained in the analyzed digital signal with the use of a small number of mathematical operations. The proposed algorithm can be applied, among others, in measuring devices to monitor basic parameters of electric energy quality as well as in devices used to determine the phasor in the power system. The proposed simplification of the algorithm for determining the sinusoidal components of the analyzed signal allows to use it in embedded devices with low computing power, which translates into lower cost of construction of devices of this type, while maintaining full functionality of the measuring system. The article contains a mathematical argument, which leads to the proposed algorithm, then the optimization of the number of performed mathematical operations is presented. The last part of the paper includes information about performed mathematical operations and presents exemplary times of execution of the algorithm for simple embedded devices.

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Three- and six-point estimators of sinusoidal signal characteristics

Cited by 2 publications

References 10 publications

Metrology and Measurement Systems

Metrology and Measurement Systems

Metrology and Measurement Systems

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