Estimation of multi-frequency signal parameters by frequency domain non-linear least squares

Zhu, Limin; Li, Han-Xiong; Ding, Han

doi:10.1016/j.ymssp.2004.08.002

Cited by 21 publications

(6 citation statements)

References 29 publications

(45 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The variances of the estimators J Â and J φˆ are given by [14], [15]: [4], [6]. Thus, (14) and (15) show that the statistical efficiency of the FLLS algorithm (i.e. the ratios between the CRLB and the related estimator variance) is equal to ) ) ( /( 1…”

Section: B the Flls Algorithmmentioning

confidence: 99%

“…In such situations the windowed 4PSF algorithm can be hardly applied due to its high processing burden. Thus, the application of the least-squares approach to frequency-domain data has been proposed in the scientific literature [13], [14]. Similarly to the timedomain approach, two different procedures have been defined: the so called Frequency-domain Linear Least-Squares (FLLS) algorithm [13] if the sine-wave frequency is known a-priori, and the Frequencydomain Nonlinear Least-Squares (FNLS) algorithm [14], when the sine-wave frequency must be estimated.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Amplitude and Phase Estimation of Real-Valued Sine Wave via Frequency-Domain Linear Least-Squares Algorithms

Belega

Petri

Dallet

2018

IEEE Trans. Instrum. Meas.

View full text Add to dashboard Cite

This paper investigates the real-valued sine-wave amplitude and phase estimates returned by two Frequency-domain Linear Least-Squares (FLLS) algorithms. Both algorithms are based on Discrete Time Fourier Transform (DTFT) samples evaluated at the sine-wave frequency in order to maximize the immunity to wideband noise. One of the analyzed procedures, called FLLS algorithm, is affected by the contribution of the spectral image component on the estimated parameters. The other one, called enhanced-FLLS (e-FLLS) algorithm, compensates this detrimental contribution which is particularly significant when a small number of sine-wave cycles is observed. The image component interference compensation is obtained at the cost of a lightly higher computational effort and noise immunity. Closed form relationships for both the analyzed estimators and their variances are provided. Analytical expressions for the estimators which avoid matrix operations are also derived under conditions of practical interest. Finally, the accuracies of the analyzed algorithms are compared with a state-of-the-art estimator based on the classical three-parameter sine-fit algorithm, through both theoretical and simulation results. Index terms -Frequency-domain analysis, least-squares approach, parameter estimation, real-valued sine-wave, windowing.number of acquired sine-wave cycles ν is not too small so that the contribution of the spectral image component can be neglected, from (4) we have [15]:noticing that the matrix V J is equal to the identity matrix I (2J+1) when the rectangular window is adopted.From the definition of B, the following estimates for the sine-wave amplitude and phase are obtained:, (14) -(16) returns: 2 CR J A J J M J 2 ] var[ CR J J J SNR M J J + ≅ SNR M J J J (22) when δ is estimated a-priori. * , T J J J e 1 * , , J w J J e J e J J e J e 2 1 , 1 * , , M W V W NNPG B J e J J e J e σ − − CR J e J J e J e J J e J e 2 , 1 CR J e B J J M J CR J e J J SNR M J J A A J J J J J − − ] var[ 0 ENBW J J A A J J ] var[ 0 ENBW J J A A J J ) ( J J j J j J J k w J w J e J e J k J k k w J w

show abstract

Section: B the Flls Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Amplitude and Phase Estimation of Real-Valued Sine Wave via Frequency-Domain Linear Least-Squares Algorithms

Belega

Petri

Dallet

2018

IEEE Trans. Instrum. Meas.

View full text Add to dashboard Cite

show abstract

“…Split the resampled data record into M subrecords within T init , and calculate the DFT of each subrecord. Finally, obtain the sample mean and the sample variance of these subrecords on the unexcited lines, consistent with (8) and (10), to obtain the variance on the unexcited lines, as follows.…”

Section: B Computation Of the Sample Variance 1) Fourier Coefficientmentioning

confidence: 99%

“…• Fourier coefficient estimation, which assumes that the fundamental frequency is available to the user [6], unlike the formulation in this paper; • Estimate of amplitude and phase of periodic signals [7]; • Construction of a window for accurate estimates of the discrete Fourier transform (DFT) coefficients, without estimating the period of the signal [8], [9]; • Nonlinear LS window-based estimation of multifrequency signal parameters [10]. • LS periodic signal modeling [11], [12], based on [2].…”

Section: Introductionmentioning

confidence: 99%

Approximate ML Estimation of the Period and Spectral Content of Multiharmonic Signals Without User Interaction

Lumori

Schoukens

Lataire

2012

IEEE Trans. Instrum. Meas.

View full text Add to dashboard Cite

The goal of this paper is to construct an approximate maximum-likelihood estimator to accurately estimate the period and spectral contents of a noisy periodic signal that has many frequency components. This is accomplished without user interaction. The signal data record has a total number of periods that is not necessarily an integer but is greater than four. Furthermore, the number of samples per period may not necessarily be an integer number. It is shown that the accuracy of the estimated results is superior to estimates that are devoid of variance weighting, such as those engendered by the least squares estimator.

show abstract

“…Thus, this method can be applied when the noise is white but not for a non-white one where the threshold should be determined individually for each tested peak. When the signal of interest is a sum of sinusoids embedded in white noise, the authors of [5] studied a local least square approach in the frequency domain. Tackling a wider signal class, the authors in [6] set up an automatic selection of the significant spectral components by using two different bandwidth resolutions.…”

Section: Introductionmentioning

confidence: 99%

Automatic data-driven spectral analysis based on a multi-estimator approach

Martin

Mailhes

2018

Signal Processing

View full text Add to dashboard Cite

In signal processing, spectral analysis is widely used but, whereas computing the power spectral density (PSD) by Fourier approaches is relatively easy, its analysis and reading are much more demanding especially for spectrally rich signals. This paper presents an original method which automatically picks out and estimates the relevant spectral structures of an unknown random stationary process, embedded in an unknown non-white Gaussian noise. First, a statistical hypothesis test is applied to each local maximum value of the estimated PSD to detect the potential spectral peaks of interest. Second, an original feature space is proposed for classifying and characterizing the detected structures. Then, one key idea of the proposed strategy is to use not only one spectral estimator but to combine the results of different ones, taking benefits of their good properties. Therefore the detection and classification steps are applied to different spectral estimations. A last fusion step outputs a complete attribute vector, including a confidence index, for each detected structure. Another key idea of this data-driven approach is that all parameters are automatically set up without a priori knowledge. This approach is fully adapted to the preventive maintenance of complex systems, as illustrated in the paper.

show abstract

Estimation of multi-frequency signal parameters by frequency domain non-linear least squares

Cited by 21 publications

References 29 publications

Amplitude and Phase Estimation of Real-Valued Sine Wave via Frequency-Domain Linear Least-Squares Algorithms

Amplitude and Phase Estimation of Real-Valued Sine Wave via Frequency-Domain Linear Least-Squares Algorithms

Approximate ML Estimation of the Period and Spectral Content of Multiharmonic Signals Without User Interaction

Automatic data-driven spectral analysis based on a multi-estimator approach

Contact Info

Product

Resources

About