On estimating the frequency of a sinusoid in autoregressive multiplicative noise

Besson, Olivier; Castanié, F.

doi:10.1016/0165-1684(93)90051-b

Cited by 60 publications

(19 citation statements)

References 20 publications

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“…It is observed that multiplicative noise may also occur in a variety of applications (see the works of Van Trees (1971, Chapter 1), Dwyer (1991), Besson and Castanie (1993), Swami (1994), Giannakis and Zhou (1995), or Prasath (2011) and the references therein) or, in other words, the received signals may be subjected to random amplitude modulation, which can be attributed, but is not limited to, the fading of communication channels, illuminance and reflectance modeling in image processing, reflection from scintillating targets, and Doppler spreading caused by changing orientations of nonpoint targets. Several methods have been suggested to estimate the parameters of superimposed exponential signals in the presence of multiplication and additive noise, such as cyclic statistics methods (e.g., Giannakis and Zhou, 1995;Zhou and Giannakis, 1995; and higher order spectra methods (e.g., Dwyer, 1991;Besson and Castanie, 1993;Swami, 1994;Zhou and Giannakis, 1994).…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

Bian¹,

Peng²,

Xing³

et al. 2013

International Journal of Applied Mathematics and Computer Science

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This paper considers parameter estimation of superimposed exponential signals in multiplicative and additive noise which are all independent and identically distributed. A modified Newton-Raphson algorithm is used to estimate the frequencies of the considered model, which is further used to estimate other linear parameters. It is proved that the modified NewtonRaphson algorithm is robust and the corresponding estimators of frequencies attain the same convergence rate with Least Squares Estimators (LSEs) under the same noise conditions, but it outperforms LSEs in terms of the mean squared errors. Finally, the effectiveness of the algorithm is verified by some numerical experiments.

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Section: Introductionmentioning

confidence: 99%

An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

Bian¹,

Peng²,

Xing³

et al. 2013

International Journal of Applied Mathematics and Computer Science

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“…In fact, received harmonic signal may be corrupted by additive as well as multiplicative noise. * corresponding author such as parametric least-square estimate [4,5], cyclicstatistics [6], high order statistics [7]. Among them, cyclic statistic based approach is one of the most popular methods because of its stable performance and mild assumptions.…”

Section: Introductionmentioning

confidence: 99%

Group Delay Based Approach for Frequency Estimation in Complex Noises

Fu¹,

Li²,

Zhang

et al. 2007

Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Com

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A novel approach for frequency estimation of one-dimensional harmonics in multiplicative and additive noises is presented. To alleviate the resolution limitation of the traditional cumulant-based algorithms, group delay (GD) function is utilized. In this new approach, GD is applied to the 2 nd order time-varying cumulants of harmonics in complex noises, called as the 2 nd order CGD. For a given frequency estimation problem, this paper derives a simple and practical algorithm.Numerical results show that the sharp peak and high resolution property of GD preserved, which outperform some traditional methods greatly.

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“…However, to our knowledge, a few [11][12][13][14] have studied the parameter estimation of more general harmonic signals that consist of more than one component and whose amplitudes are modulated by random noises. There are many signal processing applications where both multiplicative and additive noises are encountered, such as speckle imagery [15] , fading channels [16][17][18] , underwater acoustics [19] , lidar and radar [20,21] , and other amplitude modulated signals [22] , etc. Thus, the study of the harmonic signals corrupted by multiplicative and additive noises is very useful.…”

Section: Introductionmentioning

confidence: 99%

The method of separating harmonic signals from multiplicative and additive noises

Fan

Zhang

Wei

et al. 2007

J. Electron.(China)

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This paper focuses on the extraction of a harmonic signal from multiplicative and additive noises. A method is proposed in two stages: (1) to square the original discrete time series, which includes both signals and noises, and form a new time series. By this means, the multiplicative noise is converted to additive noise; and (2) to filter out the noise by using existing noise removal schemes. With a large amount of simulation, experimental results demonstrated the efficiency and effectiveness of this newly developed method in terms of Signal-to-Noise Ratio (SNR) and other criteria. From the experiment, it is also found that: the two kinds of noises affect the SNR differently. In general, the SNR is not influenced by multiplicative Gaussian noise regardless of its variance. However, if both kinds of noise exist, the SNR decreases with the incensement of the Variance of Additive Noise to Multiplicative Noise Ratio (VAMNR). This analysis is also supported by simulation work.

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On estimating the frequency of a sinusoid in autoregressive multiplicative noise

Cited by 60 publications

References 20 publications

An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

An efficient algorithm for estimating the parameters of superimposed exponential signals in multiplicative and additive noise

Group Delay Based Approach for Frequency Estimation in Complex Noises

The method of separating harmonic signals from multiplicative and additive noises

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