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Asymptotic properties of Pearson's rank-variate correlation coefficient under contaminated Gaussian model.

Ma R, Xu W, Zhang Y, Ye Z - PLoS ONE (2014)

Bottom Line: As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM).To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE).Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.

View Article: PubMed Central - PubMed

Affiliation: Department of Automatic Control, School of Automation, Guangdong University of Technology, Guangzhou, Guangdong, China.

ABSTRACT
This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means of the well known Delta method. To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE). Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.

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Schematic illustration of estimating the time-delay  in Model (4).The time-shift  with respect to the maximum of the correlation function in the bottom panel is considered as an estimate of the true time-delay .
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pone-0112215-g003: Schematic illustration of estimating the time-delay in Model (4).The time-shift with respect to the maximum of the correlation function in the bottom panel is considered as an estimate of the true time-delay .

Mentions: As remarked in Section Introduction, it is often encountered in radar, sonar or communication that we need to estimate the correlation between a prescribed “clean” signal with a distorted version corrupted by impulsive noise. Now we provide an example of time-delay estimation which is similar to this situation. In this example, the prescribed clean signal is a segment of sinusoidal wavewhereas the corrupted signal is with being a white contaminated Gaussian noise following the distribution of(52)where and . The time-delay is set to be ms. Our purpose is to estimate as accurate as possible under various signal to noise ratio . As illustrated in Figure 3, the procedure of estimating includes two steps. The first one is to construct a correlation function that corresponds to by each of , and with respect to and . The second one is to locate time-shift corresponding the maximum of the correlation function. The value of is considered to be an estimate of and restored for further analysis. Note that the number of Monte Carlo trials in this study is set to be .


Asymptotic properties of Pearson's rank-variate correlation coefficient under contaminated Gaussian model.

Ma R, Xu W, Zhang Y, Ye Z - PLoS ONE (2014)

Schematic illustration of estimating the time-delay  in Model (4).The time-shift  with respect to the maximum of the correlation function in the bottom panel is considered as an estimate of the true time-delay .
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4230981&req=5

pone-0112215-g003: Schematic illustration of estimating the time-delay in Model (4).The time-shift with respect to the maximum of the correlation function in the bottom panel is considered as an estimate of the true time-delay .
Mentions: As remarked in Section Introduction, it is often encountered in radar, sonar or communication that we need to estimate the correlation between a prescribed “clean” signal with a distorted version corrupted by impulsive noise. Now we provide an example of time-delay estimation which is similar to this situation. In this example, the prescribed clean signal is a segment of sinusoidal wavewhereas the corrupted signal is with being a white contaminated Gaussian noise following the distribution of(52)where and . The time-delay is set to be ms. Our purpose is to estimate as accurate as possible under various signal to noise ratio . As illustrated in Figure 3, the procedure of estimating includes two steps. The first one is to construct a correlation function that corresponds to by each of , and with respect to and . The second one is to locate time-shift corresponding the maximum of the correlation function. The value of is considered to be an estimate of and restored for further analysis. Note that the number of Monte Carlo trials in this study is set to be .

Bottom Line: As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM).To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE).Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.

View Article: PubMed Central - PubMed

Affiliation: Department of Automatic Control, School of Automation, Guangdong University of Technology, Guangzhou, Guangdong, China.

ABSTRACT
This paper investigates the robustness properties of Pearson's rank-variate correlation coefficient (PRVCC) in scenarios where one channel is corrupted by impulsive noise and the other is impulsive noise-free. As shown in our previous work, these scenarios that frequently encountered in radar and/or sonar, can be well emulated by a particular bivariate contaminated Gaussian model (CGM). Under this CGM, we establish the asymptotic closed forms of the expectation and variance of PRVCC by means of the well known Delta method. To gain a deeper understanding, we also compare PRVCC with two other classical correlation coefficients, i.e., Spearman's rho (SR) and Kendall's tau (KT), in terms of the root mean squared error (RMSE). Monte Carlo simulations not only verify our theoretical findings, but also reveal the advantage of PRVCC by an example of estimating the time delay in the particular impulsive noise environment.

Show MeSH