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Effect of multiplicative noise on least-squares parameter estimation with applications to the atomic force microscope
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10.1063/1.4709496
/content/aip/journal/rsi/83/5/10.1063/1.4709496
http://aip.metastore.ingenta.com/content/aip/journal/rsi/83/5/10.1063/1.4709496

Figures

Image of FIG. 1.
FIG. 1.

Histogram of the quality factor, Q, obtained from fits to synthetic data of a noisy Lorentzian; ε = 0.001, A 0 = 1, f 0 = 1, Q 0 = 100 ≫ 1, and β = 5. Similar results are obtained for all other fit parameters, and for a narrower fit range of β = 2 (not shown). Fit to Gaussian distribution (solid line).

Image of FIG. 2.
FIG. 2.

Histograms of the resonant frequencies, f R , and quality factors, Q, obtained from fits to measurements of cantilever PSD. Measured means: f 0 = 31.15 kHz, Q 0 = 43.41. Amplitude histograms affected by thermal drift (not shown). Fits to Gaussian distributions (solid lines).

Image of FIG. 3.
FIG. 3.

Averaged periodograms (N ave = 50) of the cantilever, with Lorentzian fits (solid lines), for minimum and maximum fitted quality factors: (a) Q = 36.10, and (b) Q = 53.49. Mean quality factor for the entire sample set is Q 0 = 43.41.

Tables

Generic image for table
Table I.

Comparison of relative standard deviations of simulation data (Fig. 1) and Eq. (12), for all fit parameters, for β = 5 (similar agreement found for β = 2). Variable X represents specified fit parameters and ε = 0.001 has been normalized from the results.

Generic image for table
Table II.

Comparison of relative standard deviations for resonant frequency, f R , and quality factor, Q, of cantilever measurements (Fig. 2) and Eq. (17). Variable X represents specified fit parameters.

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/content/aip/journal/rsi/83/5/10.1063/1.4709496
2012-05-16
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Effect of multiplicative noise on least-squares parameter estimation with applications to the atomic force microscope
http://aip.metastore.ingenta.com/content/aip/journal/rsi/83/5/10.1063/1.4709496
10.1063/1.4709496
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