A statistical error model for image sensors and its testing

2007 ◽  
Vol 38 (11) ◽  
pp. 1-11
Author(s):  
Hideyuki Ichihara ◽  
Toshimasa Kuchii ◽  
Masaaki Yamadate ◽  
Hideaki Sakaguchi ◽  
Hiroshi Uemura ◽  
...  
Keyword(s):  
Statistical Error ◽  
Image Sensors ◽  
Error Model

scholarly journals Statistical error model comparison for logistic growth of green algae (Raphidocelis subcapitata)

2017 ◽  
Vol 64 ◽  
pp. 213-222 ◽  
Author(s):  
H.T. Banks ◽  
Elizabeth Collins ◽  
Kevin Flores ◽  
Prayag Pershad ◽  
Michael Stemkovski ◽  
...  
Keyword(s):  
Green Algae ◽  
Model Comparison ◽  
Statistical Error ◽  
Error Model ◽  
Logistic Growth ◽  
Raphidocelis Subcapitata

scholarly journals Quantifying uncertainty in climatological fields from GPS radio occultation: an empirical-analytical error model

2011 ◽  
Vol 4 (3) ◽  
pp. 2749-2788 ◽  
Author(s):  
B. Scherllin-Pirscher ◽  
G. Kirchengast ◽  
A. K. Steiner ◽  
Y.-H. Kuo ◽  
U. Foelsche
Keyword(s):  
Radio Occultation ◽  
Sampling Error ◽  
Statistical Error ◽  
Error Component ◽  
Error Model ◽  
Atmospheric Parameters ◽  
Bending Angle ◽  
Analytical Error ◽  
Low Latitudes ◽  
Analytical Error Model

Abstract. Due to the measurement principle of the radio occultation (RO) technique, RO data are highly suitable for climate studies. Single RO profiles can be used to build climatological fields of different atmospheric parameters like bending angle, refractivity, density, pressure, geopotential height, and temperature. RO climatologies are affected by random (statistical) errors, sampling errors, and systematic errors, yielding a total climatological error. Based on empirical error estimates, we provide a simple analytical error model for these error components, which accounts for vertical, latitudinal, and seasonal variations. The vertical structure of each error component is modeled constant around the tropopause region. Above this region the error increases exponentially, below the increase follows an inverse height power-law. The statistical error strongly depends on the number of measurements. It is found to be the smallest error component for monthly mean 10° zonal mean climatologies with more than 600 measurements per bin. Due to smallest atmospheric variability, the sampling error is found to be smallest at low latitudes equatorwards of 40°. Beyond 40°, this error increases roughly linearly, with a stronger increase in hemispheric winter than in hemispheric summer. The sampling error model accounts for this hemispheric asymmetry. However, we recommend to subtract the sampling error when using RO climatologies for climate research since the residual sampling error remaining after such subtraction is estimated to be 50 % of the sampling error for bending angle and 30 % or less for the other atmospheric parameters. The systematic error accounts for potential residual biases in the measurements as well as in the retrieval process and generally dominates the total climatological error. Overall the total error in monthly means is estimated to be smaller than 0.07 % in refractivity and 0.15 K in temperature at low to mid latitudes, increasing towards higher latitudes. This study focuses on dry atmospheric parameters as retrieved from RO measurements so for context we also quantitatively explain the difference between dry and physical atmospheric parameters, which can be significant at low latitudes below about 10 km.

scholarly journals Quantifying uncertainty in climatological fields from GPS radio occultation: an empirical-analytical error model

2011 ◽  
Vol 4 (9) ◽  
pp. 2019-2034 ◽  
Author(s):  
B. Scherllin-Pirscher ◽  
G. Kirchengast ◽  
A. K. Steiner ◽  
Y.-H. Kuo ◽  
U. Foelsche
Keyword(s):  
Radio Occultation ◽  
Sampling Error ◽  
Total Error ◽  
Statistical Error ◽  
Error Component ◽  
Error Model ◽  
Atmospheric Parameters ◽  
Analytical Error ◽  
Low Latitudes ◽  
Analytical Error Model

Abstract. Due to the measurement principle of the radio occultation (RO) technique, RO data are highly suitable for climate studies. RO profiles can be used to build climatological fields of different atmospheric parameters like bending angle, refractivity, density, pressure, geopotential height, and temperature. RO climatologies are affected by random (statistical) errors, sampling errors, and systematic errors, yielding a total climatological error. Based on empirical error estimates, we provide a simple analytical error model for these error components, which accounts for vertical, latitudinal, and seasonal variations. The vertical structure of each error component is modeled constant around the tropopause region. Above this region the error increases exponentially, below the increase follows an inverse height power-law. The statistical error strongly depends on the number of measurements. It is found to be the smallest error component for monthly mean 10° zonal mean climatologies with more than 600 measurements per bin. Due to smallest atmospheric variability, the sampling error is found to be smallest at low latitudes equatorwards of 40°. Beyond 40°, this error increases roughly linearly, with a stronger increase in hemispheric winter than in hemispheric summer. The sampling error model accounts for this hemispheric asymmetry. However, we recommend to subtract the sampling error when using RO climatologies for climate research since the residual sampling error remaining after such subtraction is estimated to be only about 30% of the original one or less. The systematic error accounts for potential residual biases in the measurements as well as in the retrieval process and generally dominates the total climatological error. Overall the total error in monthly means is estimated to be smaller than 0.07% in refractivity and 0.15 K in temperature at low to mid latitudes, increasing towards higher latitudes. This study focuses on dry atmospheric parameters as retrieved from RO measurements so for context we also quantitatively explain the difference between dry and physical atmospheric parameters, which can be significant at altitudes below about 6 km (high latitudes) to 10 km (low latitudes).

Background subtraction in STEM energy-loss mapping

1984 ◽  
Vol 42 ◽  
pp. 568-569
Author(s):  
R.D. Leapman ◽  
K.E. Gorlen ◽  
C.R. Swyt
Keyword(s):  
Energy Loss ◽  
Signal To Noise Ratio ◽  
Statistical Error ◽  
Scanning Transmission Electron Microscope ◽  
Reference Image ◽  
Inverse Power Law ◽  
Transmission Electron ◽  
Least Squares Fit ◽  
Scanning Transmission ◽  
Single Number

The determination of elemental distributions by electron energy loss spectroscopy necessitates removal of the non-characteristic spectral background from a core-edge at each point in the image. In the scanning transmission electron microscope this is made possible by computer controlled data acquisition. Data may be processed by fitting the pre-edge counts, at two or more channels, to an inverse power law, AE-r, where A and r are parameters and E is energy loss. Processing may be performed in real-time so a single number is saved at each pixel. Detailed analysis, shows that the largest contribution to noise comes from statistical error in the least squares fit to the background. If the background shape remains constant over the entire image, the signal-to-noise ratio can be improved by fitting only one parameter. Such an assumption is generally implicit in subtraction of the “reference image” in energy selected micrographs recorded in the CTEM with a Castaing-Henry spectrometer.

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