Proceedings Article | 14 September 2011
KEYWORDS: Sensors, Data modeling, Mathematical modeling, Electronics, Control systems, Attenuators, Reflectivity, Signal attenuation, Statistical modeling, Calibration
Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager Radiometer Suite
(VIIRS) assume that the sensors' radiometric response in the Reflective Solar Bands (RSB) is described by a
quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For
VIIRS Flight Unit 1 (FU1) (Butler, J., Xiong, X., Oudrari, H., Pan, C., and Gleason, J., "NASA Calibration and
Characterization in the NPOESS Preparatory Project (NPP)", IGARSS, July 12-17, 2009, Cape Town, South
Africa.), the coefficients are to be determined before launch by an attenuation method, although the linear
coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic
polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the
least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the
weight. The weight not only has a contribution from the noise of the sensor's digital count, with an important
contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the
value of the dependent variable, because both the independent and the dependent variables contain random noise. In
addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood
approach demonstrates the inadequacy of the quadratic model. We show that using the inadequate quadratic model
dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their
uncertainties, considering both measurement and model errors.
