Uncertainty analysis in cross-calibration and optimization calculation of calibration coefficients

The general cross-calibration method uses the ordinary least square method to regress the calibration coefficient by data points selected after time, spatial, observation geometrics and spectral collocation. However, the ordinary least square algorithm would reduce the validity of the regressed result because of ignoring the differences in quality between each data point. An optimized method based on the calculation of uncertainty was proposed. This uncertainty analysis method was used to quantify the uncertainty of the radiation standard value for each data point, and their weight factors were calculated. The weighted least square method was used to regress the calibration coefficient. Using HYPERION as a radiance standard, the calibration coefficients of MODIS channels 1 to 7 were each regressed using the ordinary least squares method and the weighted least squares method. The regressed coefficients were compared with the official calibration coefficient. The results show that the calibration coefficients calculated using the weighted least squares method were closer to the official coefficients of MODIS channels 1, 2, 4, 5, 6, and 7. The maximum relative error reduced to 3%~5% and the average relative error decreased to 0.5%~1.5% compared with the ordinary least squares method, which indicates that the weighted least squares method proposed in this paper can further improve the calculation accuracy of cross-calibration.