The observational covariance matrix, whose diagonal square root is currently named radiometric noise, is one of the most important elements to characterize a given instrument. It determines the precision of measurements and their possible spectral inter-correlation. The characterization of this matrix is currently performed with blackbody targets of known temperature and is, therefore, an output of the calibration unit of the instrument system. We developed a methodology that can estimate the observational covariance matrix directly from calibrated Earth-scene observations. The technique can complement the usual analysis based on onboard blackbody calibration and is, therefore, a useful back up to check the overall quality of the calibration unit. The methodology was exemplified by application to three satellite Fourier transform spectrometers: IASI (Infrared Atmospheric Sounder Interferometer), CrIS (Cross-Track Infrared Sounder), and HIRAS (Hyperspectral Infrared Atmospheric Sounder). It was shown that these three instruments are working as expected based on the pre-flight and in-flight characterization of the radiometric noise. However, for all instruments, the analysis of the covariance matrix reveals extra correlation among channels, especially in the short wave spectral regions.