High resolution spectrometers, such as the CNES/UKSA MicroCarb instrument, are widely used in remote sensing applications to retrieve atmospheric trace gas concentrations. Potential radiometric errors or errors in the approximation of the Instrument Spectral Response Function (ISRF) can induce significant errors in the determination of these gas concentrations. This paper presents a new strategy for the joint estimation of a spectrometer ISRF and the potential radiometric errors affecting the spectrometer measurements. These radiometric errors are modeled as polynomial functions of the error-free spectrum. An iterative algorithm is then proposed to estimate the coefficients of these polynomials and the spectrometer ISRFs. This algorithm alternates between ISRF estimation steps using the orthogonal matching pursuit algorithm and a radiometric error estimation step using the least squares method.