In the context of radioactivity measurements, the quantitative analysis of a gamma-ray spectrum depends on the analysis algorithm. To that end, we recently introduced a Poisson statistics-based spectral unmixing approach. However, it also relies on a proper instrument recalibration as well as on an uncertainty estimation, for which no solution has been proposed so far. The goal of this article is twofold: i) we first present a novel method to correct for the instrument calibration of an HPGe detection system, which is tailored to spectral unmixing algorithms, and ii) we apply this new approach to the quantitative analysis of real data as well as on the evaluation of the uncertainty. Along with the characteristic limits determination investigated, this paper introduces the first full metrological analysis sequence of aerosol filter measurements based on spectral unmixing, which allows to quantify both the radionuclides’ activities and their associated uncertainties.