Thesis: The aim of this thesis is to improve spectral unmixing algorithms in gamma ray spectrometry in order to speed up anomaly detection and the estimation of radionuclide contributions in aerosol filter samples analyzed by the French Institute of Radiation Protection and Nuclear Safety. To this end, we have developed an unmixing algorithm that performs joint analysis of several successive measurements of the same sample. This algorithm has been improved to enable online analysis while the gamma-ray spectrum measurement is measured. Various tools had to be developed at the same time as this algorithm to enable radionuclide activities to be estimated accurately, including calibration of the spectral signatures used during the unmixing process.The results of these studies are presented in the thesis both on simulated spectra and on real spectra from the laboratory's routine analyses. The detection of a contamination of ¹²³I at 2 Bq in a sample after 2 minutes of measurement illustrates the acceleration made possible by the developments made during this thesis. Indeed, this detection would not have been possible with the tools used routinely.