The photoelectron-excited far ultraviolet dayglow provides a means for remote sensing of N2, O, O2, and temperature in the terrestrial thermosphere. This paper describes a model based on the maximum likelihood method of nonlinear discrete inverse theory, which extracts information on the state of the thermosphere from limb scans of the dayglow. We show that concentrations between about 150 and (at least) 350 km can be retrieved to a high degree of accuracy and precision, independent of instrument absolute calibration. Also, the retrieved concentrations are not strongly sensitive to errors in the photoelectron excitation cross sections. The model will allow the routine development of climatological databases on the thermosphere from satellite remote sensing missions.