Abstract : The purpose of this study is to resolve an original reverse problem, i.e. the localization of a supersonic aircraft by one single measurement station. The station-to-aircraft distance is in principle unknown, but it may vary from a few tens to several hundred kilometers. The signals analyzed in the present study are generally included in the infrasound range, below 20 Hz or even 10 Hz. In the days of the first regular transatlantic flights by the Concorde, ONERA conducted a series of measures in Brittany. Their initial exploitation consisted in using the data obtained to develop an acoustic propagation code based on the ray theory. The code was amed SIMOUN and covered the three dimensions in order to be able to take account of the current weather conditions. A number of improvements were then made, including the calculation of the acoustic attenuation as a function of the frequency and taking into account the rotundity of the Earth. This was necessary because significant errors would otherwise have been made over long distances. The calculation of the acoustic level not being very meaningful at the distances mentioned above, new methods based on spectral analysis were developed. Coupled with a goniometry technique based -among others- on the calculation of time intercorrelation functions, they enable us to to localize a supersonic aircraft through bearing and distance. A first method, valid up to about 200 kilometers, is based on the divergence of the N-shaped pressure wave (corresponding to the sonic boom) according to its distance to the aircraft. This generates a modification of the arch-shaped spectrum which characterizes this wave and can be correlated with the propagation distance, provided the N wave initially emitted -specific to the speed and shape of the aircraft- is known. Another method, and much more general one, consists in evaluating the slope increase of the spectrum of the N-shaped wave, knowing that the atmospheric absorption, proportional to the distance crossed, increases with the frequency and that the disappearance of the non-linear effects also tends to increase the slope of the signal spectrum. This method seems to be valid for distances between 200 and 1000 kilometers and has the advantage of not depending on the characteristics of the sound source. In order to compensate the limitations of this method which is mainly linked up with the signal-to-noise ratio, the analysis of the signals recorded in Sweden 3000 kms away from the aircraft suggest the use -in the case of long distances- of a method based on the total duration of the signal. This duration actually increases along with the distance because of the well known “rumble” phenomenon which turns the impulse signal of a thunderbolt into a roll of thunder.