This paper presents the design and a first evaluation of a new monitoring system based on contactless sensors to estimate sleep quality. This sensor produces thermal signals which have been used, at first, to detect a human presence in the bed and then to estimate sleep quality. To distinguish between different sleep phases, we have used methods of signal processing in order to extract the necessary features for learning an adapted statistical model. The existing monitoring systems use sensors attached to the bed or worn by the person. We propose in this paper a system based on a passive thermal sensor which has the advantage of being fixed on the wall, thus it is easier to use and more reliable. We explain different signal processing steps and describe sleep stage recognition algorithms. We propose an adaptation of the SAX method for the thermal signal. Finally, we evaluate our system in comparison with a polysomnographic recording system in the Hospital (CHU) of Limoges.