The medical remote monitoring is a today's society challenge because life expectancy is increasing in all countries and statistical forecasts announce a significant number of elderly (17% of 60-74 years in 2030) or very elderly (12% from 75 in 2030). With the progress of medicine they may be kept longer in their homes but are more fragile and therefore require technical solutions to make it easier for caregivers and increase the comfort of these people. This manuscript provides a summary of research activities conducted by the author in the field of medical remote monitoring. These research activities are structured in two themes: sound environment analysis and multimodal data fusion. The sound environment is very rich in information that can be used to detect or to predict distress, either directly or through the analysis of the activities of the person. The sound analysis is subject to the constraints of the remote audio acquisition, the presence of noise from outside and the large variability in recognizing sounds. The manuscript describes different solutions evaluated and their practical implementation in the framework of several European and national research projects. The second theme is represented by merging the output of the noise analysis with other sensors to improve the robustness of the system. Data fusion must process signals of different nature (binary or continuous), with different sample rates and different types (periodic or asynchronous). Two techniques (fuzzy logic and evidence networks) are studied, adapted and evaluated in the same research projects. This manuscript concludes with the research perspectives of the author. Six scientific papers are added in the appendix.