Abstract : Background. With the recent advent of the so-called connected objects, today largely present in our surroundings, software applications have an open door to the physical world through sensors and actuators. However, although it offers huge opportunities in many areas (e.g., smart-home, smart-cities, etc.. .), it poses a serious methodological challenge. Indeed, while classical software applications operate in the well known and delimited digital world, the so-called ambient applications operate in and through the physical world, open and subject to uncertainties that cannot be modeled accurately and entirely. These uncertainties lead the behavior of the ambient applications to potentially drift over time against requirements. In this paper, we propose a framework to estimate the behavioral drift of the ambient applications against requirements at runtime. Methodology. We rely on the Moore Finite State Machines (FSM) modeling framework to specify the ideal behavior an ambient application is supposed to meet, irrespective of the operating environment and the underlying software infrastructure. We then appeal on the control theory and propose a framework to transform the Moore FSM to its associated Continuous Density Hidden Markov Model (CD-HMM) state observer. By accounting for uncertainties through probabilities, it extends Moore FSM with viability zones, i.e. zones where the behavioral requirements of the ambient applications are acceptable. The observation of the execution of a concrete ambient application together with the statistical modeling framework underlying its associated state observer allow to compute the likelihood of an observation sequence to have been produced by the application. The likelihood then gives direct insight into the behavioral drift of the concrete application against requirements. Results. We validate our approach through a concrete use-case in the field of school lighting. The results demonstrate the soundness and efficiency of the proposed approach for estimating the behavioral drift of the ambient applications at runtime. In light of these results, one can envision using this estimation to support a decision-making algorithm (e.g., within a self-adaptive system).