This paper describes a model-based approach to the unobtrusive monitoring of elders in their home environment to assess their health, daily activities, and cognitive function. We present a semi-Markov model representation with automated learning to characterize individual elder's mobility in the home environment. The assessed mobility can be used to characterize the elder's speed of walking and can serve as one of the predictors of future cognitive functionality and the ability of elders to live independently in their home environment.