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Gait velocity has repeatedly been shown to be an important indicator and predictor of both cognitive and physical function, especially in elderly. However, clinical gait assessments are conducted infrequently and cannot distinguish between abrupt changes in function and changes that occur more slowly over time. Collecting gait measurements continuously in-home has recently been proposed and validated to overcome these clinical limitations. In this paper, we describe the longitudinal analysis of in-home gait velocity collected unobtrusively from passive infrared motion sensors. We first describe a model for the probability density function of the in-home gait velocities. We then describe estimation of the evolution of the density function over time and report empirically determined algorithm parameters that have performed well over a wide variety of different gait velocity data. Finally, we demonstrate how this approach allows detection of significant events (abrupt changes in function) and slower changes over time in gait velocity data collected from a sample of two elderly subjects in the Intelligent Systems for Assessing Aging Changes (ISAAC) study.