Activity recognizers are challenging to design for continuous, in-home settings. However, they are notoriously difficult to create when there is more than one resident in the home. Despite recent efforts, there remains a need for an algorithm that can estimate the number of residents in the house, split a time series stream into separate substreams, and accurately identify each resident's activities. To address this challenge, we introduce Gamut. This novel unsupervised method jointly estimates the number of residents and associates sensor readings with those residents, based on a multi-target Gaussian mixture probability hypothesis density filter. We hypothesize that the proposed method will offer robust recognition for homes with two or more residents. In experiments with labeled data collected from 50 single-resident and 11 multi-resident homes, we observe that Gamut outperforms previous unsupervised and supervised methods, offering a robust strategy to track behavioral routines in complex settings.