Trajectory identification with multiple users and binary proximity sensors is an important problem in design and applications of smart environment. The Current approach may quickly run into numerical difficulty when the number of users increases, besides other issues such as identifiability problem when the trajectories may cross over. An integer programming based trajectory identification approach is proposed. We show that when a state-of-the-art integer programming solver is utilized, the problem with decent sizes (measured by numbers of users and sensors) can be solved efficiently. In addition, the framework is flexible to incorporate conditions that may be encountered in practical applications: such as false data, overlapping detection regions, missing values, and existence of undetected time periods.
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