An Inverse Source Technique as a Preliminary Tool to Localize Persons in Indoor Spaces

This paper considers an inverse heat source localization problem with applications to indoor person localization from temperature measurements. In particular, this inverse problem consists in the reconstruction of the intensity and position of heat sources from observed temperature data. The proposed approach leverages the Green function method to model the heat distribution in three-dimensional intervals. This approach allows the formulation of the considered inverse problem through a Volterra integral equation, so numerical quadrature and Tikhonov regularization are employed in the approximation procedure. The validation of the proposed method is conducted through numerical experiments with synthetic data, where various configurations of heat sources in controlled indoor environments have been tested. Results demonstrate the method robustness and accuracy in localizing active heat sources while maintaining privacy and requiring minimal computational resources. Potential applications extend to smart living environments and noninvasive occupant detection also including safety issues.