Minimal Discrepancy Placement of Sniffers and Calibrators for Wireless Indoor Localization

Calibrators and sniffers have been used in the literature to proactively update the functional relationship between the received signal strength and the distance for wireless localization in time-varying indoor venue, where calibrators and sniffers are Wi-Fi transmitters and Wi-Fi receivers respectively. To be effective, these devices should be suitably placed in the indoor venue. Let there be N calibrators and M sniffers, d_{i, j} be the distance between calibrator i and sniffer j, and RSS_{i, j} be the received signal strength measured by sniffer j from calibrator i. The points (d_{1, 1}, RSS_{1, 1}), (d_{1, 2}, RSS_{1, 2}), ..., (d_{N, M}, RSS_{N, M}) are used to estimate the functional relationship between the received signal strength and the distance. It is desirable that d_{1, 1}, d_{1, 2}, ..., d_{N, M} are uniformly scattered so that the estimated functional relationship is more accurate for better localization. In this paper, we propose to minimize the discrepancy of d_{1, 1}, d_{1, 2}, ..., d_{N, M} in order to determine the optimal locations of the N calibrators and the M sniffers. We formulate this new problem (named minimal discrepancy placement problem) and design an efficient optimization method to solve it. We conduct simulation and real-world experiments to demonstrate that minimal discrepancy placement can effectively improve localization accuracy.