Spatial navigation patterns in indoor space usage can reveal important cues about the cognitive health of participants. In this work, we present a low-cost, scalable, open-source edge computing system using Bluetooth low energy (BLE) beacons for tracking indoor movements in a large, 1700 m2 facility used to carry out therapeutic activities for participants with mild cognitive impairment (MCI). The facility is instrumented with 39 edge computing systems, along with an on-premise fog server. The participants carry a BLE beacon, in which BLE signals are received and analyzed by the edge computing systems. Edge computing systems are sparsely distributed in the wide, complex indoor space, challenging the standard trilateration technique for localizing subjects, which assumes a dense installation of BLE beacons. We propose a graph trilateration approach that considers the temporal density of hits from the BLE beacon to surrounding edge devices to handle the inconsistent coverage of edge devices. This proposed method helps us tackle the varying signal strength, which leads to intermittent detection of beacons. The proposed method can pinpoint the positions of multiple participants with an average error of 4.4 m and over 85% accuracy in region-level localization across the entire study area. Our experimental results, evaluated in a clinical environment, suggest that an ordinary medical facility can be transformed into a smart space that enables automatic assessment of individuals’ movements, which may reflect health status or response to treatment.