Disappearances and falls are problems in the medical and nursing care of elderly people. There is also a shortage of nurses and caregivers, which increases the workload per person. A system that automatically monitors the movements of elderly people and alerts nurses and caregivers of emergencies would make it possible to solve problems safely and efficiently even with a small number of staff. In this study, we propose a system in which a small Bluetooth Low Energy (BLE) tag is continuously worn by an elderly person and BLE scanners are installed at various locations in medical and nursing care facilities to estimate their routes in real time with sufficient accuracy for practical use. To achieve this, several constraints must be overcome. First, the BLE beacon tags must be small enough to be worn. Second, since a tag must have relatively long battery life, we cannot avoid long-cycle and low-power beacon transmissions. Third, the locations where BLE scanners can be placed in a building are limited, resulting in their sparse deployment. Under these assumptions, we propose graph-based indoor localization for sparse scanner deployment (GILS) as a method that estimates indoor locations and movement paths of elderly people by incorporating the map matching technique in real time. By introducing heuristics to correct locations in real-time location tracking, we achieve a practical level of accuracy in location and movement path estimation even with sparse beacon transmission and scanner deployment.