Continuous GPS tracking devices always suffer short battery life when used by caregivers to reduce the risk of wandering to dangerous areas by dementia patients. Currently the best existing tracker for dementia patients on the market only supports less than 10 hours battery life with a gigantic battery. It not only requires daily battery charging from patients/caregivers, but also becomes a very restrictive device. In this paper we inspected individual energy consumption of the components in a GPS tracker and proposed a novel energy efficient, small wristband by integrating the latest LoRa communication and GPS duty cycling technologies. We verify our prototype's communication distance and energy efficiency through extensive experiments in the real world. Our model and data show the GPS wristband is able to support up to 40 hours continuous GPS tracking with a frequent 60 seconds location update rate. Its range also spans 3km, effectively monitoring patient locations.