Hospitals and residential homes have a significant need for monitoring and recognising wandering-off (e.g. elopement) older people with cognitive impairments because of the serious consequences arising from wandering-off such as disappearances and serious injuries, for example, from collisions with vehicles in parking lots. Due to increasing ageing populations across the globe we can expect wandering-off to become a significant problem of scale affecting all of us. Existing technologies used to address wandering-off are inadequate for providing close supervision as they use proximity based sensing that often lead to false alarms. In this study, for the first time, we try to mitigate false alarms by identifying the traversal direction and traversal path used by people instrumented with a single low cost batteryless UHF RFID tag. Our approach uses a particle filtering (PF) based technique with Received Signal Strength Indicator (RSSI) maps obtained from scene analysis to continuously track a person wearing an RFID tag over their attire. Using real-time spatial and temporal data obtained from the PF based tracking algorithm, we develop two algorithms: i) tag traversing direction (TD) algorithm to identify the tag bearer's moving direction (e.g. moving out of a room); and ii) tag traversing path detection algorithm (TPD) to estimate the traversal path used by the tag bearer. Our extensive experiments with 14 young adult volunteers show that: i) our TD algorithm can identify the moving direction of a person with 100% accuracy; ii) our TPD algorithm reduces the false alarms to < 9%, when detecting the traversing path used while eloping; and iii) our algorithms can be implemented in a different environment without further scene analysis.