A Problem of Detecting Stops While Tracking Moving Objects Under the Stream Processing Regime

The tracking of moving objects with the use of GPS/GNSS or other techniques is relied upon in numerous applications, from health monitoring and physical activity support, to social investigations to detection of fraud in transportation. While monitoring movement, a common subtask consists in determining the object's moving periods, and its immobility periods. In this paper, we isolate the mathematical problem of automatic detection of a stop of tracking objects under the stream processing regime (ideal data processing algorithm regime) in which one is allowed to use only a constant amount of memory, while the stream of GNSS positions of the tracked object increases in size. We propose an approximation scheme of the stop detection problem based on the fuzziness in the approximation of noise level related to the position reported by GNSS. We provide a solving algorithm that determines some upper bounds for the problem's complexity. We also provide an experimental illustration of the problem at hand.