Temporal Sampling Constraints for GeoSpatial Path Reconstruction in a Transportation Network

Abstract

In this paper, we address the problem of recovering traveled geospatial paths on a transportation network from time sampled location traces. Determining the proper sampling rate for path reconstruction has not traditionally been addressed ahead of the collection process. Instead various uncertainty models have been created and tuned to estimate possible geospatial paths from an existing set of location measurements. This paper suggests that the geospatial road density sets a fundamental constraint on the sampling frequency. The result shows that a sufficient sampling rate is determined by the maneuver that has the minimum possible travel time, which in turn is determined by maneuver length and speed limit. This is analogous to the Nyquist-Shannon Sampling Theorem for signal processing in that the sampling rate is determined by the highest frequency with which the signal changes its value; in our result the sampling rate is determined by the highest frequency with which a probe can change its route.