On the Probability Distribution of Speeds derived from Positioning Data obtained by Portable Positioning Devices

Abstract

Several possible probability distributions of speeds that can be observed in everyday life are presented in this paper. Positioning systems and devices are commonly used worldwide, for example, portable positioning devices and smartphones that have a combination of positioning mechanisms. Positioning devices can obtain the user's position and the corresponding time information, which comprises one positioning tuple. From a consecutive pair of positioning tuples, we can calculate the speed between two positions using various methods. The main problem in these systems is that the position data obtained by positioning devices have errors, and it is nearly impossible for the end-user's positioning device to identify the occurrence and number of errors. Therefore, the speed values calculated from the positioning data also have errors. Before identifying erroneous speed values from calculated speeds, one or more meaningful probability distributions of speeds are required. Statistical fitting methods are employed on the positioning data set collected by volunteers and several meaningful distributions for human movement speeds are presented and discussed. For scenarios with various ranges of speed, several good fits for the probability distributions of human movement speeds are presented.