Revisiting Trilateration Method Based on Time-of-Flight Measurements for Navigation

Abstract

This paper revisits trilateration in three-dimensional positioning. Specifically, range between a positioning target and the reference points through time-of-flight (ToF) measurements.  In a ToF, range is yielded by multiplying the time required by a wave to travel between two points and its propagation speed. Position of the target can be then estimated once the number of references are adequate, i.e. at least three for two-dimensional positioning and four for three-dimensional one. In this paper, the positioning is considered for navigation where the target moves following a trajectory whilst the ToFs take place in a certain period. The target position at the time is computed based on the ToFs through least square estimation. Through a numerical simulation, it is shown that the trilateration can track a target’s trajectory despite the decreasing performance at the end of the course.