Limits on Cooperative Positioning for a Robotic Swarm with Time of Flight Ranging over Two-Ray Ground Reflection Channel

Abstract

Autonomous robotic swarms are envisioned for a variety of applications -- from space exploration, search and rescue, to disaster management. An important capability of a robotic swarm is its ability to share information within the network, to sense spatio-temporal processes such as gas distributions, and to collaboratively enhance its navigation. In environments without infrastructure, the swarm-elements can cooperatively estimate their position, e.g. based on the time of flight of exchanged radio signals. Cooperative positioning performance depends on the radio propagation environment. Free-space path loss is commonly used for performance assessment, which is an optimistic assumption. In this work, we investigate the limits on cooperative positioning and ranging based on the time of flight of radio signals over the more realistic two-ray ground reflection channel. We show that we obtain a ranging bias caused by the radio signal component reflected from the ground, and that the ranging error becomes bias-limited. In the positioning domain, we investigate how the ranging bias affects cooperative positioning performance. As a result, we gain from cooperation, but the achievable positioning performance is significantly worsened by the ranging bias. As a conclusion, the two-ray ground reflection model should be considered, to obtain realistic cooperative positioning limits.