  We present a novel class of proof-of-position algorithms:
Tree-Proof-of-Position (T-PoP). This algorithm is decentralised, collaborative
and can be computed in a privacy preserving manner, such that agents do not
need to reveal their position publicly. We make no assumptions of honest
behaviour in the system, and consider varying ways in which agents may
misbehave. Our algorithm is therefore resilient to highly adversarial
scenarios. This makes it suitable for a wide class of applications, namely
those in which trust in a centralised infrastructure may not be assumed, or
high security risk scenarios. Our algorithm has a worst case quadratic runtime,
making it suitable for hardware constrained IoT applications. We also provide a
mathematical model that summarises T-PoP's performance for varying operating
conditions. We then simulate T-PoP's behaviour with a large number of
agent-based simulations, which are in complete agreement with our mathematical
model, thus demonstrating its validity. T-PoP can achieve high levels of
reliability and security by tuning its operating conditions, both in high and
low density environments. Finally, we also present a mathematical model to
probabilistically detect platooning attacks.
