Robust and Scalable Tracking of Radiation Sources with Cheap Binary Proximity Sensors

TL;DR

This paper introduces a scalable method for tracking moving radiation sources using inexpensive binary sensors, capable of accurately reconstructing trajectories with minimal sensors even under noisy conditions.

Contribution

The paper presents a novel, scalable approach for radiation source tracking using binary proximity sensors, including robustness analysis and trajectory reconstruction for linear and parabolic paths.

Findings

Minimum of three sensors needed for linear trajectory segments in noise-free conditions.

Up to six sensors required for parabolic trajectory segments in noise-free conditions.

Robustness of the method demonstrated through simulations with uncertainties.

Abstract

We present a new approach to tracking of radiation sources moving on smooth trajectories which can be approximated with piece-wise linear joins or piece-wise linear parabolas. We employ the use of cheap binary proximity sensors which only indicate when a radiation source enters and leaves its sensing range. We present two separate cases. The first is considering that the trajectory can be approximated with piece-wise linear joins. We develop a novel scalable approach in terms of the number of sensors required. Robustness analysis is done with respect to uncertainties in the timing recordings by the radiation sensors. We show that in the noise free case, a minimum of three sensors will suffice to recover one piece of the linear join with probability one, even in the absence of knowledge of the speed and statistics of the radiation source. Second, we tackle a more realistic approximation of trajectories of radiation sources -- piece-wise parabolic joins -- and show that no more than six sensors are required in the noise free case to track one piece of the parabola with probability one. Next we present an upper bound on the achievable error variance in the estimation of the constant speed and the angle of elevation of linear trajectories. Finally, a comprehensive set of simulations are presented to illustrate the robustness of our approach in the presence of uncertainties.