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Improved detection of particle sources with a cubic directional array using a mean test

Detection of particles from a far-field source is important in many applications, including optical communications, nuclear hazard detection, radioactivity and detection of cosmic particles. In this paper, we revisit the problem of detection of far-field particle sources using a cubical array. For the case when the source location is deterministic, assuming Poisson arrival of particles, we propose a mean test (MT) and present an asymptotic analysis for the probabilities of false-alarm and signal detection. Through extensive Monte Carlo simulations, we show that this novel and simple test outperforms the existing techniques such as the mean-difference test, generalized likelihood ratio test, the source intensity test and a linear-quadratic difference test. Next, we study the performance of MT in the case when the source location is random — in which case the other techniques cannot be employed — and highlight its utility. In all cases, we validate our analysis through Monte Carlo simulations.