A Geometric Approach to Passive Localisation

Triommatis, Theofilos; Potapov, Igor; Rees, Gareth; Ralph, Jason F.

doi:10.23919/fusion49751.2022.9841395

Cited by 1 publication

(2 citation statements)

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“…However, the occurrence in the latter is more subtle because we assume inside the polygon an object which we need to detect by the maximising probability of detection in the following scan without prior knowledge of its position. In [26], the geometric approach for passive localisation of static emitters is based on the problem of finding the maximum intersection of a polygon and a rotating FOV. For a passive sensor, a measurement is an angle with an error that points to the direction of a transmission's origin point.…”

Section: Introductionmentioning

confidence: 99%

“…In a myopic (greedy) decisionmaking strategy, a sensor moves by minimising the maximum uncertainty on its subsequent measurement, achieved by evaluating the maximal intersection of polygons that contain the emitters' position and FOVs with centres that represent sensors' available positions, see Figure 1. Experimental results in [26] were based on a heuristic to estimate the intersection. Here we provide an algorithm with proven guarantee and precision.…”

Section: Introductionmentioning

confidence: 99%

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The Maximum Cover with Rotating Field of View

Potapov,

Ralph,

Triommatis

2023

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Imagine a polygon-shaped platform $P$ and only one static spotlight outside $P$; which direction should the spotlight face to light most of $P$? This problem occurs in maximising the visibility, as well as in limiting the uncertainty in localisation problems. More formally, we define the following maximum cover problem: ''Given a convex polygon $P$ and a Field Of View (FOV) with a given centre and inner angle $\phi$; find the direction (an angle of rotation $\theta$) of the FOV such that the intersection between the FOV and $P$ has the maximum area''. In this paper, we provide the theoretical foundation for the analysis of the maximum cover with a rotating field of view. The main challenge is that the function of the area $A_{\phi}(\theta)$, with the angle of rotation $\theta$ and the fixed inner angle $\phi$, cannot be approximated directly. We found an alternative way to express it by various compositions of a function $A_{\theta}(\phi)$ (with a restricted inner angle $\phi$ and a fixed direction $\theta$). We show that $A_{\theta}(\phi)$ has an analytical solution in the special case of a two-sector intersection and later provides a constrictive solution for the original problem. Since the optimal solution is a real number, we develop an algorithm that approximates the direction of the field of view, with precision $\varepsilon$, and complexity $\mathcal{O}(n(\log{n}+(\log{\varepsilon})/\phi))$.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%