POPA: localising nodes by splitting PLA with n th‐hop anchor neighbours

Abstract

A novel distributed range-free localisation algorithm, named polygonal overlapped possible area (POPA), is proposed to accurately localise an unknown node. First, for an unknown node, to theoretically define its possible localisation area (PLA), virtual radiation regions of its nth-hop anchor neighbours are introduced. Then an effective area-splitting algorithm is employed to simplify and speed up the computation of the possible localisation area. Simulation shows localisation error can be controlled within 20% with off-the-shelf devices.

Why ( n + 1)th‐hop neighbours are more important than n th‐hop ones for localisation in multi‐hop WSNs

“…The simulation scenarios are as follows: (i) the whole network area is 2000 × 2000 m and (ii) either the degree of anchor nodes or the degree of unknown nodes is generally used in real applications [5].…”

“…The n th‐hop anchor neighbours of X are uniformly distributed (with distribution density g ) on the circumference of a circle (denoted as ) centred at X . 2. The virtual radiation radius [5] of each n th‐hop anchor neighbour is nR ( n > 0 is the hop count), and X is located within the intersection of the virtual radiation area of all n th‐hop anchor neighbours. 3. The radius of is given by nR – a , where a ∈ [0, R ) is the radius of the inscribed circle of the intersection area (mentioned in 2).…”

“…Differing from S used in our theoretical analysis, in this Section, the PLA, computed by all one‐hop anchor nodes, is employed to represent localisation accuracy. The simulation scenarios are as follows: (i) the whole network area is 2000 × 2000 m and (ii) either the degree of anchor nodes or the degree of unknown nodes is generally used in real applications [5].…”

“…In this Letter, for the purpose of improving localisation accuracy with the range‐free methods, we address that ( n + 1)th‐hop anchor neighbours, whose importance has been intuitively underestimated or even ignored in the past, are more useful than n th‐hop ones. By employing Lagrange piecewise linear interpolation [4] to analyse the possible localisation area (PLA) [5] of an unknown node, we find that the PLA and the hop count are negatively correlated, which indicates that ( n + 1)th‐hop anchor neighbours can provide more information to more accurately localise the unknown node. Meanwhile, the convergence of the computed PLA by increasing the hop count reasonably makes sense that increasing the hop count cannot unlimitedly help localisation.…”

“…2. The virtual radiation radius [5] of each nth-hop anchor neighbour is nR (n > 0 is the hop count), and X is located within the intersection of the virtual radiation area of all nth-hop anchor neighbours. 3.…”