Title: Network localisation using Lagrangian optimisation

Authors: Ananya Saha; Buddhadeb Sau

Addresses: Department of Mathematics, Jadavpur University, Kolkata, 700032, India ' Department of Mathematics, Jadavpur University, Kolkata, 700032, India

Abstract: The network localisation problem with non-convex distance constraints may be modelled as a nonlinear optimisation problem. The existing localisation techniques either eliminate the nonconvex constraints or relax them into convex constraints to employ the traditional convex optimisations like semi-definite programming (SDP), least square approximation, etc. to find the node positions. We propose a method to solve the original network localisation problem with noisy distance measurements without any modification of non-convex constraints. Using the nonlinear Lagrangian technique for non-convex optimisation, we convert the localisation problem to a root finding problem involving single variable. This problem is then solved using bisection method. For computing functional values, it involves finite mini-max problem (FMX). We use sequential quadratic programming (SQP) to fix the FMX problem. Simulations studies show that, the number of iterations in the proposed method is reasonable to achieve any desired label of accuracy in node positions.

Keywords: network localisation technique; localisation with noisy distances; Lagrange optimisation in localisation; non-convex optimisation for localisation.

DOI: 10.1504/IJSNET.2019.102183

International Journal of Sensor Networks, 2019 Vol.31 No.2, pp.65 - 77

Received: 22 May 2019
Accepted: 22 May 2019

Published online: 24 Aug 2019 *

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