Network localisation using Lagrangian optimisation Online publication date: Mon, 09-Sep-2019
by Ananya Saha; Buddhadeb Sau
International Journal of Sensor Networks (IJSNET), Vol. 31, No. 2, 2019
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.
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