Three range measurements with multiplicative noises for single source localization problem

This purpose of this paper is to locate a single localized source from three range measurements with multiplicative noises. Although some minimization approaches for additive noise have been found, studies on the existence of solutions are rare. We analyzed a situation with one or two solutions for the same multiplicative noise at three measurement sensors. A strategy for finding the best localized source when there are no solutions for the same multiplicative noise is suggested that involves adjusting the multiplicative noise ratio. The numerical simulation is conducted for three randomly generated measurement locations and their distances to the source.