Source localization using a maximum likelihood/semidefinite programming hybrid

This paper considers source localization using Received Signal Strength (RSS) values at sensor locations, under the assumption of lognormal shadowing. It is known that such localization can be sensitive to path loss parameter estimates. We derive a cost function whose global minimum provides the ML estimate of the source localization. It turns out that this cost function is manifested with multiple local minima, leading to potentially poor gradient descent performance. The contribution of this paper are two fold. First, we show that in the noise free case the local minima are insensitive to the path loss parameter value. Traditional nonlinear stability theory suggests that this would imply an insensitivity of the ML algorithm to the value of the path loss parameter. Second, we propose a SDP based algorithm to initialize the ML minimization algorithm, that provides good performance, by avoiding local minima.