Optimum sensor placement for localization under log-normal shadowing

In source localization one estimates the location of a source using a variety of relative position information. Such relative position information is often provided by the received signal strength (RSS) which is in turn affected by log normal shadowing. This paper considers optimal sensor placement in two dimensions so that a source can be localized optimally from the RSS at various non-collinear sensors. We assume that the source to be localized is uniformly distributed in a circle. The goal is to optimally place sensors outside a larger concentric circle, by maximizing the smallest eigenvalue or the determinant of the expectation of an underlying Fisher Information matrix, or minimizing the trace of its inverse. We show that optimality is achieved if and only if the the expected value of the FIM is a scaled identity, and provide methods for achieving this condition.