Optimum sensor placement for source monitoring under log-normal shadowing in three dimensions

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. A related issue is to place sensors around a localized source in a manner in which they can optimally monitor it. This paper considers optimal sensor placement in three dimensions so that a source can be monitored optimally from the RSS at various non-coplanar sensors. The mathematical problem becomes one of maximizing the smallest eigenvalue or the determinant of an underlying Fisher Information matrix, or minimizing the trace of the inverse of the FIM, subject to the constraint that no sensor be closer than a specified distance from the source. We show that optimality is achieved if and only if the underlying Fisher Information Matrix is a scaled diagonal, and provide methods for achieving this condition.