On the Uniqueness of Maximum Likelihood Estimation of Nuclear Sources

In an earlier paper, [1], we have considered the Maximum Likelihood (ML) localization of a stationary nuclear source using the time of arrival of particles modeled as a Poisson process. In this paper we consider whether the ML location estimate characterized in [1] is unique. In particular, we show that the question of uniqueness is equivalent to whether or not the root locus of a certain transfer function admits a single pair of nonzero imaginary axis crossing.