On the CRLB when measurements are of uncertain origin

In many estimation situations measurements are of uncertain origin. This is best exemplified by the target-tracking situation in which at each scan a number m_t of measurements are obtained, and it is not known which, if any, of these is target-originated. In several earlier papers the surprising observation was made that the Cramer-Rao lower bound (CRLB) for the estimation of a fixed parameter vector (e.g., initial position and velocity) that characterizes the target motion, for the special case multidimensional measurements in the presence of additive white Gaussian noise, is simply a multiple of that for the case with no uncertainty. That is, there is a scalar information-reduction factor. In this paper we explore this result to determine how wide the class of such problems is