Matrix CRLB scaling due to measurements of uncertain origin

Abstract—In many estimation situations, measurements are of uncertain origin. This is best exemplified by the target-tracking situation in which at each scan (of a radar, sonar, or electro-optical sensor), a number of measurements are obtained, and it is not known which, if any, of these is target originated. The source of extraneous measurements can be false alarms—especially in low-SNR situations that force the detector at the end of the signal processing chain to operate with a reduced threshold—or spu-rious targets. In several earlier papers, the surprising observation was made that the Cramér–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 of 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; this is particularly useful as it allows comparison in terms of a scalar. In this paper, we explore this result to determine how wide the class of such problems is. It turns out to include many non-Gaussian situations. Simulations corroborate the analysis