Matrix CRLB scaling due to measurements of uncertain origin

In many estimation situations, measurements are of uncertain origin. This i s 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 l ow-SNR situations that force the detector at the end of the signal processi ng chain to operate with a reduced threshold-or spurious targets, In severa l earlier papers, the surprising observation was made that the Cramer-Rao l ower bound (CRLB) for the estimation of a fixed parameter vector (e,g,, ini tial position and velocity) that characterizes the target motion, for the s pecial case of multidimensional measurements in the presence of additive wh ite Gaussian noise, is simply a multiple of that for the case with no uncer tainty. That is, there is a scalar information-reduction factor; this is pa rticularly useful as it allows comparison in terms of a scalar, In this pap er, we explore this result to determine how wide the class of such problems is. It turns out to include many non-Gaussian situations, Simulations corr oborate the analysis.