Cramer Rao bounds on direction estimates for closely spaced emitters in multi-dimensional applications

The main results presented are characterizations of the Cramer-Rao (CR) bound on the variance of direction estimates for closely spaced emitters in multiple parameter (multi-D) scenarios. Specifically, simple analytic expressions for the CR bound are presented for colinear emitter configurations, which show the bound to be very sensitive to the maximum spacing between emitters (δω). Results also are cited for CR bound sensitivity to δω for emitter configurations in which the emitters are not colinear. The latter results exhibit greatly reduced sensitivity to the direction separation factor δω. Thus, the results show that degeneracies are present in multi-D parameter estimation scenarios that are not present in 1-D scenarios. Specifically, emitter resolution and direction estimation can be expected to be much more challenging for some emitter configurations than for others. The case of colinear emitters appears to be a particularly stressful one