Approximate expressions for the Cramer-Rao lower bounds on parameter estimates for a pair of closely spaced cisoids

It is demonstrated that the Cramer-Rao lower bounds on unbiased estimates of amplitude and phase for a uniformly sampled data record containing a pair of cisoids closely spaced in frequency can be approximated by simple, non-matrix expressions which offer considerable insight into how the bounds vary with, for instance, frequency separation, signal-to-noise ratios, and the number of data points. Over a broad range of parameter values, the root-mean-square errors in the approximations to the true bounds are about 10%. (C) 1999 Elsevier Science B.V. All rights reserved.