Worst Case Cramér-Rao Bounds for Parametric Estimation of Superimposed Signals with Applications

The problem of parameter estimation of superimposed signals in white Gaussian noise is considered. The effect of the correlation structure of the signals on the Cramer-Rao bounds is studied for both the single and multiple experiment cases. The best and worst conditions are found using various criteria. The results are applied to the example of parameter estimation of superimposed sinusoids, or plane-wave direction finding in white Gaussian noise, and best and worst conditions on the correlation structure and relative phase of the sinusoids are found. This provides useful information on the limits of the resolvability of sinusoid signals in time series analysis or of plane waves in array processing. The conditions are also useful for designing worst-case simulation studies of estimation algorithms, and for the design of minimax signal acquisition and estimation procedures, as demonstrated by an example.