On the Misspecified Cramér-Rao Bound and Elliptically Symmetric Distributions

Parameter estimation is among the many goals of engineering systems and scientific applications, and parameter bounds have provided significant insights into achievable system performance. These bounds are based on an assumed distribution for the data that may differ from the true data distribution, i.e. often the impacts of model misspecification are inevitable. Thus, researchers have derived Slepian-Bangs-type formulas for elliptically symmetric distributions under model misspecification to explore these effects. The present work continues this exploration by establishing a simple version of the Slepian formula applicable to circular complex compound Gaussian distributed data (a special class of non-Gaussian distributions, also sometimes called Gaussian mixtures), when the data distribution assumed for algorithm development is complex Gaussian.