Slepian-Bangs-type formulas and the related Misspecified Cramér-Rao Bounds for Complex Elliptically Symmetric distributions

In this paper, Slepian-Bangs-type formulas for Complex Elliptically Symmetric distributed (CES) data vectors in the presence of model misspecification are provided. The basic Slepian-Bangs (SB) formula has been introduced in the array processing literature as a convenient and compact representation of the Fisher Information Matrix (FIM) for parameter estimation under (parametric) Gaussian data model. Extending recent results on this topic, in this paper, we provide a new generalization of the classical SB formula to parametric estimation problems involving non-Gaussian, heavy-tailed, CES distributed data in the presence of model misspecification. Moreover, we show that our proposed formulas encompass the special cases of the SB formula for CES distributions under perfect model specification, the SB formulas in the presence of misspecified Gaussian models, and the SB formula for the estimation of the scatter matrix of a set of CES distributed data under misspecification of the density generator.