Estimation and Detection Under Misspecification and Complex Elliptically Symmetric Distributions
Parameter estimation and detection theory play critical roles in the development of signal and array processing algorithms, especially in applications such as radar, sonar, and wireless communications. Theoretical bounds in detection and estimation are tied to the true underlying data probability distribution. In practice, however, the assumed data model is often imperfect, i.e., it is commonly misspecified at some level. Firstly, we develop the Cramér–Rao bound (CRB) under model misspecification, including a multivariate generalization of Blyth’s theorem that guarantees an inequality of the Cramér–Rao type. Secondly, we explore the classic problem of adaptive radar detection under a class of complex multivariate elliptically symmetric (CMES) distributions known as the compound Gaussian. The generalized likelihood ratio test (GLRT) is derived along with its finite sample receiver operating characteristics (ROC). Lastly, the asymptotic (large sample) distribution of the GLRT in general is explored under model misspecification.
