Detection of Swerling III-IV rank-one signals in Gaussian noise with unknown statistics

Abstract

We consider the classical radar problem of detecting a target in Gaussian noise with unknown covariance matrix, based on multiple primary data and a set of secondary data containing noise only. The most celebrated approach to this problem is Kelly’s generalized likelihood ratio test (GLRT), derived under the hypothesis of deterministic target amplitudes. However, for a Swerling I-II target (Gaussian amplitudes), it has been shown lately that the associated GLRT, which can outperform Kelly’s GLRT for small sample sizes, is the product of Kelly’s GLRT and a corrective, data dependent, term. We show that at high signal-to-noise ratio (SNR), the GLRT associated to a Swerling III-IV target is “almost surely”’ equivalent to the newly-proposed GLRT for Swerling I-II target, and outperforms, as well, Kelly’s GLRT for small sample sizes at intermediate-to-high SNR values.