Rao, Wald, and Gradient Tests for Adaptive Detection of Swerling I Targets

We consider adaptive detection of a Gaussian rank-one component known up to a scaling factor buried in Gaussian noise with unknown statistics, a problem which arises when detecting Swerling I targets in radar systems. From the joint distribution of the samples under test and the training samples, the score function and the Fisher information matrix are derived, which enables us to formulate the Rao, Wald and gradient tests associated with the composite hypotheses problem. The Rao test is shown to bear resemblance with its deterministic counterpart and the Wald test is essentially based on the target power maximum likelihood estimate. The gradient test sort of blends the two other tests. All of them are shown to have a constant false alarm rate. Their performance is evaluated through numerical simulations in matched and mismatched cases.