Rao, Durbin and gradient tests for adaptive detection of Rician targets

We consider adaptive radar detection of Rician targets which, when present, result in a shift of the mean of the observations as well as a rank-one modification of the covariance matrix. In the paper, we first derive the Fisher information matrix for the statistical model under consideration. This enables us to obtain the expressions of Rao, Wald, Durbin and gradient tests statistics whose distributions are parameter-free under the null hypothesis. Numerical simulations illustrate their probability of detection in both matched and mismatched cases, i.e., when the signature under test coincides or not with the actual target signature. They indicate that under some scenarios Rao, Durbin and gradient tests may be valuable alternatives to the GLRT.