Coincidence of the Rao Test, Wald Test and GLRT for Radar Target Detection in Generalized Pareto Clutter

The design of detectors for radar targets embedded in the generalized Pareto clutter background is studied in this paper. Because the likelihood ratio test includes the unknown parameters, the generalized likelihood ratio test (GLRT) can be used to derive the suboptimal detectors. However, there are other two tests, named as the Rao and Wald tests, whose asymptotical performance is the same as the GLRT and the computation complexity is lower than the GLRT. In addition, the heavy-tailed non-Gaussian clutter can be characterized well by the generalized Pareto model with inverse-Gamma texture. Therefore, the Rao and Wald tests are used to derive two detectors in generalized Pareto clutter respectively. Mathematical analysis show that from the view of statistics two detectors are the same as the GLRT in generalized Pareto clutter. This result illustrates that the Rao and Wald tests coincide with the GLRT in generalized Pareto clutter.