Comparison of GLR and maximal invariant detectors under structured clutter covariance

There has been considerable recent interest in applying maximal invariant (MI) hypothesis testing as an alternative to the generalized likelihood ratio (GLR) test. This interest has been motivated by several attractive theoretical properties of MI tests including: exact robustness to variation of nuisance parameters, finite-sample min-max optimality (in some cases), and distributional robustness. However, in the deep-hide target detection problem, there are regimes for which either of the MI and the GLR tests can outperform the other. We discuss conditions under which the MI tests can be expected to outperform the GLR tests in the context of a radar imaging and target detection application. We also show that the relative advantage of the MI tests is robust to boundary estimation errors