Abstract-This paper addresses a target detection problem in radar imaging for which the covariance matrix of unknown Gaussian clutter has block diagonal structure. This block diagonal structure is the consequence of a target lying along a boundary between two statistically independent clutter regions. Here, we design adaptive detection algorithms using both the generalized likelihood ratio (GLR) and the invariance principles. There has been considerable recent interest in applying invariant hypothesis testing as an alternative to the GLR test. This interest has been motivated by several attractive properties of invariant tests including: exact robustness to variation of nuisance parameters and possible finite-sample min-max optimality. However, in our deep-hide target detection problem, there are regimes for which neither the GLR nor the invariant tests uniformly outperforms the other. We will discuss the relative advantages of GLR and invariance procedures in the context of this radar imaging and target detection application.

There has been considerable recent interest in applying maximal invariant (MI) hypothesis testing as an alternative to the generalized likelihood ratio test (GLRT). 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, i.e. insensitivity to changes in the underlying probability distribution over a particular class, Furthermore, in some important cases the MI test gives a reasonable test while the GLRT has worse performance than the trivial coin flip decision rule [ 11. However, in other cases, like the deep hide target detection problem, there are regimes (SNR, number of wireless users, coherence bandwidth) for which either of the MI and the GLRT can outperform the other. We will discuss conditions under which the MI tests can be expected to outperform the GLRT in the context of a radar imaging and target detection application.

We present and compare adaptive detection algorithms developed for synthetic aperture radar (SAR) targets in structured clutter, utilizing both generalized likelihood ratio (GLR) tests and maximal invariant (MI) tests. We consider the problem of detecting a target straddling a known boundary between two independent clutter regions inducing a clutter covariance matrix with block diagonal structure. GLR and MI tests are presented for various clutter scenarios: two totally unknown clutter types, one of the clutter types known except for its variance, and one of the clutter types completely known. Numerical comparisons will illustrate that GLR tests and MI tests are complementary-neither test strategy uniformly outperforms the other-suggesting that it may be worthwhile to hybridize these tests for overall optimal performance.

No abstract