Comparison of GLR and Invariance

This paper addresses a target detection problem for which the covariance matrix of the unknown Gaussian clutter background has block diagonal structure. This block diagonal structure is the consequence of the target lying along a boundary between two statisticallyindependentclutter regions. Here, we design adaptive detection algorithmsusing both the generalized likelihood ratio (GLR) and invariance principles. By exploiting the known covariance structure a set of maximal invariants is obtained. These maximal invariants are a compression of the image data which retain target information while being invariant to clutter parameters. We consider three diierent assumptions on knowledge of the clutter covariance structure: both clutter types totally unknown, one of the clutter types known except for its variance, and one of the clutter types completely known. By means of simulation, the GLR and maximal invariant (MI) tests are shown to outperform the previously proposed invariant test by Bose and Steinhardt which is derived from a similarly structured covariance matrix. Numerical comparisons are presented which illustrate that the GLR and MI tests are complementary, i.e. neither test strategy uniformly outperforms the other over all values of SNR, number of chips, and false alarm rate. This suggests that it may be worthwhile to combine these two tests into a hybrid test to obtain overall optimal performance.