Invariance Theory for Adaptive Detection in Non-Gaussian Clutter

This paper studies the problem of detecting range-spread targets in (possibly non-Gaussian) clutter whose joint distribution belongs to a very general family of complex matrix-variate elliptically contoured distributions. Within the family, we explore invariance with respect to both the distributional type and relevant parameters. Several groups are used to describe these invariance mechanisms, and a relationship is revealed between the group invariance and the constant false alarm rate (CFAR) properties in terms of model parameters, the generator function, or both. We then build a maximal invariant framework for the detection problem. This involves deriving the corresponding maximal invariants as well as their statistical characterizations. Using these results, we put forward several maximal invariant detectors, all of which are fully CFAR in that their false alarm rates are completely independent of the underlying clutter distribution. Numerical results show that all the proposed fully CFAR detectors are effective, and for the considered simulation setup, one of them outperforms the others and several existing ones.