The problem of space-time adaptive processing (STAP) in non-Gaussian clutte
r is addressed. First, it is shown that actual ground clutter returns are h
eavy-tailed, and their statistics can be accurately characterised by means
of alpha-stable distributions. Then, a new class of adaptive beamforming te
chniques is developed, based on fractional lower-order moment theory. The p
roposed STAP methods adjust the radar array response to a desired signal wh
ile discriminating against non-Gaussian heavy-tailed clutter modelled as a
stable process. Experimental results with both simulated and actual clutter
data show that the new class of STAP algorithms performs better than curre
nt gradient descent state-of-the-art methods, in localising a target both i
n space and Doppler, and thus offers the potential for improved airborne ra
dar performance in STAP applications.