Like the hypothetical shadow watchers of Plato's cave, ATR researchers have spent years in the study of one and two-dimensional signals, collected from three dimensional targets. Three-dimensional geometric invariance theory of radar returns from moving targets gives us a new opportunity to escape the study of two-dimensional shadows on the cave wall, emerging into light of the fully three-dimensional information which is present, with probability one, in the signals from any randomly moving target. Target recognition for moving targets is fundamentally harder than for stationary targets, if one remains in a two-dimensional paradigm. Viewing geometry calculations based on sensor flight lines become false, due to uncontrolled target rotations. Three-dimensional analysis shows that even the most optimal purely two-dimensional approach will generically construct false target measurements and distorted target images. But the geometric facts also show that all types of three-dimensional Euclidean invariants, such as true (not projected) lengths, surface areas, angles, and volumes of target components can be extracted from moving target data. These facts have profound implications for target recognition, and for the dynamic tracking of target movements, allowing target signals to be correlated by comparing fundamental three-dimensional invariants, which are not confounded by changing illumination directions.
