  Parallax and Time-of-Flight (ToF) are often regarded as complementary in
robotic vision where various light and weather conditions remain challenges for
advanced camera-based 3-Dimensional (3-D) reconstruction. To this end, this
paper establishes Parallax among Corresponding Echoes (PaCE) to triangulate
acoustic ToF pulses from arbitrary sensor positions in 3-D space for the first
time. This is achieved through a novel round-trip reflection model that
pinpoints targets at the intersection of ellipsoids, which are spanned by
sensor locations and detected arrival times. Inter-channel echo association
becomes a crucial prerequisite for target detection and is learned from feature
similarity obtained by a stack of Siamese Multi-Layer Perceptrons (MLPs). The
PaCE algorithm enables phase-invariant 3-D object localization from only 1
isotropic emitter and at least 3 ToF receivers with relaxed sensor position
constraints. Experiments are conducted with airborne ultrasound sensor hardware
and back this hypothesis with quantitative results.
