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.

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