# 3-Dimensional Sonic Phase-invariant Echo Localization

arXiv: https://arxiv.org/abs/2306.08281 · HTML: https://mlsanity.com/paper/2306.08281/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 4 of 4)

- [BatVision: Learning to See 3D Spatial Layout with Two Ears](https://mlsanity.com/paper/1912.07011/) (2019)
- [Beyond Image to Depth: Improving Depth Prediction using Echoes](https://mlsanity.com/paper/2103.08468/) (2021)
- [Baseline and Triangulation Geometry in a Standard Plenoptic Camera](https://mlsanity.com/paper/2010.04638/) (2020)
- [Multimodal Exponentially Modified Gaussian Oscillators](https://mlsanity.com/paper/2209.12202/) (2022)

## Built on by (most cited first, 2 of 2)

- [Geometric Ultrasound Localization Microscopy](https://mlsanity.com/paper/2306.15548/) (2023)
- [StofNet: Super-resolution Time of Flight Network](https://mlsanity.com/paper/2308.12009/) (2023)

## Abstract (arXiv)

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.