Multilateration 3D Positioning

Python library and Blender pipeline for 3D localization: estimate a tag’s position from known anchor positions and measured distances. Supports trilateration (3 coplanar anchors), multilateration (4+ anchors via least-squares or closed-form), and brute-force optimization. Blender scripts export scene data to CSV; demos read CSV and run the solvers; results feed into the Baretag positioning pipeline. Demonstrates numerical geometry (Cayley–Menger, least-squares), Python scientific stack, and Blender scripting for validation.

multilat_lib.py Core solvers. trilateration(anchors, distances) uses three anchors (same Z unless ignore=True): builds a triangle, computes volume via a Cayley–Menger–style determinant, then tag height and position from the plane normal. multilateration_minimum_squared does Larsson-style linear least squares; multilateration_closed_form solves exactly for 4 anchors. brute_force minimizes squared distance error (optionally fixing x,y and solving for z). geo_to_local_xyz / local_to_geo convert between lat/lon/alt and local ENU (meters).

trilateration.py Demo that reads tag_data.csv, builds anchor positions and distances to the tag (Sphere), calls trilateration(), and prints estimated vs actual position and error in Z.

tag_response.py and demos tag_response.py is a Blender script (bpy): it reads Sphere and Cube objects, computes Euclidean distances from the sphere to each cube, and writes a CSV (Point, X, Y, Z, Distance to Sphere) for use by the Python solvers. Other scripts (real_geodata.py, multilateration.py) use the same library and CSV/geodetic conventions for real-world or multi-anchor demos.

Research references The implementation was informed by Xu et al., A Precise 3D Positioning Approach Based on UWB with Reduced Base Stations; Martin Larsson, Localization using Distance Geometry: Minimal Solvers and Robust Methods for Sensor Network Self-Calibration; and Rainer Mautz, Washington Ochieng, Gary Brodin, and Andy Kemp, 3D Wireless Network Localization from Inconsistent Distance Observations.