TDoA (Time Difference of Arrival) is a technique used for high-precision localization, especially in Ultra-Wideband (UWB) systems like those standardized in IEEE 802.15.4z (Enhanced UWB PHY). Below is an overview of open-source implementations and resources related to TDoA for UWB-based localization.

1. IEEE 802.15.4z & TDoA Basics

  • 802.15.4z enhances UWB with improved security (STS, AES-128) and ranging accuracy (HRP/LRP modes).
  • TDoA vs. ToF (Time of Flight)
    • TDoA: Uses multiple anchors (fixed reference nodes) to compute tag position based on signal arrival time differences (better for large-scale deployments).
    • ToF (Two-way ranging): Measures round-trip time between two devices (used in Apple AirTag, Samsung SmartTag).

2. Open-Source TDoA Implementations list

2.1 Decawave (Now Qorvo) DW1000-based Solutions

The DW1000 UWB transceiver is widely used in open-source UWB projects.

Some key Github repos are:

  1. Pozyx.io: Supports TDoA and ToF localization, and, Works with Arduino & Raspberry Pi.
  2. Bitcraze Crazyflie (UWB TDoA for Drones), Uses LPS (Loco Positioning System) with DW1000, and, Supports TDoA2 (improved version of TDoA).

2.2 ESP32 + UWB (Cheaper Alternative)

2.3 Apple & Android Ecosystem (Closed but Relevant)

  • Apple U1 Chip (UWB-based AirTags): Uses proprietary TDoA-like methods.
  • Android UWB Stack (Samsung, Google Pixel): Based on FiRa Consortium standards.

3. TDoA Algorithm Implementation

A basic TDoA algorithm involves:

  1. Anchor Synchronization (Clock sync between anchors).
  2. Time Difference Calculation (e.g., Cross-Correlation of received signals).
  3. Hyperbolic Positioning (Solving nonlinear equations(hyperbolic curves) via LS/ML estimation): requires at least 3 anchors for 2D (4 ones for 3D).

3.1 Visulaze 2D TDoA :

Anchors: A0[0, 0], A1[5, 0], A2[0, 5]

Tag: [2, 3]

illustrating with a text figure

Y-axis
  |
5 +      A2 (0,5)
  |       *
  |      / \
  |     /   \  hyperbola points (A0-A2)
  |    /     \
  |   /       \
3 +  * Tag (2,3)
  |   \       /
  |    \     /  hyperbola points (A0-A1)
  |     \   /
  |      \ /
0 +------*------- X-axis
  A0 (0,0) A1 (5,0)

3.2 Python code and running result:

import numpy as np
from scipy.optimize import least_squares

# Anchor positions (same as original)
anchors = np.array([[0, 0], [5, 0], [0, 5]])

# True tag position (for synthetic data generation)
true_pos = np.array([2.0, 3.0])

# Simulate TDoA measurements (add slight Gaussian noise)
c = 3e8  # Speed of light (m/s)
noise_std = 1e-9  # 1 ns standard deviation (realistic for UWB)

# Theoretical time differences (no noise)
d_true = np.array([
    np.linalg.norm(true_pos - anchors[1]) - np.linalg.norm(true_pos - anchors[0]),
    np.linalg.norm(true_pos - anchors[2]) - np.linalg.norm(true_pos - anchors[0])
])

# Add noise to simulate real measurements
tdoa_meas = d_true / c + np.random.normal(0, noise_std, size=2)

# original TDoA solver function as residuals f(x)  for later least_squares
def tdoa_error(x, anchors, tdoa_meas):
    return [
        np.sqrt((x[0]-anchors[1][0])**2 + (x[1]-anchors[1][1])**2) -
        np.sqrt((x[0]-anchors[0][0])**2 + (x[1]-anchors[0][1])**2) - tdoa_meas[0]*c,
        np.sqrt((x[0]-anchors[2][0])**2 + (x[1]-anchors[2][1])**2) -
        np.sqrt((x[0]-anchors[0][0])**2 + (x[1]-anchors[0][1])**2) - tdoa_meas[1]*c
    ]

# Solve using nonlinear least-squares optimizer
result = least_squares(tdoa_error, [0, 0], args=(anchors, tdoa_meas))
estimated_pos = result.x

# Print results
print(f"Tag True position: {true_pos}")
print(f"Tag Estimated position: {estimated_pos}")
print(f"Error (meters): {np.linalg.norm(true_pos - estimated_pos):.4f}")

running result:

~ % python3 tdoa.py
Tag True position: [2. 3.]
Tag Estimated position: [1.97366561 2.86600114]
Error (meters): 0.1366

4. Challenges in Open-Source TDoA

  • Clock Synchronization: Requires precise anchor sync (PTP, wired sync, or wireless sync).
  • Multipath Interference: UWB signals reflect in indoor environments.
  • Security: 802.15.4z adds AES-128 for secure ranging (hard to implement in open-source).

5. Further Resources

NOTE: subject to change in the future