Impact of Altitude, Bandwidth, and NLOS Bias on TDOA-Based 3D UAV Localization: Experimental Results and CRLB Analysis

This paper investigates unmanned aerial vehicle (UAV) localization using time difference of arrival (TDOA) measurements under mixed line-of-sight (LOS) and non-line-of-sight (NLOS) conditions. A 3D TDOA Cramér-Rao lower bound (CRLB) model is developed accounting for varying altitudes and signal bandwidths. The model is compared to five real-world UAV flight experiments conducted at different altitudes (40 m, 70 m, 100 m) and bandwidths (1.25 MHz, 2.5 MHz, 5 MHz) using Keysight N6841A radio frequency (RF) sensors of the NSF AERPAW platform. Results show that altitude, bandwidth, and NLOS obstructions significantly impact localization accuracy. Higher bandwidths enhance signal time resolution, while increased altitudes mitigate multipath and NLOS biases, both contributing to improved performance. However, hovering close to RF sensors degrades accuracy due to antenna pattern misalignment and geometric dilution of precision. These findings emphasize the inadequacy of traditional LOS-based models in NLOS environments and highlight the importance of adaptive approaches for accurate localization in challenging scenarios.

💡 Research Summary

This paper presents a comprehensive study of unmanned aerial vehicle (UAV) three‑dimensional (3‑D) localization using time‑difference‑of‑arrival (TDOA) measurements under mixed line‑of‑sight (LOS) and non‑line‑of‑sight (NLOS) conditions. The authors first derive a theoretical framework for TDOA‑based positioning. The time‑of‑arrival (TOA) at each synchronized passive RF sensor is estimated with a maximum‑likelihood (ML) estimator, yielding a Gaussian measurement noise whose variance σi depends on the signal‑to‑noise ratio (SNR) and the effective signal bandwidth β as σi = (1/2)√(2π)·SNRi·β⁻¹. SNRi is modeled with the free‑space path‑loss (FSPL) equation, incorporating transmit power, antenna gains, wavelength, and the true distance di between the UAV and the i‑th sensor. By differencing TOA values, the TDOA for each sensor pair is obtained, eliminating dependence on the unknown UAV transmission time.

The measurement vector Δt has a mean determined by the true range differences and a covariance matrix Q(x) that reflects the common reference sensor: diagonal entries contain σr²+σi² while off‑diagonal entries contain σr². The Fisher Information Matrix (FIM) for the 3‑D position x =