# Robust Direction-of-Arrival Estimation Using Zero-Crossing-Based Time Delay Measurement for Navigation in GNSS-Denied Environments

## TL;DR

This paper proposes a robust method for estimating signal direction using Loran-C signals to aid navigation when GPS is unavailable.

## Contribution

A novel zero-crossing-based least squares method for DOA estimation is introduced, offering improved robustness and accuracy.

## Key findings

- ZC-LS reduces variance and bias compared to Corr-LS under signal interference.
- MUSIC provides accurate estimates but at higher computational cost.
- ZC-LS balances accuracy, robustness, and real-time performance for compact Loran-C receivers.

## Abstract

This paper investigates Direction-of-Arrival (DOA) estimation of Long-Range Navigation-C (Loran-C) signals using an Ultra-Short Baseline (USBL) receiving array. Two least-squares angle estimation approaches based on inter-element delay measurements are examined, including Correlation-based Least-Squares (Corr-LS) and a Zero-Crossing-based Least Squares (ZC-LS). In both methods, relative delays are extracted only within the local array and subsequently mapped to azimuth through a geometric least squares formulation; the approach is, therefore, distinct from distributed time difference-of-arrival (TDOA) localization. For comparison, the Multiple Signal Classification (MUSIC) algorithm is implemented as a covariance-based DOA estimator that operates without explicit delay extraction. Experiments were conducted using Loran-C transmissions from the Xuancheng, Xi’an, and Rongcheng stations, with 100 valid pulse groups collected for each station. Statistical analysis using boxplots shows that Corr-LS exhibits the largest variance due to broadened or shifted correlation peaks, particularly under skywave–groundwave interference. ZC-LS reduces both variance and bias by exploiting the deterministic zero-crossing structure of the Loran-C waveform. MUSIC produces the most concentrated azimuth estimates but requires a well-conditioned covariance matrix and substantially higher computational costs. The results demonstrate that ZC-LS achieves a favorable balance among angular accuracy, robustness, and real-time feasibility, making it suited for compact Loran-C receivers and complementary navigation applications in GNSS-challenged environments.