Bayesian FDOA-Only Localization Under Correlated Measurement Noise: A Low-Complexity Gaussian Conditional-Based Approach

This paper presents the Gaussian conditional method (GCM) for the problem of frequency difference of arrival (FDOA)-only source localization under correlated noise. GCM identifies the source position through approximating its posterior distribution using a Gaussian mixture model (GMM) and applying successive conditioning to the measurement likelihood. The algorithm development leverages the fact that FDOA measurements follow a multivariate Gaussian distribution with a non-diagonal covariance. Simulation results demonstrate that GCM can achieve the Cramér–Rao lower bound (CRLB) under moderate noise levels, while having lower computational complexity than baseline techniques including the recently developed Gaussian division method (GDM). The proposed algorithm is particularly effective for passively locating narrowband sources, where the time difference of arrival (TDOA) measurements become unreliable, and it can operate without the need for accurate initialization.