We consider the DIFAR sonobuoy bearing estimation problem for underwater acoustic sources. The standard arctangent based approach utilises the orthogonality between the observation noises for the different channels to form the bearing estimates, and ignores the correlation structure of the actual source signal. In this paper, we propose a new state space technique, which exploits the correlations structure in the source signal to achieve enhanced performance, particularly in low signal-to-noise (SNR) conditions, compared to the standard arctangent estimator. The analysis is supported by simulations using some realistic classes of signals.