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The instantaneous direction-of-arrival (DOA) of sound is a crucial parameter in the analysis of acoustic scenes. More complex acoustic scenes are often modelled as a sum of two plane waves, which requires a DOA estimator that can provide two DOAs per time and frequency. This paper proposes an approach which computes two DOAs per time and frequency from a B-format microphone signal. The proposed estimator outperforms the state-of-the-art approach by considering also diffuse sound and microphone noise in the signal model. The estimator includes an averaging process prior to computing the DOA estimates, as well as a fallback solution in case no valid results can be obtained. Simulation results demonstrate the practical applicability of the presented algorithm.