This paper proposes a sound source orientation estimation method that is suitable for a distributed microphone arrangement. The proposed method is based on orientation-extended beamforming (OEBF), which has four features: (a) robustness against reverberations, (b) robustness against noises, (c) free arrangements of microphones and (d) feasibility for real-time processing. In terms of (a) and (c), since OEBF is based on a general propagation model using transfer functions (TFs) that include all propagation phenomena such as reflections and diffractions, OEBF causes no model errors for the propagation phenomena, and is applicable to arbitrary microphone arrangements. Regarding (b), OEBF overcomes noise effects by incorporating three additional processes (Amplitude extraction, time-frequency mask and histogram integration) that are also proposed in this paper. As for (d), OEBF is executable in real-time basis as the execution process is the same as usual beamforming processes. A numerical experiment was performed to confirm the theoretical validity of OEBF. The results showed that OEBF was able to estimate sound source positions and orientations very precisely. Practical experiments were carried out using a 96-channel microphone array in real environments. The results indicated that OEBF worked properly even under reverberant and noisy environments and the averaged estimation error was given only 4°.