Single particle diffraction imaging experiments at free-electron lasers (FEL) have a great potential for structure determination of reproducible biological specimens that can not be crystallized. One of the challenges in processing the data from such an experiment is to determine correct orientation of each diffraction pattern from samples randomly injected in the FEL beam. We propose an algorithm (see also O. Yefanov et al., Photon Science - HASYLAB Annual Report 2010) that can solve this problem and can be applied to samples from tens of nanometers to microns in size, measured with sub-nanometer resolution in the presence of noise. This is achieved by the simultaneous analysis of a large number of diffraction patterns corresponding to different orientations of the particles. The algorithms efficiency is demonstrated for two biological samples, an artificial protein structure without any symmetry and a virus with icosahedral symmetry. Both structures are few tens of nanometers in size and consist of more than 100 000 non-hydrogen atoms. More than 10 000 diffraction patterns with Poisson noise were simulated and analyzed for each structure. Our simulations indicate the possibility to achieve resolution of about 3.3 {AA} at 3 {AA} wavelength and incoming flux of 10^{12} photons per pulse focused to 100times 100 nm^2.
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