We want the equation that relates the fractional atomic coordinates to octahedral tilting angle.
There are many review papers showing up in upon searching "octahedra tilting" and perovskites in google. Only a short comment on the relation of your actual question with the second sentence of your enquiry: Relation between atomic coordinates and tilting angles can be done independent the the actual Rietveld analysis (or another type of structural analysis). It is a purely geometric problem.
We have calculated the octahedral tilt angle in doped LaMnO3 in our paper T. Chatterji et al., PRB 66, 054403 (2002). The octahedral tilt angle \phi around the pseudocubic [111] direction can be calculated by the two Mn-O-Mn angles \theta1 and \theta2 by the relations given in equation (13) and (14) of this paper. The equations can be found in the paper M. O'Keeffe and B.G. Hyde, Acta Cryst. B 33, 3802 (1977).
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