It is well-known that pose can be estimated linearly from at least 4 coplanar reference points using a special linear algorithm [3,6]. The points must be affinely independent, i.e. no three of them collinear.
It is important to note that configurations of 4 or more coplanar points are not generically critical for our 4-point algorithm. This is easily proven since the configuration is still constrained by six independent distances as in the non-coplanar case. This suggests important practical consequences of the linear method. In the experiments, the accuracy and stability of our linear 4-point algorithm will be compared with the standard linear algorithm for coplanar points. Also note that SVD step of our algorithm implicitly detects any critical configurations leading to rank deficiency.