Analysis and solutions of the three point perspective pose estimation problem

The major direct solutions to the three-point perspective pose estimation problems are reviewed from a unified perspective. The numerical stability of these three-point perspective solutions are discussed. It is shown that even in cases where the solution is not near the geometric unstable region considerable care must be exercised in the calculation. Depending on the order of the substitutions utilized, the relative error can change over a thousand to one. This difference is due entirely to the way the calculations are performed and not to any geometric structural instability of any problem instance. An analytical method is presented which produces a numerically stable calculation