Sensitivity of a 3-dimensional position and attitude measurement device using 4 LEDs on the apices of a tetrahedron and a PSD

It is known that the position and the attitude of a little plate can be calculated from a picture of more than 4 specific spots on the plate. Usually. 4 LED are arranged at the corners of a 2D square. However, calculated results are shown to be too sensitive to erroneous reading of the picture. This paper proposes an arrangement of 4 LED´s at the apices of a tetrahedron or similar 3D arrangement. The sensitivities are compared for 2D and 3D arrangements of 4 LED.