# Evaluation of the SteamVR Motion Tracking System with a Custom-Made Tracker
## 3 Measurement Results
### Position  
The position of the tracker changed when the tripod was moved to the next measuring point, as well as with the change of the launcher orientation, as the tracker's centre was not in the tripod head's axis of rotation. The attachment point of the launcher was selected to correspond to the place where the launcher rests against the user's arm in the actual application. The position of the tracker at each of the nine points where the tripod was placed should have values belonging to five circles, the radius of which will depend on the  
Figure 4: Translation and rotation between the real coordinate system and the SteamVR system. The hatched area represents the floor. angle of the tripod inclination \(\theta\). The average values of the tracker positions are shown in the XZ plane in Figure 5. The chart also shows circles whose parameters were determined using the least-squares method. The chart shows four circles for each tripod position. The fifth circle for the elevation angle of 40\({}^{\circ}\) is almost invisible, as the average radius of the circles is about 9 mm. The maximum differences between the radii of the circles for the same elevation angle are about 5 mm for a 0-40\({}^{\circ}\) elevation, and increase to almost 10 mm for an 80\({}^{\circ}\) elevation. In part, these values may be due to an inaccurate setting of angle \(\theta\) on the tripod head. The circles projected onto the XZ plane should be concentric. However, especially at the corner points of the working space, the centres of the circles are shifted. The greatest shift values were observed near the base stations, where the centres of the circles are 27 mm apart near the BS1 stations, and 22 mm near the BS2 stations. The circles in the centre of the working space are closest to one another, with the distance between their centres not exceeding 4 mm. The results show a systematic error of approximately 160 mm for the X coordinate and 12 mm for the Z coordinate. This error results from the shift of the SteamVR coordinate system relative to the centre of the working space. It can be eliminated at the VR application stage. Often, however, there is no need for this, as the same shift is observed for the positions of the HMD goggles which are positioned in the same coordinate system. As a result, when the user sees the virtual world through the HMD goggles, such a shift is difficult to notice, and has no impact on the working environment. In addition to the parameters of circles discussed above, there is also the Y coordinate of the centre of the circle, and a vector normal to the plane of the circle, which describes its orientation in space. A graphical representation of the above parameters is presented in Figure 6, showing the data projected onto the XY plane (side view). Figure 5: Tracker positions during measurements (top view). The dots indicate the tracker’s position, the red lines represent the circles with a radius determined from the results, and the crosses indicate their centres. For points with a greater value of X, the readout for the tracker's height decreases, which indicates the rotation of the SteamVR coordinate system with respect to the room. As a result, the \"virtual\" floor plane in the SteamVR system is tilted relative to the actual floor. The tilt angle is 0.5\({}^{\circ}\), which, for a 2 by 2 m working space, translates into a height change of less than 20 mm between the extreme points. These values are small, and can be compensated for in a virtual environment. There were no significant differences between the deviation of the height of the circles at different elevation angles. The rotation of the planes to which the individual circles belong was also observed. The mean difference between the reference plane normal (0, 1, 0) and the determined circle plane norm is 1\({}^{\circ}\) with a standard deviation of 1\({}^{\circ}\). The worst results of deviation from the horizontal direction (3.5\({}^{\circ}\)) were recorded for the measurements at the point where x = \(-\)1, z = 0.