Calibration

Calibration of the base station involves the following three steps:

• Ensuring that the lighthouses are mutually perpendicular.
• Measuring the offsets of the lighthouse centers $x_0$ and $z_0$.
• Determining $C^b, C^\beta, C^\gamma, C^\delta$ for each of the two lighthouses.

Figure 10: Ensuring mutually perpendicular lighthouses.

In order to ensure that the two lighthouses are mutually perpendicular, we placed the base station at the corner of a rectangular room as depicted in Figure 10, such that the rotation axes of the two lighthouses are at distance $x$ from the two perpendicular walls. We disabled the motors that drive the rotating mirrors and one of the two lasers of each lighthouse. Then we adjusted the mirror so that the remaining laser beam points at the opposite wall. Due to the rotating lighthouse platforms, the laser spots draw two circles on the walls. The centers of these two circles mark the position where the lighthouse rotation axes hit the wall as depicted in Figure 10. Now we adjust the lighthouses on the common chassis such that the centers of these circles also have a distance $x$ from the walls. In our measurement setup, we placed the base station at $x = 20$cm in a room with a size of about 5m by 5m.

As mentioned in Section 4.2, the lighthouse center offsets $x_0$ and $z_0$ from the origin of the coordinate system defined by the lighthouse rotation axes are not critical for the accuracy of the system. Therefore, we measured them directly at the base station device.

In order to determine the $C^\ast$ values, we placed the observer at the four locations $(x,z) \in \{(50, 50), (480, 80), (80, 480), (340, 340)\}$ (all values in centimeters) on the floor in the base station coordinate system. The respective lighthouse distance and height values are obtained from the $(x,z)$ values as follows:

$$\begin{array}{rcl} (d_x,h_x) & := & (z,x-x_0) \\ (d_z,h_z) & := & (x,z-z_0) \end{array}$$ (13)

At each of the locations we performed ten measurements of $\alpha$ for each lighthouse and computed the mean value. For each of the two lighthouses we then solved Equation System 12 in order to obtain the $C^\ast$ values.