# Calibration of a Rotating or Revolving Platform with a LiDAR Sensor
## 4 Evaluation
### Discussion  
The plots in Figure 7 indicate an improvement of the extrinsic parameters compared to the respective initial guess, as measured with the plane deviation. The tendency to the optimal configuration goes to a sweet spot at a distance between sensor and targets of 3.5 m and a high resolution for the grid search (blue and red bars). This is indicated by a very low plane deviation for these configurations. Other configurations with close targets or a low resolution of the search grid also improve the initial pose, but scored less, compared to the sweet spot. \begin{table}
\begin{tabular}{c c c c} \hline \hline _Resolution [rad]_ & _Total [s]_ & _Grid [s]_ & _Local [s]_ \\ \hline
**0.005** & **7.588** & **0.618** & **0.018 + 6.951** \\ \hline
0.0025 & 13.116 & 6.678 & 0.029 + 6.408 \\ \hline
0.001 & 54.782 & 49.5  
It is significant that targets placed at great distances lead to better results, at least for the promising grid configurations. The score gets better up to 3.5 m. Calibration runs with targets placed in 4.0 m range come up with worse scores. We believe that this is caused by the increasing error from sphere center estimation, dominating the benefit of targets placed farther away. In general, calibration runs with targets placed close to the platform result in less sharp point clouds. As predicted by our expectations, this can possibly be explained via the sensitivity of the objective function to optimize (see Section 3.2) and with the fact that a divergent angle has less effect at close range. This could possibly shift or widen minima to saddles to which the optimiser converges. This makes it necessary to place the targets as far as possible from the platform as long as an accurate sphere center estimation can be expected. It was also expected to get better results using the higher resolution for the parameter grid used for the search of promising extrinsic parameter sets to start a gradient decent optimisation at. In fact, the results contain no evidence for a good result on low resolved search grids. Thus, a high resolution search seems to be not only beneficial, but also necessary. Surprisingly, the angle between the target pairs (see Figure 5) had no strong or even any effect on the results. The fact that the 45\({}^{\circ}\) arrangement even scores best can arguably be explained by an inferior estimation of sphere centers when the data for the 90\({}^{\circ}\) arrangement were recorded. There is no theoretical reason for the acute-angle to be an advantage, known to us. The plane deviation measure gives evidence that the initially guessed sensor pose does not need to be very accurate. The deteriorated initial pose parameters, shown in the right plot of Figure 7, result in similar qualities as the parameters estimated from the originally measured initial pose (left plot). Furthermore, Figure 8 supports this observation. The figure shows the point clouds recorded with the initial pose guesses in the first row--on the left side with the measured and on the right side with the deteriorated pose. The results with the best quality scores are shown below their respective initial guess. Both present fairly sharp point clouds. In addition, the objects, cube and cylinder placed in the scene got congruent. This is especially noticeable in the right column starting from the deteriorated initial pose. Figure 7: Results of experiments calibrating the LiDARs extrinsic parameters under different circumstances and with different quality measures. The graphs in the left diagram show the quality of recorded point clouds after calibration from a pose we actually measured at the platform construction, rated with the _plane deviation_ (above) and the _cispness measure_ (below). The graphs in the right diagram depict the same ratings but applied to results from an initial pose guess with an artificially upscaled error. All graphs contain ratings of calibration results produced from different target arrangements, each calibrated with a high (0.00025) and a relatively low (0.005) resolution of the pose parameter grid.