## 32

Theory and Design

nalysis

In this thesis a pose estimation method is proposed that assumes model points are known to high precision. This method uses quaternions to describe the orientation of camera modules. n iterative method is used to refine the estimate of the modules’ orientations. From the orientation, the position can be determined. In future research bundle adjustment [51] could produce much better results by removing the assumption that the model points

are known precisely.

3.3.1

## Bundle adjustment

Bundle adjustment is a broader topic compared with pose estimation.

s well as being

used to solve the same problem, i.e., that of estimating the pose of an object, it can also be used to refine the positions of model points. Depending on the bundle adjustment algorithm used, the intrinsic camera parameters can also be refined as part of the optimisa- tion process. Triggs [51] gives a detailed overview of bundle adjustment methods. Triggs defines bundle adjustment as follows “Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal 3D structure and viewing parameter (camera pose and/or

calibration) estimates.”.

Triggs continues that bundle adjustment is a large geometric parameter optimisation prob- lem. The optimisation seeks to minimise an error function that in some way describes the difference between measured data and data predicted using a system model. Instead of the model parameters remaining constant as in the case of the pose estimation algorithms above, they are allowed to vary during the bundle adjustment.

In this research the measured data are the 2D centroids of the marker images. The model data include the pose of the hub enclosure, the coordinate frames of the cameras with respect to the hub enclosure, the focal lengths, and principal points of the cameras (intrinsic parameters), and the positions of the markers in 3D coordinates.

Implementing a bundle adjustment algorithm is beyond the scope of this research but the author believes that bundle adjustment is necessary to achieve the accuracy in the system specification. Ideas for how to approach this are given in the future work section of this thesis.

3.4

# Beacon configuration analysis

brief analysis of a possible configuration of the system is given in this section. To decide on the number of beacons and camera modules required to provide tracking throughout a 3 m × 3 m × 3 m volume, the effect a single beacon has on the tracking volume must be considered. Consider a single beacon fixed in space. For this calculation the beacon is