# Using Geometric Algebra to determine a set of consistent rotations from multiple local observations

Presenter: Joan Lasenby, Cambridge University Engineering Department, UK

Joint work with Stuart Bennett

A variety of applications provide us with data which consists of noisy estimates of relative rotations: when looked at globally, these rotations are not consistent. For example, the rotations taking us from camera 1 to camera 2 ($R_{12}$), from camera 1 to camera 3 ($R_{13}$) and from camera 2 to camera 3 ($R_{23}$), can all be estimated from real world data – but these estimates will generally not satisfy $R_{13} = R_{23} R_{12}$, as they should. This talk will show how we can use Geometric Algebra to obtain optimal (in a defined sense) estimates from any numberof relative rotations. The results are compared with standard linear algebra solutions to this problem and specific applications are discussed.