Relative Bundle Adjustment

This report derives a relative objective function for bundle adjustment – driven by the desire for a truly large scale simultaneous localization and mapping algorithm that can operate incrementally in constant time. It is precisely the choice of a single privileged coordinate frame that makes bundle adjustment expensive to solve. This is especially true during loop closures, when the single frame approach necessitates adjusting all parameters in the loop. We give a relative formulation that is designed specifically to avoid the cost of optimizing all parameters at loop closure. Instead of optimizing in a single Euclidean space, relative bundle adjustment works in a metric-space defined by a connected Riemannian manifold. We find evidence that in this space, the global maximum likelihood solution can be found incrementally in constant time – even at loop closure.