  Visual Simultaneous Localisation and Mapping (VSLAM) is a key enabling
technology for small embedded robotic systems such as aerial vehicles. Recent
advances in equivariant filter and observer design offer the potential of a new
generation of highly robust algorithms with low memory and computation
requirements for embedded system applications. This paper studies observer
design on the symmetry group proposed in previous work by the authors, in the
case where inverse depth measurements are available. Exploiting this symmetry
leads to a simple fully non-linear gradient based observer with almost global
asymptotic and local exponential stability properties. Simulation experiments
verify the observer design, and demonstrate that the proposed observer achieves
similar accuracy to the widely used Extended Kalman Filter with significant
gains in processing time (linear verses quadratic bounds with respect to number
of landmarks) and qualitative improvements in robustness.
