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Visual Simultaneous Localisation and Mapping (VSLAM) is a key enablingtechnology for small embedded robotic systems such as aerial vehicles. Recentadvances in equivariant filter and observer design offer the potential of a newgeneration of highly robust algorithms with low memory and computationrequirements for embedded system applications. This paper studies observerdesign on the symmetry group proposed in previous work by the authors, in thecase where inverse depth measurements are available. Exploiting this symmetryleads to a simple fully non-linear gradient based observer with almost globalasymptotic and local exponential stability properties. Simulation experimentsverify the observer design, and demonstrate that the proposed observer achievessimilar accuracy to the widely used Extended Kalman Filter with significantgains in processing time (linear verses quadratic bounds with respect to numberof landmarks) and qualitative improvements in robustness.

An Observer Design for Visual Simultaneous Localisation and Mapping with Output Equivariance