Invariant observer design for scan matching-aided localization: A tutorial

Aided localization, a nonlinear observer design problem, is critical to a range of mobile robotics applications. This paper provides a tutorial presentation of the required background, design steps and calculations of a scan matching-aided localization observer using the novel invariant (symmetry-preserving) observer design methodology. The Invariant Extended Kalman Filter approach is used to systematically obtain the gains of the resulting design, and compared against a conventional, non-invariant Extended Kalman Filter design.