Non-uniform Observability for Fast Moving Horizon Estimation with application to the SLAM problem

This paper first formalises a new observability concept, called weak regular observability, that is adapted to Fast Moving Horizon Estimation where one aims to estimate the state of a nonlinear system efficiently on rolling time windows in the case of small initial error. Additionally, sufficient conditions of weak regular observability are provided in a problem of Simultaneous Localisation and Mapping (SLAM) for different measurement models. In particular it is shown that following circular trajectories leads to weak regular observability in a second order 2D SLAM problem with several possible types of sensors.