Cascaded Bearing Only SLAM with Uniform Semi-Global Asymptotic Stability

Bearing only simultaneous localization and mapping (SLAM) is an extensively researched topic, where the nonlinearity of the problem leads to consistency, bias and stability challenges for the filter. In this article we combine two newly developed filters for bearing-only SLAM, with global stability results in a cascade structure; inspired by the newly presented eXogenous Kalman filter (XKF). We prove that this cascade structure has uniformly semi-globally asymptotic stability (USGAS), and through simulations, we show how this setup can increase the robustness of the filtering against nonlinear measurement noise. In addition, it is shown how the nonlinear observer smooths the bearing measurements.