H∞ Filter-Based SLAM with the Observation on an a priori Known Landmark

The authors consider the simultaneous localization and mapping (SLAM) problem with an H∞ filter and with an observation of a landmark that is known a priori. With this observation, the system satisfies observability, and the estimated error is suppressed and the determinant of its covariance matrix becomes small compared with that of the original H∞ filter. As a result, the proposed method avoids finite escape time, the divergence of the error covariance matrix that occurs in the estimation when using the original H∞ filter. We prove the convergence of the error covariance matrix. In addition, with simulations and experimental results, we confirm that finite escape time is avoided, that the derived theorems for the convergence are correct, and that we can accurately estimate the state of the robot and the environment.