Simultaneous localization and mapping problem via the H∞ filter with a known landmark

This paper deals with the simultaneous localization and mapping (SLAM) problem via the H∞ filter with a known landmark. By adding the observation of a known landmark to those of unknown landmarks, the linearized SLAM model satisfies its observability, and its estimation accuracy is improved. To prove the improvement theoretically, this paper shows that the determinant of the estimated error covariance matrix with the observation of a known landmark becomes small compared with that of the conventional H∞ filter. The convergence of the error covariance matrix is also proven in this paper. With simulations and experimental results, we confirm that the derived theorems for the convergence are correct and that we can accurately estimate the state of the robot and the environment.