Bearings-only localization using nonlinear second-order extended H∞ filter

Simultaneous localization and mapping (SLAM) is an important issue in intelligent robotic research. The existing works perform robot localization using several nonlinear Bayesian filter such as extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter, etc. To cope with different types of disturbances other than Gaussian noise, this work proposes a nonlinear filter mechanism based on the H∞ control theory. First, a nonlinear system is introduced to be expanded by using Taylor's theorem. The 3rd and higher order term are ignored. The second order extended (SOE) Kalman filter is applied to show it performance comparing with the second order extended (SOE) H∞ filter. When the noise component is not perfect Gaussian distribution, which would usually happen in practical situation, the SOE H∞ filter outperform SOE Kalman filter. Also, the SOE H∞ filter requires less computation than particle filter which is more adequate to. A simulation result is shown and an experiment is design to test its real-time function.