Moving Horizon Estimation for Mobile Robots with Multirate Sampling

This paper investigates the multirate moving horizon estimation (MMHE) problem for mobile robots with inertial sensor and camera, where the sampling rates of the sensors are not identical. In the sense of the multirate systems, some sensors may have no measurements at certain sampling times, which can be regarded as measurement missing and may significantly degrade the estimation performance. A binary switching sequence is introduced to model the multirate sampling process, and an explicit mathematical description of this process is proposed where a prediction value activated by a prediction generator is used for the output of missing sampling for slow measurement. The prediction generator provides a set of predictions to make the estimation system achieve the desired performance. By choosing a cost function, the optimal estimator is obtained by solving a regularized least-squares problem with unconstraints. The constrained MMHE problem is studied by using the interior-point algorithm. The input-to-state stability is investigated for the optimal estimator in the presence of bounded disturbances and noises. Finally, a mobile robot tracking platform is designed, and both simulations and experiments are presented to demonstrate the effectiveness of the proposed method.