Ultra-Wideband Localization of Mobile Robots Based on Moving Horizon Optimization

In order to solve the indoor mobile robot localization problem with non-Gaussian noise existed in the nonlinear measurement equation, an Ultra-wideband (UWB) localization algorithm for mobile robots based on moving horizon optimization is proposed. By integrating the kinematic model of the mobile robot and the reference poses, we establish the error system model for the robot. Furthermore, we incorporate a modeled representation of the heavy-tailed noise that occurs during UWB ranging. The optimal estimate is attained through the solution of an unconstrained regularized least squares problem, where the selection of an appropriate cost function is crucial. Subsequently, the estimated positions of the mobile robot are inverted by combining the known reference positions. The input-to-state stability (ISS) for the optimal estimator is demonstrated for two-way ranging (TWR) when bounded noise is present. Ultimately, a mobile robot is designed to execute curvilinear motion, and the effectivity for the localization method is confirmed through an example.