Moving Horizon Estimation with a huber penalty function for robust pose estimation of tethered airplanes

This paper presents a Moving Horizon Estimator (MHE) for estimating the position and orientation (pose) of moving objects, in particular for tracking tethered airplanes for Airborne Wind Energy systems. In this application, absolute pose measurements are captured by a marker based stereo vision system. These measurements are fused with measurements of the angular velocity and linear acceleration from an Inertial Measurement Unit (IMU). In our MHE, the IMU measurements in the intervals between camera frames are modeled as samples of a superposition of orthonormal polynomial basis functions. This results in a MHE formulation that requires fewer optimization variables, enabling faster solution. In order to achieve robustness to marker detection errors, a formulation based on the Huber penalty is also presented. We show that our robust MHE formulation outperforms a MHE formulation using the ℓ₂-norm and a traditional extended Kalman filter.