A Computationally Efficient Moving Horizon Estimation for Flying Robots' Localization Regarding a Single Anchor

With a low-cost inertial measurement unit (IMU) and a single ultra-wideband (UWB) anchor, one can conveniently estimate a flying robot's position with high cost-performance. To guarantee the position estimation precision during the flight, a moving horizon estimation algorithm is proposed in this work, which utilizes past measurements during a time horizon rather than a concurrent single measurement in accumulated works. Mathematically, a nonlinear least squares approach is utilized to formulate this estimation problem. According to observability analysis, directly fusing the UWB odometry with the IMU measurement may lead to an estimation failure under unobservable conditions. To tackle this issue, an additional magnitude constraint on the velocity is introduced to avoid estimation divergence in this work. On this basis, a gradient aware Levenberg-Marquardt (GALM) algorithm is further proposed to enhance the computational efficiency for the nonlinear least squares problem. Finally, experiments are carried out to verify the effectiveness of the proposed method. The results demonstrate that the method can well estimate the trajectory with an average estimation error of 0.2 m.