Abstract
This paper proposes a nonlinear stochastic complementary filter design for inertial navigation that takes advantage of a fusion of Ultra-wideband (UWB) and Inertial Measurement Unit (IMU) technology ensuring semi-global uniform ultimate boundedness (SGUUB) of the closed loop error signals in mean square. The proposed filter estimates the vehicle's orientation, position, linear velocity, and noise covariance. The filter is designed to mimic the nonlinear navigation motion kinematics and is posed on a matrix Lie Group, the extended form of the Special Euclidean Group $\mathbb{SE}_{2}\left(3\right)$. The Lie Group based structure of the proposed filter provides unique and global representation avoiding singularity (a common shortcoming of Euler angles) as well as non-uniqueness (a common limitation of unit-quaternion). Unlike Kalman-type filters, the proposed filter successfully addresses IMU measurement noise considering unknown upper-bounded covariance. Although the navigation estimator is proposed in a continuous form, the discrete version is also presented. Moreover, the unit-quaternion implementation has been provided in the Appendix. Experimental validation performed using a publicly available real-world six-degrees-of-freedom (6 DoF) flight dataset obtained from an unmanned Micro Aerial Vehicle (MAV) illustrating the robustness of the proposed navigation technique. Keywords: Sensor-fusion, Inertial navigation, Ultra-wideband ranging, Inertial measurement unit, Stochastic differential equation, Stability, Localization, Observer design.
Abstract (translated)
本文提出了一种非线性随机互补滤波设计,用于惯性导航,利用 Ultra-wideband (UWB) 和惯性测量单元 (IMU) 技术,确保半全局均匀的终极限制(SGUUB)的闭环误差信号平方meanSquare的平均值。该滤波估计了车辆的方向、位置、线性速度和噪声责任。该滤波设计模拟非线性导航运动学,并将其放置在矩阵Lie Group,即特别欧几里得组$\mathbb{SE}_{2}\left(3\right)的扩展形式。该滤波基于Lie Group的结构提供了独特的和全球表示,以避免 singularities( Euler 角度的常见缺点)和 non-uniqueness(单位元quaternion的常见限制)。与Kalman类型的滤波不同,该滤波成功地解决了IMU测量噪声,考虑未知的upper-bounded责任密度。虽然导航估计器是连续形式的,但离散形式也呈现。此外,单位元quaternion实现已提供附录。使用从无人Micro Aerial Vehicle (MAV) 获得的公开可用的现实世界六自由度(6 DoF)飞行数据集,通过实验验证展示了该导航技术的可靠性。关键词:传感器融合、惯性导航、UWB超宽带测量、惯性测量单元、随机微分方程、稳定性、定位、观测设计。
URL
https://arxiv.org/abs/2308.13393
