基于不确定椭球的全局姿态估计
Global Attitude Estimation using Uncertainty Ellipsoids
摘要：
姿态估计通常是机械系统姿态或方向控制的先决条件。目前的姿态估计算法使用坐标表示法的刚体取向的组。方位组的所有坐标表示法都有相关的问题。虽然最小坐标表示法表现出运动学奇异性的大旋转，非最小坐标，如四元数需要满足额外的约束。研究了测量误差有界的刚体确定性姿态估计问题。给出了一种全局最小化姿态估计误差的姿态估计算法。假设初始姿态、初始角速度和测量噪声都在给定的椭球范围内，得到了刚体姿态和角速度的不确定椭球。不确定性椭球的中心提供点估计，不确定性椭球的大小度量估计的准确性。点估计和不确定性椭球分别使用李群变分积分器和其线性化进行传播。在姿态估计误差和不确定椭球尺寸最小的意义下，姿态估计是最优的。
英文摘要：
Attitude estimation is often a prerequisite for control of the attitude or orientation of mechanical systems. Current attitude estimation algorithms use coordinate representations for the group of rigid body orientations. All coordinate representations of the group of orientations have associated problems. While minimal coordinate representations exhibit kinematic singularities for large rotations, non-minimal coordinates like quaternions require satisfaction of extra constraints. A deterministic attitude estimation problem for a rigid body with bounded measurement errors is considered here. An attitude estimation algorithm that globally minimizes the attitide estimation error, is obtained. Assuming that the initial attitude, the initial angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and the size of the uncertainty ellipsoid measures the accuracy of the estimates. The point estimates, and the uncertainty ellipsoids are propagated using a Lie group variational integrator, and its linearization, respectively. The attitude estimation is optimal in the sense that the attitude estimation error and the size of the uncertainty ellipsoid is minimized.
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