基于Lagrange-d 'Alembert原理的渐近稳定最优多速率刚体姿态估计
Asymptotically Stable Optimal Multi-rate Rigid Body Attitude Estimation based on Lagrange-d'Alembert Principle
摘要：
刚体姿态估计问题的处理使用离散时间拉格朗日-达朗贝尔原理。对于姿态角速度测量和方向矢量测量之间的多速率关系，考虑了三种不同的可能性：1）采样速率之间的整数关系，2）采样速率的时变关系，3）采样速率之间的非整数关系。在所有情况下，假设角速度测量值以比惯性矢量更高的速率采样。在弹体固定坐标系下，由两个或多个矢量测量值确定姿态的问题被表述为Wahba问题。在方向矢量测量不存在的时刻，姿态运动学的离散时间模型被用来传播过去的测量。离散时间拉格朗日函数被构造为在角速度估计误差中为二次的类动能项与从Wahba的代价函数获得的类人工势能项之间的差。引入一个附加的耗散项，并将离散时间拉格朗日-达朗贝尔原理应用于具有该耗散的拉格朗日量，以获得最优滤波方案。离散时间李雅普诺夫分析表明，最优滤波方案是渐近稳定的，在没有测量噪声和收敛域几乎是全局的。为了现实的评估方案，数值实验进行有界测量噪声损坏的输入。这些数值模拟表现出收敛的估计状态的实际状态的有界邻域。
英文摘要：
The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states.
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