四元数

The former can provides a shorter path and least action to reach the desired equilibrium point; and the latter proposes a class of linear sliding-mode, which not only guarantees global nonsingular but also uncouples the original control system.

改进的PID控制律保证了闭环系统能够沿最短路径趋于稳态值；解耦变结构控制律直接针对完整的四元数设计一类线性滑模，从而避免了奇异问题，而且对原控制系统解耦。

While by introducing the spherical simplex UT, a better-behaved sigma point selection strategy, the number of sigma points required to the same transformation accuracy can be dramatically reduced, and accordingly, the computation burden can be avoided.

在有陀螺模式下，设计了基于误差修正罗德里格参数的SUKF姿态估计算法，在计算过程中同时能够保证四元数始终归一化。在无陀螺模式，基于MRPs的姿态表示和卫星刚体动力学方程，实现了SUKF姿态估计算法。

Adopt project practical quaternion algorithm of strapdown navigation system, Analyze systematic error source, emulation prove the output change of SINS in there is device error of inertia and the initial condition of collimation error.

采用了工程上实用的四元数捷联导航系统的算法，分析了系统误差源，仿真验证了捷联惯导系统在有惯性器件误差及初始对准误差情况下的输出变化。

Based on the estimation of the directions of arrival and the Doppler frequencies of the sources, a quaternion model was proposed, which made the estimation of the DOA and the Doppler frequencies similar to that of one-dimensional azimuths so as to avoid direct and indirect pairing with the complex model.

针对阵列信号处理中方向角、多普勒频率的同时估计问题，提出了方向角、多普勒频率的四元数模型，使估计方向角、多普勒频率二维问题与估计一维问题相类似，从而避免了在经典的二维复数模型估计中直接或间接的配对。

Muti antennae GPS/Gyro integrated navigation system is studied too in this paper. Using single difference GPS carrier phase observations and quaternion error, state equation and measurement equation is established for muti antennae GPS/Gyro integrated navigation system.

本文也对多天线GPS/Gyro组合捷联航姿系统进行了研究，利用单差载波相位测量的方法，建立了基于四元数误差的多天线GPS与Gyro组合航姿系统的状态方程和量测方程。

The use of quaternions can replace tensors in representation.

四元数可以用来取代张量表示。

The algebra of quaternions, the first noncommutative algebra was thus suddenly born.

四元数的代数，第一非交换的代数，就这样在一夜之间诞生了。

The algebra of quaternions, the first noncommutative algebra was thus suddenly born

四元数的代数，第一非交换的代数，就这样突然诞生了。

The argument finds the angle of the 4- vector quaternion from the unit scalar i.e.

辐角函数可找出一4-向量四元数偏离单位纯量(即：1)之角度。

First, according to the tracking error dynamics and kinematics described by unit quaternion error and angular velocity error, a sliding mode controller is derived based on Lyapunov theory.

首先根据由误差四元数和误差角速度描述的跟踪误差动力学和运动学方程，设计了基于李亚普诺夫方法的滑模变结构控制律。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。