Error analysis of quaternion transformations [inertial navigation]

Three transformation formulas that relate the quaternions to the direction cosine matrix used in strapdown inertial systems are derived. An error model associated with the computed direction cosine matrix is briefly discussed. Error analysis is fully evaluated analytically and tabulated for comparison. Transformation errors associated with these formulas are analyzed. The drift errors evaluated under constant angular velocity are shown to vary slightly among three different transformations. It is shown that the skew errors in three transformation schemes are not all intrinsically zero. The scale errors may differ largely by two orders of magnitude among transformation schemes. This may become a criteria for selection of altitude transformation schemes     

Multilateration Error Ellipsoids

Formulas are derived for the lengths and direction cosines of the semiaxes of error ellipsoids in three-dimensional multilateration, in terms of the rms errors and direction cosines of the distance measurements, for the case in which random measurement errors are normally distributed and systematic errors are negligible. Two-dimensional error ellipses also are discussed.     

Analysis Strapdown Navigation Using Quaternions

A brief review of the theory of strapdown inertial navigation is presented in which the attitude of the sensor box with respect to inertial space is represented by the four-parameter quaternion vector. . A 4X4 matrix R is defined which aids in relating quaternions to direction cosines and facilitates interpretation of the equations for error propagation, which are also derived. In the interpretation, it is shown that the error in the quaternion vector causes aor-(correctable) scale factor error and an equivalent tilt vector error that propagates the same way as the platform tilt vector in a gimbaled system.     

刚体姿态仿真方法研究

首先论述了姿态描述的四种方法:欧拉角、欧拉轴旋转参数、方向余弦和四元数法,重点介绍了四元数法在飞行器运动学上的应用,它消除了欧拉方程的奇异性,计算效率也远远优于其他三种方法;最后讨论了数值仿真的方法及误差。     

Gyro Misalignment and Encoder Quantization Effects During Multi-Axis Evaluation of Strapdown Gyros

This paper presents a quantitative discussion of two error sources which affect the accuracy of data comparison between instrument outputs and reference angle computations during multi-axis evaluation of strapdown gyros. The error due to misalignment of gyro input axes is formulated in terms of closed-form solutions for typical relationships between the three table gimbal rotation histories. If the angular positions of the table gimbal axes are measured by shaft encoders, then any measurement has an uncertainty in the range from plus to minus one-half of the quantization level. It is shown that the effect of encoder quantization error on the computer transformed angles in the bodyfixed coordinate system can be divided into two parts: the initial uncertainty of the zero positions of the gimbals before table motion is begun, and all subsequent error contributions during table test. Typical data for gyro misalignment and encoder quantization error effects are presented.     

伺服加工平台的综合误差建模与补偿

伺服加工平台的几何误差是影响工件加工形貌精度的重要因素。在多体系统理论的基础上,首先,运用低序体阵列描述伺服平台多体系统的拓扑结构,建立各相邻体间的齐次变换矩阵,构建其综合误差模型;其次,利用雷尼绍测量系统对平台的定位误差、直线度误差、俯仰误差、偏摆误差以及两轴之间的垂直度误差进行辨识,将辨识得到的误差值代入构建的模型得出平台几何综合误差;最后,选择凸锥面、平面、球面3种面型工件补偿试验,对误差模型进行原理性验证。研究表明,经补偿后加工所得3种面型工件表面精度均提高了25%左右,证实了提出的补偿方法可用于伺服加工平台几何误差控制。     

控制体有限元方法中的一种高阶插值格式

针对控制体有限元方法对流动方向不平行于坐标轴方向的回流问题数值模拟采用各种迎风格式都容易产生假扩散的问题,本文给出了一种由插值单元及其迎风相邻单元所确定的高阶插值格式。通过对Re=1000时三种不同形状的二维四边形空穴流模拟,表明该格式与局部斜迎风格式的适当组合可有效地减小控制体有限元方法对回流问题数值模拟的假扩散。      

Principles Involved in the LM Rendezvous Radar Redundant Gyro System

For typical failure rates the probability of two or more of four gyros failing is very much less than one or both of two. Thus, a single redundancy system of four gyros greatly enhances system reliability. The orientation of the sensitive axes of four gyros is specified and means of generating outputs dependent only on gyro inconsistencies are defined. The voting logic and plots of switching decision zones are developed. The hardware required to implement this logic is shown to be simple and thus reliable. The use of rate integrating gyros requires the limitation of error integration time in order to avoid spurious failure signals. This is achieved by a reset cycle which realigns the four gyros at regular intervals. False error signals can be generated if inputs are large enough to exceed linear ranges of various components downstream of the gyros.     

线性极化敏感阵列的极化平滑算法及相干源参数估计

 研究了基于极化敏感阵列的相干信号参数估计问题。首先,提出一种利用均匀线性极化敏感阵列的新型极化平滑算法(ULAPSA),其能够处理更多相干信号的参数估计,且具有更小的计算量。然后,基于ULAPSA给出了波达方向（DOA）和极化参数估计的两种方法：第1种方法利用角度搜索得到信号的DOA估计,适应任何多分量的电磁矢量传感器阵列;第2种方法结合传播算子算法,无需奇异值分解和角度搜索,能够同时估计信号的DOA和极化参数。该方法适应完备的电磁矢量传感器、三偶极子或三磁环构成的矢量传感器。最后,通过仿真实验比较和分析了所提算法的性能。     

导航中单位矢量的二次旋转乘法观测模型

视线矢量观测是实现自主导航的重要方式。本文针对单位矢量的加法观测模型中观测矢量非单位化问题和乘法观测模型中测量噪声与实际情况不符的问题,提出二次旋转乘法观测模型。通过真实矢量在正交方向上进行的两次刚体旋转,获得了与现有乘法观测模型形式相同、但旋转角服从瑞利分布的正确观测方程。推导了测量误差的统计特性和双矢量观测的性质,并从空间几何角度给予了解释。数值仿真结果表明,二次旋转乘法观测模型弥补了由加法观测模型线性化所引起的问题,具有更精确的误差形式,由此给出了模型的潜在应用范围。     

Insight into an Integration Algorithm

This paper develops, in a unique manner, a numeric algorithm for an integration and extrapolation scheme. The purpose of presenting it in this manner is to develop in the reader a complete understanding of how the algorithm is derived. It is also intended to give an insight into the limitations of the algorithm and to serve as a tool to derive additional integration schemes.     

Estimation of ballistic coefficients of space debris using the ratios between different objects

This paper proposes a new method to estimate the ballistic coefficient (BC) of low earth orbit space debris.The data sources are the historical two-line elements (TLEs).Since the secular variation of semi-major axes is mainly caused by the drag perturbation for space objects with perigee altitude below 600 km,the ballistic coefficients are estimated based on variation of the mean semi-major axes derived from the TLEs.However,the approximate parameters used in the calcu lation have error,especially when the upper atmosphere densities are difficult to obtain and always estimated by empirical model.The proportional errors of the approximate parameters are cancelled out in the form of ratios,greatly mitigating the effects of model error.This method has been also been validated for space objects with perigee altitude higher than 600 km.The relative errors of esti mated BC values from the new method are significantly smaller than those from the direct estimation methods used in numerical experiments.The estimated BC values are used for the prediction of the semi-major axes,and good performance is obtained.This process is also a feasible method for prediction over a long period of time without an orbital propagator model.     

Event-triggered adaptive control for attitude tracking of spacecraft

Plug-and-play technology is an important direction for future development of spacecraft and how to design controllers with less communication burden and satisfactory performance is of great importance for plug-and-play spacecraft. Considering attitude tracking of such spacecraft with unknown inertial parameters and unknown disturbances, an event-triggered adaptive backstepping controller is designed in this paper. Particularly, a switching threshold strategy is employed to design the event-triggering mechanism. By introducing a new linear time-varying model, a smooth function, an integrable auxiliary signal and a bound estimation approach, the impacts of the network-induced error and the disturbances are effectively compensated for and Zeno phenomenon is successfully avoided. It is shown that all signals of the closed-loop system are globally uniformly bounded and both the attitude tracking error and the angular velocity tracking error converge to zero. Compared with conventional control schemes, the proposed scheme significantly reduces the communication burden while providing stable and accurate response for attitude maneuvers. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

Fiber-optic strapdown inertial system with sensing cluster continuous rotation

This research describes a technique and a performance analysis of a fiber-optic strapdown inertial system with sensing cluster continuous rotation around the vertical body axis of the vehicle. The bias errors of these inertial sensors, gyros and accelerometers with cluster rotation, will have periodically varying corresponding components along the body axes. The modulated sensor errors produce reduced system errors. Simulation results indicate that, compared with the conventional method, the proposed approach attenuates the navigation errors and alignment errors due to the gyros' error and the accelerometers' error.     

后置静叶周向弯曲对表面非定常压力脉动的影响

在目前的叶轮机械中,普遍存在着旋转动叶与后置静叶干涉产生的非定常流动现象。这种流动现象会导致静叶表面产生非定常性压力脉动。这种脉动可分为旋转动叶的速度亏损尾迹引起的叶片表面的周期性脉动和气流本身的湍流脉动及其他涡团导致的随机脉动两个方面。采用一工业用单级通风机,对其动静叶的干涉现象进行研究。通过在后置静叶表面沿弦长及叶高方向布置动态压力传感器的方法,研究静叶的周向弯曲（倾斜）角度对静叶表面的非定常力的影响。研究结果表明：采用周向弯曲静叶会改变动叶尾迹所引起的后置静叶周期性脉动的幅值在静叶表面的分布特点,静叶顶部压力脉动的幅值与原始径向静叶相比能够有效地降低,同时与中部的压力幅值相比有一定提高,但整体呈现下降趋势;另一方面,静叶表面随机性的压力脉动强度受周向弯曲的影响较小。     

Strapdown inertial navigation using dual quaternion algebra: error analysis

In a strapdown inertial navigation system (INS), the general displacement of a rigid body is traditionally separately modeled and analyzed, i.e., direction cosine matrix or quaternion for rotation analysis and vector for translation analysis. As a subsequent work of a companion paper (Wu et al., 2005), this paper adopts dual quaternion algebra, a most concise and unified mathematical tool for representing the general displacement of a rigid body, to analyze error characteristics of the strapdown INS. Two new error models in terms of quaternion algebra are developed: the additive dual quaternion error (ADQE) model and multiplicative dual quaternion error (MDQE) model. Both are expected to facilitate the future inertial navigation-based integrated navigation filter.     

MEMS加速度计组合在分度头上的标定方法

提出了一种在分度头上标定MEMS加速度计组合的测试方法,该方法可以标定出加速度计组合的刻度系数误差、加速度计零偏、三轴不正交度误差、安装误差角,同时可以分离出分度头转位机构角位置误差.首先通过建立一系列坐标系,推导了重力加速度在加速度计敏感轴的分量表达式.然后采用谐波分析法给出了误差标定方程,利用最小二乘法和Kalman滤波器进行误差参数的估计,并对估计结果进行了对比分析.最后通过三次独立实验标定结果的重复性和残差验证了该方法的正确性.     

无尾布局纵向操纵的嵌入式舵面概念研究

基于提高W型无尾翼身融合布局大迎角俯仰操纵能力的设想,探索一种机身下表面嵌入式俯仰操纵舵面的新概念。采用CFD方法,研究纵向两个位置、两种弦向长度组成的四种机身下表面嵌入式舵面构型对无尾气动布局性能的影响及其流动机理,分析了嵌入式舵面提供纵向操纵控制的作用原理。研究结果表明,下表面嵌入式舵面可作为无尾布局大迎角俯仰操纵的有效补充措施,为无尾布局大迎角俯仰操纵提供了新的技术途径,具有进一步深入研究的价值。     

基于INS/前视声纳组合的输水隧洞AUV巡检定位方法

当潜航器(AUV)进行输水隧洞巡检时,多普勒测速仪(DVL)声波会对前视声纳图像产生干扰,针对这一问题提出了一种从AUV上卸载DVL,直接从前视声纳图像中提取栽体速度,而后和惯性测量单元(IMU)进行组合导航的方法.该方法根据前视声纳成像原理,建立起每相邻两帧声纳图像间载体的相对位移与配对特征点的图像坐标之间的联系,针对水底为局部平坦区域的情况,对特征点仰角进行了估算.通过惯导速度约束和随机抽样一致(RANSAC)算法,剔除误差较大的配对点,然后利用提取出的载体速度作为观测量进行卡尔曼滤波.经实际数据测试,惯性导航系统(INS)/前视声纳组合的总体性能和INS/DVL组合非常接近,以输水隧洞内的接缝线作为定位基准,INS/前视声纳组合导航在沿隧洞方向上的最大相对定位误差小于行程的1％.     

磁悬浮定中偏差对陀螺加速度计精度的影响

在陀螺加速度计磁悬浮定中测试实验中发现,当加表处于斜置状态时,磁悬浮不能使浮子轴精确定中,浮子轴两端出现了周期性的摆动。本文分析了这一现象的产生机理,并进一步从不同方面研究了磁悬浮不能使浮子轴精确定中对加表测量精度的影响,推导了误差公式。