捷联惯性导航传统比力积分算法与对偶四元数算法的比较研究

捷联惯性导航速度更新算法中,将载体坐标系中的比力积分增量变换到导航参考坐标系中,载体姿态变化的影响通常采用一阶近似模型进行计算。本文分析了包括角振动和加速运动的动态运动下一阶近似模型的局限,在典型角振动及加速运动条件下对忽略姿态变化二阶项造成的速度更新误差进行了理论分析。通过比较,揭示了对偶四元数比力积分算法精度高于传统比力积分算法的原因,即和传统比力积分算法相比,对偶四元数比力积分算法等价于考虑了载体姿态变化影响的二阶项。通过典型角振动及加速运动条件下传统捷联惯性导航算法和对偶四元数导航算法的仿真比较,对理论分析结果进行了验证。     

基于对偶四元数的捷联惯导算法在发射点惯性系下的应用研究

针对导弹类载体在做复杂的高动态机动时,采用传统的捷联惯导算法容易产生圆锥误差与划船误差,从而导致解算精度降低的问题,在发射点惯性系下设计了基于对偶四元数的捷联惯导算法。在建立发射点惯性系下的捷联惯导解算模型的基础上,详细推导了基于对偶四元数的捷联惯导解算算法,通过对比分析其中的速度更新过程与传统算法的差异,说明该算法可以有效提高速度和位置解算精度。在设计的多条机动飞行轨迹下,以三子样更新为例,对对偶四元数算法和传统算法的性能进行了仿真对比分析。仿真结果表明,对偶四元数导航算法可以有效提高速度和位置解算精度,且姿态机动情况越复杂、持续时间越长,改善效果越显著。     

Strapdown inertial navigation system algorithms based on dual quaternions

The design of strapdown inertial navigation system (INS) algorithms based on dual quaternions is addressed. Dual quaternion is a most concise and efficient mathematical tool to represent rotation and translation simultaneously, i.e., the general displacement of a rigid body. The principle of strapdown inertial navigation is represented using the tool of dual quaternion. It is shown that the principle can be expressed by three continuous kinematic equations in dual quaternion. These equations take the same form as the attitude quaternion rate equation. Subsequently, one new numerical integration algorithm is structured to solve the three kinematic equations, utilizing the traditional two-speed approach originally developed in attitude integration. The duality between the coning and sculling corrections, raised in the recent literature, can be essentially explained by splitting the new algorithm into the corresponding rotational and translational parts. The superiority of the new algorithm over conventional ones in accuracy is analytically derived. A variety of simulations are carried out to support the analytic results. The numerical results agree well with the analyses. The new algorithm turns out to be a better choice than any conventional algorithm for high-precision navigation systems and high-maneuver applications. Several guidelines in choosing a suitable navigation algorithm are also provided.     

Strapdown INS error model for multiposition alignment

The relationship between quaternion errors and tilt angles from true navigation frame to analytic platform frame is newly derived for strapdown inertial navigation system (SDINS). Using the relationship it is shown that the quaternion error model for attitude and velocity is equivalent to the conventional perturbation error model. Based upon the equivalency, the quaternion errors during a multiposition alignment are determined and analyzed. Furthermore, it is shown that the heading rotation of 180 deg achieves the minimal quaternion error for 2-position ground alignment     

一种圆锥运动条件下的等效旋转矢量算法研究

传统旋转矢量姿态算法一般采用陀螺的角增量信号来构造积分算法,当应用于输出为角速率的光纤陀螺捷联系统时,通过角速率提取角增量,算法会损失一定精度。提出了一种以陀螺角速率信号与角增量信号同时作为输入的改进旋转矢量姿态算法,进一步补偿了圆锥误差,提高了计算精度。仿真结果表明,该算法与传统二子样算法相比较,计算量相当,姿态精度、速度精度、位置精度有大幅度的提升。     

基于对偶四元数的INS/GPS组合导航算法研究

在基于对偶四元数的捷联惯导解算方法的基础上,推导了以惯性系作为导航系的惯导误差方程,在此基础上设计了卡尔曼滤波组合导航算法。通过激光惯导跑车采集数据,进行了仿真分析,试验结果表明,该组合导航算法能有效的消除惯导累积的速度误差和位置误差,相比于目前广泛应用的INS/GPS组合导航算法,本文描述了INS/GPS组合导航的另一种实现方式,获得了相当的精度,具有一定的工程应用价值。     

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.     

Interlaced optimal-REQUEST and unscented Kalman filtering for attitude determination

 Aimed at low accuracy of attitude determination because of using low-cost components which may result in non-linearity in integrated attitude determination systems, a novel attitude determination algorithm using vector observations and gyro measurements is presented. The various features of the unscented Kalman filter (UKF) and optimal-REQUEST (quaternion estimator) algorithms are introduced for attitude determination. An interlaced filtering method is presented for the attitude determination of nano-spacecraft by setting the quaternion as the attitude representation, using the UKF and optimal-REQUEST to estimate the gyro drifts and the quaternion, respectively. The optimal-REQUEST and UKF are not isolated from each other. When the optimal-REQUEST algorithm estimates the attitude quaternion, the gyro drifts are estimated by the UKF algorithm synchronously by using the estimated attitude quaternion. Furthermore, the speed of attitude determination is improved by setting the state dimension to three. Experimental results show that the presented method has higher performance in attitude determination compared to the UKF algorithm and the traditional interlaced filtering method and can estimate the gyro drifts quickly.     

旋转三子样高精度捷联惯性导航算法

针对捷联惯导系统高精度导航的需求,以螺旋理论为基础,采用螺旋补偿三子样推导出对偶四元数所表示的捷联惯导算法,并同时对载体的姿态、速度、位置进行更新,并以四阶截断三角级数近似三角函数进行对偶四元数更新和螺旋矢量更新。仿真和跑车实验结果表明：螺旋三子样捷联惯性导航算法的导航精度比一般四元数算法提高约15%,为相关领域的研究与实际应用提供参考。     

一种新的低成本组合导航系统初始对准算法

基于低成本惯性测量单元的组合导航系统已经逐步成为导航领域的研究热点和主要发展方向。但是,低成本惯性元件精度低,无法进行自主初始对准。基于规范化四元数的概念,研究了一种仅利用GPS的位置和速度数据对组合系统进行初始对准的新算法,克服了传统滤波方法进行初始对准存在的诸多局限性。理论分析和仿真计算表明,这种算法仅受组合系统自身硬件条件的约束,可以较好地应用于组合系统中低成本惯性单元的初始对准。     

An improved quaternion Gauss–Newton algorithm for attitude determination using magnetometer and accelerometer

For the vector attitude determination, the traditional optimal algorithms which are based on quaternion estimator(QUEST) measurement noise model are complicated for just two observations. In our application, the magnetometer and accelerometer are not two comparable kinds of sensors and both are not small field-of-view sensors as well. So in this paper a new unit measurement model is derived. According to the Wahba problem, the optimal weights for each measurement are obtained by the error variance researches. Then an improved quaternion Gauss–Newton method is presented and adopted to acquire attitude. Eventually, simulation results and experimental validation employed to test the proposed method demonstrate the usefulness of the improved algorithm.     

扰动线运动对惯性系粗对准影响分析及优化方法

针对扰动线运动对惯性系粗对准精度影响较大的问题,通过分析惯性体坐标系下重力加速度积分矢量的物理含义,给出了受扰动线运动影响的惯性系粗对准的误差分析。并在此基础上提出了基于位移积分矢量构造定姿矢量矩阵的抗扰动粗对准算法,利用对速度积分矢量进一步积分得到的3个时间点的位移积分矢量构建姿态解算矩阵,抑制扰动线运动对粗对准精度的影响。仿真结果表明,该算法可有效减小扰动线运动影响下的对准结果振动幅值,能够快速收敛到满足精对准使用的精度范围,从而提高武器装备环境适应性。     

扰动线运动对惯性系粗对准影响分析及优化方法

针对扰动线运动对惯性系粗对准精度影响较大的问题，通过分析惯性体坐标系下重力加速度积分矢量的物理含义，给出了受扰动线运动影响的惯性系粗对准的误差分析。并在此基础上提出了基于位移积分矢量构造定姿矢量矩阵的抗扰动粗对准算法，利用对速度积分矢量进一步积分得到的3个时间点的位移积分矢量构建姿态解算矩阵，抑制扰动线运动对粗对准精度的影响。仿真结果表明，该算法可有效减小扰动线运动影响下的对准结果振动幅值，能够快速收敛到满足精对准使用的精度范围，从而提高武器装备环境适应性。     

基于改进容积卡尔曼滤波的奇异避免姿态估计

 利用矢量进行卫星姿态估计可以归结为非线性滤波问题。为了提高卫星姿态估计的精度,利用龙贝格-马尔塔(LM)迭代算法改进了容积卡尔曼滤波(CKF)。继而,提出改进容积卡尔曼滤波与四元数结合的容积四元数估计器(CQE),有效地避免了卫星大角度机动出现的奇异现象。进一步,给出了一种与影子修正罗德里格参数切换的容积修正罗德里格参数估计器(CME)。仿真对比表明,初始误差较大时容积修正罗德里格参数估计器具有更好的收敛速度和鲁棒性。     

Comparison of SDINS in-flight alignment using equivalent errormodels

The psi-angle model and the equivalent tilt (ET) model have been widely used for in-flight alignment (IFA) to align and to calibrate a strapdown inertial navigation system (SDINS) on a moving base. However, these models are not effective for a system with large attitude errors because the neglected error terms in the models degrade the performance of a designed filter. In this paper, with an odometer as an external aid, a velocity-aided SDINS is designed for IFA. Equivalent error models applicable to IFA with large attitude errors are derived in terms of rotation vector error and additive and multiplicative quaternion errors. It is found that error models in terms of additive quaternion error (AQE) become linear. Thus the proposed error models reduce unmodeled error terms for a linear filter. From a number of van tests, it is shown that the proposed error models effectively improve the performance of IFA     

提高飞行器姿态角计算精度的方法研究

分析了传统的通过方向余弦矩阵、四元数形式的飞行器转动微分方程数值积分结果确定姿态角方法的不足,介绍了基于改进的牛顿法确定飞行器姿态角的方法.基于多次测量均值效应原理,介绍多使用上述两种方法中的元素提高飞行器姿态角计算精度的算法及仿真结果.     

卫星拒止情况下低精度惯导系统航姿算法研究

在卫星拒止情况下,低精度MEMS惯导系统由于惯性器件性能较差,无法长时间保持姿态精度。从重力矢量及飞行器的动力学特性出发,提出了一种基于动态检测和Kalman数据融合的航姿算法。该算法从导航与飞控一体化的理念出发,实时判断飞行器机动和飞控状态,在低动态时利用Kalman滤波器对水平加速度和惯性解算的姿态角进行数据融合,估计和修正水平姿态误差,从而提高水平姿态精度。经过飞行仿真验证,该算法可有效完成飞行器的动态检测,并保证在系统机动情况下水平姿态误差在2°以内。     

基于改进UKF的组合导航系统航向角估计方法研究

为满足运载体长航时、高精度的导航需求,解决系统可观测性弱导致的航向角易发散的问题,提出了一种基于MEMS非线性组合导航系统的用于提高航向角估计精度的算法。通过采用单天线GNSS航向角作为量测量进行航向约束,解决了MEMS-SINS/GNSS姿态估计中航向角可观测性弱、估计值收敛差的问题;通过转弯判断规则和常规无迹卡尔曼滤波改进算法,抑制了偏流角对系统估计精度的影响。仿真结果表明,该算法有效地抑制了航向角估计精度差的问题,水平姿态精度达到0.01°,航向角精度达到0.1°,提高了系统的导航精度及可靠性。     

航天器太阳圆面速度差/太阳视方向组合导航

针对航天器，尤其是深空探测器的自主导航问题，提出了一种新的太阳圆面速度差天文量测信息，该信息利用太阳的较差自转所造成的太阳圆面各点速度不同的特性，是探测器当前位置的函数，其几何本质是一个探测器的位置圆锥。在此基础上，基于太阳圆面速度差和太阳视方向互补的特性，提出了一种太阳圆面速度差/太阳视方向组合导航新方法，将太阳圆面速度差与太阳视方向2种量测量结合起来，实现了量测量之间的优势互补，进一步提高了导航性能。以太阳探测器为例进行了仿真，仿真结果表明相比较于单独用太阳圆面速度差或太阳视方向的导航方法，基于太阳圆面速度差/太阳视方向的组合导航方法精度分别提升了10.2%和16.0%。此外，还分析了光谱仪精度、采样周期和光谱仪数量对导航性能的影响，为深空探测自主导航提供了新的理论与方法。     

Pseudo-linear inertial navigation algorithm

A new method is illustrated for processing the output of a set of triad orthogonal rate gyros and accelerometers to reconstruct vehicle navigation parameters (attitude, velocity, and position). The paper introduces two vectors with dimensions 4 × 1 as velocity and position quaternions. The navigation equations for strapdown systems are nonlinear but after using these parameters, the navigation equations are converted into a pseudo-linear system. The new set of navigation equations has an analytical solution and the state transition matrix is used to solve the linear time-varying differential equations through time series. The navigation parameters are updated using the new formulation for strapdown navigation equations. Finally, the quaternions of velocity and position are converted into the original position and velocity vectors. The combination of the coning motion and a translational oscillatory trajectory is used to evaluate the accuracy of the proposed algorithm. The simulations show significant improvement in the accuracy of the inertial navigation system, which is achieved through the mentioned algorithm.