Comparison of strapdown inertial navigation algorithm based on rotation vector and dual quaternion

 For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in accuracy is analyzed in the case of the rotation of navigation frame. By comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as much as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations are carried out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm.     

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。     

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.     

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     

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。     

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.     

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.     

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。     

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。     

视觉辅助惯性定位定姿技术研究

在利用视觉系统辅助捷联惯性导航系统( SINS)进行定位定姿时,由于两者输出的位置表示方法不同,在信息融合时会存在匹配问题。以相对地理坐标系作为定位定姿系统的导航坐标系,重新对SINS进行了力学编排,分析了其误差传递特性,建立了相对地理坐标系下的状态方程模型,并利用Kalman滤波器实现了视觉辅助惯性定位定姿算法。仿真结果表明,方法避免了信息融合时位置匹配问题,同时降低了系统的计算量,满足了定位定姿系统的精度要求。     

用于微机械捷联式航姿系统的四元素算法卡尔曼滤波器

介绍了一种卡尔曼滤波器 ,它适用于由微机械惯性传感器构成的捷联式航姿系统。文中阐述了系统构成和原理 ,基于四元素算法公式推导了姿态算法和系统误差模型 ,并设计了实时卡尔曼滤波器。仿真结果表明 ,当没有横向加速度干扰时系统精度优于 0 .0 4度 ,当出现 0 .1g/1Hz的横向交变加速度干扰时 ,精度降为 0 .4 4度。初步测试结果表明系统的静态精度为 :俯仰和横滚 /-0 .2度 ,航向 /- 0 .3度。     

Inner Attitude Integration Algorithm Based on Fault Detection for Strapdown Inertial Attitude and Heading Reference System

This article proposes a new inner attitude integration algorithm to improve attitude accuracy of the strapdown inertial attitude and heading reference system(SIAHRS), which, by means of a Kalman filter, integrates the calculated attitude from the accelerometers in inertial measuring unit(IMU), called damping attitudes, with those from the conventional IMU. As vehicle's acceleration could produce damping attitude errors, the horizontal outputs from accelerometers are firstly used to judge the vehicle's motion so as to determine whether the damping attitudes could be reasonably applied. This article also analyzes the limitation of this approach. Furthermore, it suggests a residual chi-square test to judge the validity of damping attitude measurement in real time, and accordingly puts forward proper information fusion strategy. Finally, the effectiveness of the proposed algorithm is proved through the experiments on a real system in dynamic and static states.     

双轴连续旋转调制捷联惯导系统大失准角初始对准技术

由于可以补偿惯性器件在三个轴向上的输出误差，双轴旋转调制技术被广泛应用于捷联惯导系统(SINS)。选择了一种合理且实用的十六次序双轴转位方案，并对其调制原理和误差进行了分析。初始对准技术是捷联惯导系统的一项重要技术，其对准精度直接决定了后续导航的精度。在粗对准完成后，当姿态误差角较大时，后续的精对准误差模型呈非线性特性，故选择了滤波精度高、稳定性强的平方根容积Kalman滤波算法(SCKF)来解决这一问题。考虑到在实际对准过程中，量测噪声的统计特性易发生变化，将SCKF算法与Sage-Husa算法相结合，在传统Sage-Husa SCKF算法的基础上提出了一种改进的自适应滤波算法(ASCKF)。该算法采用QR分解来完成对噪声协方差的平方根矩阵估计，从而避免了传统Sage-Husa SCKF算法中所估噪声协方差矩阵不正定的问题。最后，通过仿真证实了ASCKF算法可被很好地应用于量测噪声统计特性发生变化的初始对准中。     

Modeling quaternion errors in SDINS: computer frame approach

We propose new equivalent tilt error models which are applicable to the analysis of the terrestrial strapdown inertial navigation systems (SDINS), based on the quaternions. The currently available equivalent tilt error models, like the conventional Φ model of the gimbaled inertial navigation systems (GINS), are derived only by the true frame approach. The true frame approach has a computational disadvantage that it produces an error model where the attitude error equation is coupled with its position and velocity error equations. The motivation of this work is to solve this problem. As a result, two kinds of error models are derived. Among them, one is derived by the computer frame approach for practical onboard implementations. Thus, like the conventional GINS Ψ model, its attitude error equation is decoupled from the position and velocity error equations. The other is derived in order to show the relationship between the true frame approach and the computer frame approach which are applied to the quaternion-based SDINS. Thus, like the GINS δΘ model, it can be used to transform the error variables into each other which are calculated by the two different approaches     

基于卫星和星敏感器的冗余激光惯组在轨标定

采用高精度卫星导航速度、位置信息以及星敏感器提供的姿态信息设计十表冗余捷联惯组的标定模型,包含陀螺和加速度计的零次项和标度因数,对卫星和星敏感器辅助的冗余激光陀螺捷联惯组进行实时在轨标定.利用标准Kalman滤波和Sage-Husa自适应滤波作为估计算法,对十表冗余捷联惯组参数进行在线估计.数值仿真结果表明:参数标定精度均在7％以内,是一种实时的在轨标定方法,满足误差补偿要求.冗余惯组在轨标定方法为航天器高精度定姿和定轨提供了一种理论参考.     

空间平台机动变轨自主导航研究

针对空间平台在高轨道机动变轨过程中自主导航的需求,采用了基于Kalman滤波器的捷联惯导与星敏感器的组合导航方案。结合Kalman滤波中协方差更新的误差分配分析方法,分析了影响空间平台状态估计误差的主要因素。采用适用于高轨道的球谐重力模型,运用STK工具包设计了变轨机动轨迹,将该轨迹应用于组合导航方案的仿真验证。仿真结果表明,量测噪声是影响空间平台姿态精度的主要因素,加速度计零偏对变轨过程速度精度有决定性影响,改善两者的精度可以实现空间平台机动变轨的高精度自主导航。     

纬度未知条件下捷联惯导系统晃动基座的初始对准

针对纬度未知条件下捷联惯导系统(SINS)晃动基座的初始对准问题,提出晃动基座下的纬度估计算法和初始对准方法。前者通过惯性坐标系下两个不同时刻的重力加速度向量的夹角来求取纬度;后者利用惯性坐标系下的姿态更新来实时地反映载体在晃动干扰下的姿态变化,结合初始姿态的最优估计实现初始对准。理论分析表明,本文提出的纬度估计算法的误差主要由加速度计误差决定,陀螺误差和晃动干扰对其影响很小。仿真结果表明,本文提出的纬度估计算法和初始对准方法适用于纬度未知条件下晃动基座的初始对准。     

晃动基座捷联惯导系统初始对准迭代方法

由于受风力或发动机启动等因素的影响,惯导系统载体(如导弹、飞机、舰船和车辆)经常遇到低频晃动的情况。晃动干扰使得陀螺测量到的地球自转角速度信噪比大幅下降,从而导致常用的对准方法无法满足高精度初始对准要求。针对这一问题,提出了一种基于晃动基座的捷联惯导系统迭代初始对准方法。本方法由惯性导航计算出水平速度误差,利用最小二乘法估算出水平角速度误差、姿态误差和航向误差,然后进行迭代计算,从而算出导航初始时刻的姿态和航向。车载(发动机启动)试验结果表明,该算法既提高了晃动基座条件下的初始对准精度,航向角误差的方差采用静态对准时为0.39244°,摇摆对准为0.03331°,本文采用的迭代对准为0.00883°,缩短了对准时间,迭代对准2min的航向角精度等效于静态对准和摇摆对准5min的精度。     

捷联惯性制导系统的圆锥误差及其补偿

圆锥误差是捷联惯导系统,特别是激光陀螺捷联惯导系统重要的误差源,为提高激光捷联惯性系统的导航精度,防止姿态误差的积累,本文研究了圆锥补偿算法和圆锥补偿误差特性,给出了常用的8种圆锥补偿算法,针对激光陀螺惯组的实际应用背景,开展了弹道仿真研究,给出了圆锥误差对激光陀螺捷联惯导系统导航精度的影响和补偿修正的效果。     

低成本多传感器组合导航系统在小型无人机自主飞行中的研究与应用

为了满足小型无人机自主控制系统对导航系统性能的要求,研究低成本的基于微机电系统的捷联惯性导航系统(MEMS-SINS)/全球定位系统(GPS)/磁强计组合导航系统。提出一种利用磁强计辅助MEMS-SINS的静基座初始姿态确定方法,采用四元数误差模型对MEMS-SINS/GPS/磁强计组合导航系统进行信息融合的建模,采用基于正交三角(QR)分解的平方根无色卡尔曼滤波(UKF)非线性估计方法对组合导航系统进行数据融合,克服由于计算机舍入误差引起的状态协方差阵的计算值失去非负定性甚至对称性,通过小型无人机的自主飞行试验,证实MEMS-SINS/GPS/磁强计组合导航算法满足小型无人机自主控制系统的要求。