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.     

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。     

车载捷联惯导与里程计组合导航技术研究

惯导的误差随着时间增长是积累的,可采用里程计辅助捷联惯导构成纯自主的车载组合导航系统.利用捷联惯导的速度和里程计测量的速度之差作为观测量,通过卡尔曼滤波技术校正惯导的导航参数,可以有效地抑制惯导误差的积累,提高导航参数的精度.本文推导了组合导航系统的模型,从理论上用特征值方法分析了系统的可观测度,进而设计轨迹进行了仿真...     

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     

极区格网阻尼导航方法

针对舰艇在极区航行时,其常用惯性导航系统机械编排存在精度下降、无北向基准等问题,设计了适用于极区工作的格网坐标系捷联惯性导航系统机械编排.在构建了格网坐标系参考框架的基础上,建立了格网坐标系捷联惯导系统的机械编排,并分析了其误差传播特性.通过误差分析,确定了格网坐标系捷联惯导系统中存在的周期性振荡,并提出了适用于格网坐标系捷联惯导系统的阻尼技术,有效抑制了周期性振荡.最后,通过仿真实验验证了该系统在极区工作的可行性和阻尼技术的有效性.     

单轴旋转捷联惯导系统重力扰动补偿方法研究

随着惯性器件精度的提升以及系统级补偿技术的应用,惯性导航系统精度得到不断提升。原先忽略的一些误差源如重力扰动,成为制约惯导精度进一步提升的关键。针对该问题,研究了单轴旋转捷联惯导系统重力扰动补偿,补偿所需重力扰动信息通过德国波尔茨坦GFZ研制的EIGEN-6C4计算得到。仿真结果表明,经重力扰动补偿后,单轴旋转捷联惯导系统精度有显著提升。     

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。     

捷联惯性导航系统动静态误差特性分析研究

捷联惯性导航系统动静态误差特性是基于惯性的组合导航系统的主要误差来源。为此,根据捷联惯性导航系统的误差状态方程,本文分析了不同动静态情况下的捷联惯导系统的误差漂移特性。针对静基座和动基座的不同特点,分别采用了特征根和基于数值仿真分析的方法,并建立了相应的误差特性分析模型。重点研究了陀螺常值漂移、加速度计零位偏置和随机性误差对惯性导航系统误差漂移特性的影响;全面分析验证了惯性导航系统的动静态误差特性。本文的研究工作将为惯性组合导航系统误差分析建模提供了有益的参考。     

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.     

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.     

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     

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。     

The Psi-Angle Error Equation in Strapdown Inertial Navigation Systems

A detailed development is presented of the psi-angle vector differential equation as applied to the error analysis of strapdown inertial navigation systems. The coordinate systems involved and the psi misalignment vector are clearly defined. It is proven that apart from a sign change the psi-angle differential equation in the error analysis of strapdown inertial navigation systems is identical to the one used in conventional gimbaled inertial navigation systems.     

基于INS/GNSS紧耦合组合的逐步诱导式欺骗检测算法研究

传统惯性辅助GNSS欺骗信号检测方法对小于纯惯导误差漂移的逐步拉偏不敏感。针对这一问题,提出了一种基于INS/GNSS紧耦合组合的逐步诱导式欺骗信号检测方法。基于短时间内纯惯性导航结果和短时间惯导系统位置误差传播模型,利用惯导提供的位置和速度对伪距和伪距率时间序列进行预测估算,并结合伪距、伪距率实际测量结果,分别构造位置/伪距和速度/伪距率时间序列模型做参数拟合。基于真实信号得到的模型参数都是由惯导系统误差造成的,具有一致性;而基于逐步诱导式欺骗信号得到的模型参数还与欺骗策略的设定、载体飞行轨迹的观测以及干扰源的位置有关,具有不一致性。通过对比模型参数可判别欺骗信号的存在,对于真实信号,采用紧耦合组合导航修正INS输出;对于欺骗信号,继续惯性导航并采取相应措施。最后,根据逐步诱导式欺骗原理进行实验仿真,验证了算法的可行性和有效性。     

激光捷联惯导车载重力测量试验

惯性导航系统中加速度计测量的比力是载体运动加速度与重力加速度的矢量和,当载体运动加速度能够被有效分离时,满足一定精度水平的惯性导航系统就可以成为动态重力仪。捷联式惯性导航系统体积小、重量轻、系统组成简单,可以在记录下惯性器件原始输出信息之后,通过离线处理过程进行数据处理和精度挖掘。本文通过对某高精度激光捷联惯导进行相应的软硬件更改,获得了兼具导航及重力测量功能的一体式动态重力仪。地面车载试验是验证动态重力仪的测量精度的有效手段之一,本文将一组高速公路重复测线的数据进行了处理和分析,结果表明在平均车速72km/hr的条件下,半波长分辨率2km,自由空间重力异常内符合精度优于1mGal。     

基于组合导航技术的光纤捷联系统在线标定

 将光纤捷联系统惯性测量单元（IMU）输出误差分解成零偏误差、标度因数误差、失准角误差和随机白噪声几个部分,建立了系统误差模型,基于此模型设计卡尔曼滤波器引入高精度外部信息源对IMU进行在线标定。将此方法应用于某光纤捷联系统进行跑车试验,结果表明：引入外部信息源进行在线标定与补偿后系统纯惯导精度显著提高,本文建立的系统误差模型和在线估计方式有效估计了IMU输出误差,实现了系统在线标定,提高了系统实用精度。     

准实时性前斜视INS/SAR组合导航滤波算法研究

为消除常规利用正侧视SAR图像辅助导航信息对惯性误差进行修正时的滞后影响,结合前斜视SAR成像工作特性,本文分析提出了新的准实时性组合导航滤波方案和算法,以解决SAR/INS组合导航系统中的量测滞后影响;本文分析了前斜视SAR成像辅助导航系统工作特点,分析了SAR量测输出模型;建立了准实时性前斜视INS/SAR组合导航滤波算法模型,并通过仿真分析了组合导航系统性能。仿真结果表明：采用所提出的惯性/SAR组合方案和算法,可以有效克服成规正侧视SAR辅助匹配输出滞后的影响,有效满足组合系统性能要求。     

SINS/DVL水下组合导航系统的误差分析与改进技术

探讨了一种适用于SINS/DVL组合导航系统的滤波原理,通过分别建立捷联惯导系统误差模型和多普勒误差模型,利用间接卡尔曼滤波原理和反馈校正法,对系统进行仿真与分析,由惯性器件的误差方差通过导航系统的误差模型得出导航参数的误差方差,结果表明,该组合导航系统的定位精度要远远高于单纯捷联惯导系统。同时,针对SINS/DVL组合导航系统工作特点及特定情况下AUV的定位精度要求,提出了一种GPS辅助SINS/DVL组合导航系统导航定位的方案。