Comments on "The Psi-Angle Error Equation in Straplown Inertial Navigation Systems"

The negative sign on the psi-angle differential equation for strapdow inertial navigation error analysis discussed by Weinreb and Bar-ltzhack is not due to differences in error propagation between gimbaled and strapdown systems, but to the definition of strapdown gyro drift rate given by them. If a consistent definition of gyro drift rate for gimbaled and strapdown systems error analysis is used, the sign change does not occur.     

On the orientation vector differential equation in strapdowninertial systems

An alternate derivation of the orientation vector differential equation is given, together with an assessment of the error inherent in the simplified form of this equation commonly utilized in strapdown inertial systems     

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 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     

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.     

Augmenting the Linear Variance Equation

A technique is developed to convert the covariance analysis ofcertain time-varying linear systems into time-invariant form, thusallowing an arbitrary time step for the solution of the differentialequations. The result is accomplished by augmenting the linearvariance equation and augmenting the state vector if necessary. Themethod is illustrated with an example showing the covariancepropagation of ring laser gyro errors in a strapdown inertial systeminto navigation errors during turns.     

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。     

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     

Propagation and System Accuracy Impact of Major Sensor Errors on a Strapdown Aircraft Navigator

A strapdown system is considered as an unaided inertial navigator aboard an aircraft. Presented here are simulation results detailing the propagation of navigation errors (in nautical miles) due to strapdown sensor errors for four trajectories. They indicate the type of performance that can be expected from a strapdown system utilizing good ?off the shelf? gyros and accelerometers, and dramatically illustrate the improvements necessary in these components to obtain navigation performance comparable to that available from a good gimballed inertial system. The total navigation error for each trajectory is broken down to show the contribution from each of the various error sources. This breakdown quickly reveals which are the critical error sources for a given trajectory class, and also points up the relationship that exists between each individual error source, aircraft maneuvers, and the resulting navigation error. Several of the error mechanisms are discussed at length and a set of linearized differential equations which can be used to analyze error propagations is presented. These results should be of particular interest to the system designer who is faced with the problem of specifying the sensor error parameters necessary to meet mission performance requirements. With an analysis similar to the one presented here, but structured around his own expected mission trajectories, the designer should be able to confidently predict system accuracies and intelligently perform tradeoffs on the critical system parameters.     

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.     

旋转式SINS的自标校技术研究

惯性器件常值及慢变误差是影响捷联惯导系统精度的主要因素之一,所以在捷联惯导系统出厂前需要对常值及慢变误差参数进行标定。但这些误差参数会随时间发生变化,对于高精度捷联惯导系统,每次启动后需要对惯性器件的误差参数进行重新标校。针对光纤惯导系统,建立了IMU误差模型,并根据提出的旋转式捷联惯导系统自标校转位方案原则设计出了一种8位置自标校方案,对惯性器件标定参数进行激励和辨识,并建立了Kalman滤波状态方程及量测方程,对惯导系统误差参数进行在线标定。实验结果表明,该方案对其惯性器件误差参数能进行准确估计,具有一定的参考价值。     

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。     

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。     

一种统一惯性导航方法

捷联式和平台式惯性导航系统的导航方程不同:同一惯性测量系统选取不同导航坐标系时,导航方程也不同;各类力学编排形式多样、结构复杂且输出结果具有局限性.针对这些问题,提出一种统一惯性导航方法.惯性导航试验结果表明,基于统一惯性导航方程与基于传统惯性导航方程解算的结果一致,验证了统一惯性导航方程的有效性.     

基于速度误差的系统级标定方法

为降低捷联惯导系统误差参数标定过程对高精度转台的要求,提出一种基于速度误差的系统级标定方法。在惯性器件误差参数模型和捷联惯导系统误差方程的基础上,以惯导系统转动前后的导航速度误差为观测量,编排设计旋转方案,对加速度计和陀螺的误差参数进行拟合标定。仿真结果表明,与传统的分立式标定方法相比,在保证标定精度的同时,对高精度转台的要求更低,可应用于外场标定。     

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.     

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...     

Kalman filter mechanization for INS airstart

A strapdown mechanization and associated Kalman filter are developed to provide both ground align and airstart capabilities for inertial navigation systems (INSs) using Doppler velocity and position fixes, while not requiring an initial heading estimate. Position update during coarse mode is possible by defining sine and cosine of wander angle as filter states and modeling the position error in geographic frame while integrating velocity in the wander frame. INS Global Positioning System (GPS) differential position due to GPS antenna moment arm can aid heading convergence during hover turns in helicopter applications. Azimuth error state in the fine mode of the filter is defined as wander angle error to provide continuous estimation of navigational states, as well as inertial/aiding sensor errors, across the coarse-to-fine mode transition. Though motivated by a tactical helicopter application, the design can be applied to other vehicles. Advantages over conventional systems in addition to the airstart capability include robustness and versatility in handling many different operational conditions     

Advanced Development of ESG Strapdown Navigation Systems

The fundamental problem of inertial navigation, double integration of acceleration to obtain position, is defined and discussed. Mechanizations of both space-stable and local-vertical platform systems are exhibited. The synthesis problem for an electrically suspended gyro (ESG) strapdown system is defined and discussed: readout, readout errors due to vehicle motion, synchronization of readout with system computer, alignment, correction and calibration for mass unbalance drift, and digital mechanization. Alignment, calibration, and acceleration measurement are also discussed. Sources of error involved in the electronic gimbaling including those peculiar to strapdown configuration are discussed and compared to mechanically gimbaled systems. Advanced developments required in the component and systems areas are listed, and it is shown that such development will lead to reduced complexity, higher accuracy, and increased reliability and utility for inertial systems.