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.     

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.     

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。     

Spectral Analysis of Optimal and Suboptimal Gyro Monitoring Filters

Gyro monitoring filters are used to estimate and correct gyro drift rates of local-level inertial navigation systems. Conventional gyro monitoring filters are usually designed based on a simplified model of gyro drift rate. Furthermore, the effectiveness of these filters-and of many filters of the "Kalman" type-is often measured in terms of the root mean square (rms) criterion in contrast to the spectral content criterion typical of classical Wiener filtering theory. This paper has two objectives: to propose a gyro monitoring filter which is based on a more detailed model of gyro drift rate; and to propose a method of filter performance evaluation which uses as criterion a measure of the spectral content of the error process. The proposed gyro monitoring filter is shown to have improved spectral contents resulting in superior navigation performance for the gyro error models used in the calculations (comparable to commercial-grade aircraft gyros).     

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     

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.     

Inertial System Platform Rotation

Differential error equations are derived for the navigation errors of a local level undamped pure inertial platform that continuously rotates in azimuth. From these, the time response equations for the vector position error produced by a constant level gyro drift error, as a function of platform rotation rate, are computed and evaluated. It is shown that platform rotation attenuates the system position error due to level gyro bias and that this attenuation is a nonlinear function of rotation rate.     

无定向激光陀螺捷联惯组标定方法的对比研究

对三种无定向激光陀螺捷联惯组标定方法进行了对比研究,详细分析了各种方案的标定原理,提出了利用标准差作为评价标定方法优劣的指标.结合对某一激光陀螺捷联惯组标定试验结果的分析,得到了在无北向基准的情况下,三种标定方法在标定时间和标定精度两个指标上的对比结果,为无定向激光捷联惯组的标定提供了指导,具有较大的工程应用价值.     

光纤陀螺仪中尖峰脉冲引起漂移 的误差分析及其抑制

首次分析了光纤陀螺仪探测器输出信号中频率固定的尖峰脉冲对光纤陀螺 仪零偏漂移的影响机理,给出了尖峰脉冲影响光纤陀螺仪零偏漂移的误差模型;根据干 涉式数字闭环光纤陀螺仪探测器输出信号的特点,提出了一种基于高速集成模拟开关的 时域选通尖峰脉冲抑制具体实现方法,实验验证了尖峰脉冲引起的零偏漂移大小和理论 分析接近,表明了误差模型的正确性,同时表明该方法能够有效降低尖峰脉冲引起的光 纤陀螺仪零偏漂移。     

旋转捷联惯导系统原理及典型方案分析

旋转捷联惯导系统采用旋转调制误差补偿技术对陀螺仪和加速度计误差进行调制,可以提高系统导航精度。文章借助捷联系统基本误差方程,简要分析了旋转调制误差补偿的机理;通过对几种典型IMU旋转方案的分析和仿真,验证了旋转调制误差补偿技术的有效性并比较了不同旋转方案的特点。     

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     

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。     

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.     

Strapdown Guidance Error Analysis

A crucial part of so-called ?strapdown? techniques for inertial guidance systems is the generation of the matrix of direction cosines relating the body axes to the reference axes. This is generally done by direct integration of a set of differential equations having the body angular velocities as inputs. This paper is devoted to an error analysis of two commonly used integration schemes, namely, direction cosines and quaternions. Scale, skew, and drift errors are defined, and the susceptibility of the integration schemes to these types of error is examined. It is concluded that the quaternion scheme offers an advantage because it intrinsically yields zero skew error. The paper is presented in two parts, for convenience.     

激光陀螺及其误差补偿

 本文介绍国外研制环形激光陀螺(RLG)的经验和现状,把误差产生机理及其补偿方法作为研究重点,这是取得成果的基础。机械抖动偏频技术有优点,得到了广泛应用,但在精度上尚不能满足精密惯性导航的要求。近年来国外正在研究的速率偏置技术显著地降低了RLG的随机误差,并可补偿常值漂移。本文讨论了这一技术的优点。     

D-最优试验设计在动力调谐陀螺测试中的应用

 为了提高动力调谐陀螺的静态漂移误差测试精度,针对简化静态漂移误差模型,并且考虑陀螺安装角误差的影响,依据D-最优试验设计理论以及正交设计的均匀分散性试验设计思路,设计了一种满足D-最优性质的正交八位置试验方案,并在整个正交空间内采用全局搜索的方法验证了其D-最优性。在相同试验环境下,采用力反馈位置试验法,以全正交空间预测误差平方和最小为评价准则,对该八位置试验方案和国军标GJB1183—91中的八位置试验方案进行比较与评价,试验结果表明该八位置试验方案优于国军标GJB1183—91中八位置试验方案。     

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.     

The Least-Square Approximation of Inertial Platform Drift

The drift angle of an inertial platform which is gyro-stabilized with respect to inertial space is equal to the integral of the gyro drift rate. Under controlled laboratory environment the drift angle, denoted by y, may be measured and plotted against time in an interval [0, T]. Without loss in generality, one may take y(0)= 0. A straight line yf can be found, such that the quantity E2 is minimized, where begin{equation*}E^2 = {frac{1}{T}int^{T}_{0}(y-y_f)^{2}}dt.end{equation*} The equation for yf is of the form yf = at + b and, in general, both a and b are nonzero. It is desirable to determine a statistical relationship between the gyro drift rate and the expected value of the minimum E2 for any given interval T. An analysis in this paper determines this relationship and derives a general expression for , where the symbol <*> denotes statistical expectation. It is found that increases linearly with the variance of the gyro drift rate. This general formula is then developed in detail for the case of a first-order Markovian gyro drift. is evaluated numerically and its square root plotted vs. the interval T and the gyro correlation time. The same problem is also solved for the case when yf is constrained to intersect the origin, i.e., when b=0.     

基于多参量模型的光纤陀螺温度误差补偿

温度漂移误差是制约光纤陀螺精度的重要因素之一。针对传统光纤陀螺温度补偿方法仅对温度项建模导致补偿精度差的问题,提出了一种新型多参量模型来补偿光纤陀螺温度误差的方法。通过对陀螺零漂误差和温度各相关项进行相关性分析,将温度和温度速率的乘积项及温度梯度滞后项引入到温度漂移误差模型中,建立了多参量分段补偿模型对零偏进行补偿,显著改善了光纤陀螺的零偏稳定性。使用实测光纤陀螺数据对提出的补偿方法进行实验验证,结果表明采用该方法补偿后,零偏误差平方和降低2个数量级,陀螺漂移均值、方差稳定在零点附近,补偿效果优于温度项分段拟合方法,与非线性模型预测效果相当。     

Low-frequency Periodic Error Identification and Compensation for Star Tracker Attitude Measurement

The low-frequency periodic error of star tracker is one of the most critical problems for high-accuracy satellite attitude determination.In this paper an approach is proposed to identify and compensate the low-frequency periodic error for star tracker in attitude measurement.The analytical expression between the estimated gyro drift and the low-frequency periodic error of star tracker is derived firstly.And then the low-frequency periodic error,which can be expressed by Fourier series,is identified by the frequency spectrum of the estimated gyro drift according to the solution of the first step.Furthermore,the compensated model of the low-frequency periodic error is established based on the identified parameters to improve the attitude determination accuracy.Finally,promising simulated experimental results demonstrate the validity and effectiveness of the proposed method.The periodic error for attitude determination is eliminated basically and the estimation precision is improved greatly.