Precession–nutation correction for star tracker attitude measurement of STECE satellite

Space Technology Experiment and Climate Exploration(STECE) is a small satellite mission of China for space technology experiment and climate exploration. A new test star tracker and one ASTRO 10 star tracker have been loaded on the STECE satellite to test the new star tracker's measurement performance. However,there is no autonomous precession–nutation correction function for the test star tracker,which causes an apparent periodic deflection in the inter-boresight angle between the two star trackers with respect to each other of up to ±500 arcsec,so the precession and nutation effect needs to be considered while assessing the test star tracker. This paper researches on the precession–nutation correction for the test star tracker's attitude measurement and presents a precession–nutation correction method based on attitude quaternion data. The periodic deflection of the inter-boresight angle between the two star trackers has been greatly eliminated after the precession and nutation of the test star tracker's attitude data have been corrected by the proposed method and the validity of the proposed algorithm has been demonstrated. The in-flight accuracy of the test star tracker has been assessed like attitude noise and low-frequency errors after the precession–nutation correction.     

Linearization errorʼs measure and its influence on the accuracy of MEKF based attitude determination method

Multiplicative Extended Kalman Filter (MEKF) is one of the most widely used satellite attitude estimation methods. However, the linearization error?s influence is an inherent limitation of this method. In this paper, we aim to analyze this linearization error in the typical satellite attitude determination system with star sensors and gyros. The formulation of linearization error is first derived and the curvature metric is then employed to measure the linearization error. Additionally, we show the reason why linearization error has influence on the performance of MEKF. Based on these analyses, we point out that star sensors? sampling frequency, initial estimated error and accuracy of gyro?s measurement model are the factors that could enlarge the system model?s linearization error. They all affect the linearization error and attitude determination accuracy by decreasing the predicted accuracy. More concretely, the influence of star sensor?s sampling frequency is large, while initial estimated error and gyro?s measurement error within a certain range have little influence on MEKF. Finally, combined with plenty of experiments, validity of the above analyses is verified.     

一种星敏感器-陀螺组合定姿的实时在轨标定方法

研究了一种星敏感器一陀螺组合定姿方式中的姿态敏感器误差的实时在轨标定方法。首先,选择直观的欧拉角作为姿态描述参数,根据星敏感器和陀螺的测量原理建立星敏感器一陀螺在轨标定的测量方程和状态方程,并以此建立数学模型。其次,采用简单高效的EKF（ExtendedKalmanFilter,扩展卡尔曼滤波）作为估值算法,进行了在轨标定数值仿真。对于航天器姿态定向中出现的姿态角和星敏感器安装角之间的耦合问题,通过在特定姿态通道上施加简单姿态机动实现了解耦。数值结果表明,该实时在轨标定方法,尤其是所提出的姿态角和星敏感器安装角解耦策略,可以实现对航天器姿态的实时精确估计以及对星敏感器安装误差、陀螺常值漂移和相关漂移等误差的实时在轨标定。该方法可用于航天器姿态测量设备的实时在轨标定和航天器姿态的高精度实时确定。     

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.     

激光陀螺机械抖动偏频对等效转动矢量姿态计算的影响

研究了激光陀螺机械抖动偏频影响等效转动矢量姿态计算精度的机理。用双子样N次迭代算法推导了载体实际姿态角运动与机械抖动发生谐振时产生的姿态计算误差项,指出其误差作用机理与惯性导航比力方程计算中划摇误差的相似性。针对三轴激光陀螺共一个机械抖动轴和3个单轴激光陀螺构成惯性组合两种情况进行了讨论。根据对静态条件下惯性组合中激光陀螺采样信号的功率谱密度分析,指出当采样频率较低时,会产生与抖动有关的低频周期分量,与低频的载体姿态运动谐振将产生姿态计算误差,应尽量提高采样频率及等效转动矢量计算频率。     

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.     

Star trackers for attitude determination

One problem comes to all spacecrafts using vector information. That is the problem of determining the attitude. This paper describes how the area of attitude determination instruments has evolved from simple pointing devices into the latest technology, which determines the attitude by utilizing a CCD camera and a powerful microcomputer. The instruments are called star trackers and they are capable of determining the attitude with an accuracy better than 1 arcsecond. The concept of the star tracker is explained. The obtainable accuracy is calculated, the numbers of stars to be included in the star catalogue are discussed and the acquisition of the initial attitude is explained. Finally the commercial market for star trackers is discussed     

弹载大视场星惯组合深度融合导航技术

为了降低弹载星惯组合（Stellar-INS）飞行中段对调姿观星的要求，提高星惯组合姿态精度，提出了大视场（LFOV）星惯组合深度融合导航方法。小视场（NFOV）星敏感器输出星矢量为主，大视场星敏感器可同时输出姿态和星矢量信息，分别推导了基于星敏感器输出姿态和星矢量信息的观测方程，分析了星矢量和姿态观测方法之间的关联性。建立了包含星惯安装误差、陀螺误差以及初始平台误差角的星惯组合全误差项模型，基于线性卡尔曼滤波给出了深度融合导航方法。开展了数学仿真验证，分析了不同调姿观星路径约束下，大/小视场星惯组合性能差异。结果表明，大视场星惯组合深度融合导航方法不仅可以降低调姿观星约束要求，还可以实现组合姿态性能提升。     

基于纵向滤波的星敏感器低频误差在线估计

多敏感器数据融合是获得更高精度姿态测量的有效方法，敏感器数据融合前必须先修正低频误差。首先，介绍了星敏感器低频误差（LFE）的产生机理及对其在线估计的必要性。其次，针对传统算法的不足，提出了基于纵向滤波的低频误差在线估计算法，该算法将传统低频误差估计问题转化为若干个常值误差估计问题，提高了估计精度。最后，给出了该算法具体实施方式，说明相关参数物理意义及选取原则。通过理论分析及仿真，算法误差可忽略不计。通过在轨数据仿真，星敏感器轨道周期低频误差可被消除。     

一种基于NGA-QPF的航天器姿态估计方法

针对航天器姿态确定中的非线性非高斯的滤波问题,提出一种基于遗传算法的粒子滤波的航天器姿态估计方法。该方法将姿态四元数作为采样粒子进行粒子滤波,并将小生境遗传算法（NGA）引入粒子滤波算法中,以改善粒子滤波的性能;用遗传算法单独进行陀螺偏差估计,以减少粒子滤波的状态维数。该姿态估计方法保持了四元数的归一化性质,通过引入小生境遗传算法解决了重采样阶段的粒子退化问题,并且由于单独估计陀螺偏差避免了粒子滤波状态的扩展。该方法能够在较少粒子的情况下实现高效率高精度的定姿,仿真结果说明了方法的有效性。     

Recursive mode star identification algorithms

Star identification can be accomplished by several different available algorithms that identify the stars observed by a star tracker. However, efficiency and reliability remain key issues and the availability of new active pixel cameras requires new approaches. Two novel algorithms for recursive mode star identification are presented here. The first approach is derived by the spherical polygon search (SP-search) algorithm, it was used to access all the cataloged stars observed by the sensor field-of-view (FOV) and recursively add/remove candidate cataloged stars according to the predicted image motion induced by camera attitude dynamics. Star identification is then accomplished by a star pattern matching technique which identifies the observed stars in the reference catalog. The second method uses star neighborhood information and a catalog neighborhood pointer matrix to access the star catalog. In the recursive star identification process, and under the assumption of "slow" attitude dynamics, only the stars in the neighborhood of previously identified stars are considered for star identification in the succeeding frames. Numerical tests are performed to validate the absolute and relative efficiency of the proposed methods.     

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).     

一种全天时星跟踪器相对惯导的安装阵在线快速估计方法

全天时星跟踪器与捷联惯导组成的惯性/天文组合导航系统具有精度高、自主性强等优点，在飞机、无人机、船舶等领域具有广泛的应用前景。组合导航系统长时间工作中力热变化导致安装矩阵漂移进而影响导航系统精度，全天时星跟踪器由于天空光影响视场小，一次只能观测一颗恒星，无法根据一副星图直接进行安装阵估计。提出了一种基于Levenberg-Marquart （L-M）算法的捷联惯性/天文组合导航系统安装阵在线快速高精度估计方法，利用捷联惯导姿态测量值，将不同时刻的观测星矢量转移到同一时刻同一坐标系中，构造多颗观测星的观测矢量误差与导航星矢量最小二乘目标函数，利用自适应步长的L-M算法对其进行迭代求解，实时得到系统安装矩阵的变化量。试验结果表明，使用该方法后星跟踪器在捷联惯导本体坐标系的输出恒星投影矢量精度提升了1倍以上，在线估计时间优于5 ms，满足用户实时性和高精度要求。     

SINS辅助的星敏感器在线标定方法

航天器在飞行过程中,星敏感器受到外界温度、地面标定精度等因素影响存在较大的安装误差,这将严重影响星敏感器的定姿精度。为提高星敏感器精度,对其安装误差进行严格的在轨实时标定与修正是确保星敏感器测量精度的关键。提出了一种SINS辅助的在线标定方法,将SINS/星敏感器输出的姿态信息进行配准,构建了组合导航系统的Kalman滤波模型。该方法只需航天器在飞行过程中做简单的机动,即可对星敏感器的安装误差角进行实时在线标定。仿真结果表明,采用该标定方法可使星敏感器和惯导的安装误差角的总体估计率达到95%以上,具有较高的工程应用价值。     

一种新的高精度天文导航方法

介绍了一种新的高精度天文导航方法,该方法构建了在天球坐标系中的天文导航姿态与航向解算模型。该模型在不利用惯导姿态数据的前提下进行计算,通过构建的模型演变得到运载体的精确姿态及航向,可以有效校正惯导设备因惯性陀螺漂移而导致的姿态误差与航向误差。     

Accuracy performance of star trackers - a tutorial

An autonomous star tracker is an avionics instrument used to provide the absolute 3-axis attitude of a spacecraft utilizing star observations. It consists of an electronic camera and associated processing electronics. The processor has the capability to perform star identification utilizing an internal star catalog stored in firmware and to calculate the attitude quaternion autonomously. Relevant parameters and characteristics of an autonomous star tracker are discussed in detail     

一种双轴旋转惯性导航系统的重要参数快速自标定方法

为了提高双轴旋转惯导重要参数标定的快速性和精度，提出一种快速自标定方法。通过设置不同的标定路径可以在10 min内完成陀螺和加速度计的零偏以及标度因数误差的标定。该方法利用基于姿态误差观测的卡尔曼滤波完成陀螺零偏的估计。通过六位置翻滚并以速度误差作为观测量进行卡尔曼滤波，完成加速度计的零偏及标度因数误差的标定。使天向陀螺绕方位轴旋转4周，使水平陀螺绕水平轴转动4周，通过计算旋转前后的姿态误差完成陀螺标度因数误差的估计。仿真和试验结果表明，该方法可以实现双轴旋转惯导重要参数10 min内完成自标定，且具有较高的精度。     

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.     

北斗GEO卫星南北控制对半长轴影响分析

在北斗GEO（Geostationary Earth Orbit，地球静止轨道）卫星南北控制期间，陀螺漂移、姿态控制、轨道平面变化等因素都会对卫星轨道半长轴产生影响，进而影响卫星星下点经度漂移，而在实际工程中难以提前准确预估南北控制对半长轴的影响。根据GEO卫星南北控制特点，分析了各因素对半长轴影响的原因，通过影响因素剥离的方法建立了各因素对半长轴影响的模型，利用在轨GEO卫星历次南北控制的实际数据，验证了模型的准确性并给出了各个因素的影响量级。结果表明，该模型可使得南北控制对半长轴影响的预测精度达到1 km以内，可用于北斗GEO卫星南北控制时半长轴补偿控制。     

Fast alignment and calibration algorithms for inertial navigation system

Algorithms for fast estimating the azimuth misalignment angle and calibrating gyro drift rates are approached from the point of view of control theory. By introducing the Lyapunov transformation, the equivalence of Strapdown Inertial Navigation System (SINS) and Gimbaled Inertial Navigation System (GINS) is discussed, and it shows that the analysis results of GINS can be applied to SINS directly by using such kind of equivalence. A similar transformation that based on physical essence is introduced, so that the true states can be replaced by the so-called pseudo-states, and then the observable states of INS can be dynamically decoupled with the unobservable states. Consequently, the best completely observable subsystem model of INS can be obtained. Based on the simplified subsystem model of INS, the algorithms for fast estimating the azimuth misalignment angle and calibrating gyro drift rates are proposed. The proposed algorithms show that the azimuth misalignment angle and gyro drift rates can be estimated from the rates of leveling misalignment angles without using the gyro output signals.