Integrated orbit and attitude hardware-in-the-loop simulations for autonomous satellite formation flying

Development and experiment of an integrated orbit and attitude hardware-in-the-loop (HIL) simulator for autonomous satellite formation flying are presented. The integrated simulator system consists of an orbit HIL simulator for orbit determination and control, and an attitude HIL simulator for attitude determination and control. The integrated simulator involves four processes (orbit determination, orbit control, attitude determination, and attitude control), which interact with each other in the same way as actual flight processes do. Orbit determination is conducted by a relative navigation algorithm using double-difference GPS measurements based on the extended Kalman filter (EKF). Orbit control is performed by a state-dependent Riccati equation (SDRE) technique that is utilized as a nonlinear controller for the formation control problem. Attitude is determined from an attitude heading reference system (AHRS) sensor, and a proportional-derivative (PD) feedback controller is used to control the attitude HIL simulator using three momentum wheel assemblies. Integrated orbit and attitude simulations are performed for a formation reconfiguration scenario. By performing the four processes adequately, the desired formation reconfiguration from a baseline of 500–1000 m was achieved with meter-level position error and millimeter-level relative position navigation. This HIL simulation demonstrates the performance of the integrated HIL simulator and the feasibility of the applied algorithms in a real-time environment. Furthermore, the integrated HIL simulator system developed in the current study can be used as a ground-based testing environment to reproduce possible actual satellite formation operations.     

Hardware-In-the-Loop Simulations of spacecraft attitude synchronization using the State-Dependent Riccati Equation technique

A nonlinear control technique pertaining to attitude synchronization problems is presented for formation flying spacecraft by utilizing the State-Dependent Riccati Equation (SDRE) technique. An attitude controller consisting of relative control and absolute control is designed using a reaction wheel assembly for regulator and tracking problems. To achieve effective relative control, the selective state-dependent connectivity is also adopted. The global asymptotic stability of the controller is confirmed using the Lyapunov theorem and is verified by Monte-Carlo simulations. An air-bearing-based Hardware-In-the-Loop Simulator (HILS) is also developed to validate the proposed control laws in real-time environments. The SDRE controller is discretized for implementation of a real-time processor in the HILS. The pointing errors are about 0.2° in the numerical simulations and about 1° in the HILS simulations, and experimental simulations confirm the effectiveness of the control algorithm for attitude synchronization in a spacecraft formation flying mission. Consequently, experiments using the HILS in a real-time environment can appropriately perform spacecraft attitude synchronization algorithms for formation flying spacecraft.     

Radio beacons/IMU integrated navigation for Mars entry

High precision entry navigation capability is essential for future Mars pinpoint landing missions, together with the entry guidance and aerodynamic lift control. This paper addresses the issue of Mars entry navigation using inertial measurement unit (IMU) and orbiting or surface radiometric beacons. The range and Doppler information sensed from orbiting or surface radio beacons and the entry vehicle state information derived from IMU are integrated in Unscented Kalman filter to correct the inertial constant bias and suppress the navigation measurement noise. Computer simulations show that the integrated navigation algorithm proposed in this paper can achieve 50 m position error and 2 m/s velocity error, which satisfies the need of future pinpoint Mars landing missions.     

Multi-Sphere Method for modeling spacecraft electrostatic forces and torques

The use of electrostatic (Coulomb) actuation for formation flying is attractive because non-renewable fuel reserves are not depleted and plume impingement issues are avoided. Prior analytical electrostatic force models used for Coulomb formations assume spherical spacecraft shapes, which include mutual capacitance and induced effects. However, this framework does not capture any orientation-dependent forces or torques on generic spacecraft geometries encountered during very close operations and docking scenarios. The Multi-Sphere Method (MSM) uses a collection of finite spheres to represent a complex shape and analytically approximate the Coulomb interaction with other charged bodies. Finite element analysis software is used as a truth model to determine the optimal sphere locations and radii. The model is robust to varying system parameters such as prescribed voltages and external shape size. Using the MSM, faster-than-realtime electrostatic simulation of six degree of freedom relative spacecraft motion is feasible, which is crucial for the development of robust relative position and orientation control algorithms in local space situational awareness applications. To demonstrate this ability, the rotation of a cylindrical craft in deep space is simulated, while charge control from a neighboring spacecraft is used to de-spin the object. Using a 1 m diameter craft separated by 10 m from a 3 by 1 m cylindrical craft in deep space, a 2 °/s initial rotation rate can be removed from the cylinder within 3 days, using electric potentials up to 30 kV.     

PROBA-3 mission and the Shadow Position Sensors: Metrology measurement concept and budget

PROBA-3 is a space mission of the European Space Agency that will test, and validate metrology and control systems for autonomous formation flying of two independent satellites. PROBA-3 will operate in a High Elliptic Orbit and when approaching the apogee at 6·10⁴ Km, the two spacecraft will align to realize a giant externally occulted coronagraph named ASPIICS, with the telescope on one satellite and the external occulter on the other one, at inter-satellite distance of 144.3 m. The formation will be maintained over 6 hrs across the apogee transit and during this time different validation operations will be performed to confirm the effectiveness of the formation flying metrology concept, the metrology control systems and algorithms, and the spacecraft manoeuvring. The observation of the Sun’s Corona in the field of view [1.08;3.0]R_Sun will represent the scientific tool to confirm the formation flying alignment. In this paper, we review the mission concept and we describe the Shadow Position Sensors (SPS), one of the metrological systems designed to provide high accuracy (sub-millimetre level) absolute and relative alignment measurement of the formation flying. The metrology algorithm developed to convert the SPS measurements in lateral and longitudinal movement estimation is also described and the measurement budget summarized.     

EKF/UKF在编队飞行卫星GPS相对导航中的应用

 　航天器编队飞行协调工作,必须精确确定各航天器的相对位置和相对速度,即进行编队飞行相对导航。将扩展卡尔曼滤波(EKF,extended Kalman filter)和非线性滤波unscented Kalman filter(UKF)算法同时应用于编队飞行卫星的载波相位差分GPS相对导航。EKF与UKF算法原理不同,UKF算法的精度比EKF的精度高。在实际应用中,可以将两种算法组成互为备份的相对导航滤波器,这样可提高滤波系统冗余性能。     

Onboard orbit determination using GPS observations based on the unscented Kalman filter

Spaceborne GPS receivers are used for real-time navigation by most low Earth orbit (LEO) satellites. In general, the position and velocity accuracy of GPS navigation solutions without a dynamic filter are 25 m (1σ) and 0.5 m/s (1σ), respectively. However, GPS navigation solutions, which consist of position, velocity, and GPS receiver clock bias, have many abnormal excursions from the normal error range for space operation. These excursions lessen the accuracy of attitude control and onboard time synchronization. In this research, a new onboard orbit determination algorithm designed with the unscented Kalman filter (UKF) was developed to improve the performance. Because the UKF is able to obtain the posterior mean and covariance accurately by using the second-order Taylor series expansion through the sampled sigma points that are propagated by using the true nonlinear system, its performance can be better than that of the extended Kalman filter (EKF), which uses the linearized state transition matrix to predict the covariance. The dynamic models for orbit propagation applied perturbations due to the 40 × 40 geo-potential, the gravity of the Sun and Moon, solar radiation pressure, and atmospheric drag. The 7(8)th-order Runge–Kutta numerical integration was applied for orbit propagation. Two types of observations, navigation solutions and C/A code pseudorange, can be used at the user’s discretion. The performances of the onboard orbit determination were verified using real GPS data of the CHAMP and KOMPSAT-2 satellites. The results of the orbit determination were compared with the precision orbit ephemeris (POE) of the CHAMP and KOMPSAT-2 satellites.     

Geostationary orbit determination using SATRE

A new strategy of precise orbit determination (POD) for GEO (Geostationary Earth Orbit) satellite using SATRE (SAtellite Time and Ranging Equipment) is presented. Two observation modes are proposed and different channels of the same instruments are used to construct different observation modes, one mode receiving time signals from their own station and the other mode receiving time signals from each other for two stations called pairs of combined observations. Using data from such a tracking network in China, the results for both modes are compared. The precise orbit determination for the Sino-1 satellite using the data from 6 June 2005 to 13 June 2005 has been carried out in this work. The RMS (Root-Mean-Square) of observing residuals for 3-day solutions with the former mode is better than 9.1 cm. The RMS of observing residuals for 3-day solutions with the latter mode is better than 4.8 cm, much better than the former mode. Orbital overlapping (3-day orbit solution with 1-day orbit overlap) tests show that the RMS of the orbit difference for the former mode is 0.16 m in the radial direction, 0.53 m in the along-track direction, 0.97 m in the cross-track direction and 1.12 m in the 3-dimension position and the RMS of the orbit difference for the latter mode is 0.36 m in the radial direction, 0.89 m in the along-track direction, 1.18 m in the cross-track direction and 1.52 m in the 3-dimension position, almost the same as the former mode. All the experiments indicate that a meter-level accuracy of orbit determination for geostationary satellite is achievable.     

一种多步的基于切换星间测量的多星自主导航算法

针对基于星间测量的多星自主导航问题,从载荷优化和节约成本考虑,提出了一种单套敏感器切换测量的导航方案。建立了该导航方案下的系统状态空间模型,并基于扩展卡尔曼滤波方程给出了导航估计算法。基于多步卡尔曼滤波方法,将集中的滤波算法解耦为多个平行的子滤波器,使计算量降低到原算法的50%以下,并且在切换测量的导航方案下,部分解耦出的子滤波器可以只预测不更新,能够进一步地降低计算负担。给出了多步滤波算法的推导过程,证明了其与标准卡尔曼滤波的数学等价性,故算法的估计性能及计算结果与标准卡尔曼滤波一致,但计算速度有明显提升。最后,通过具体算例给出了算法的仿真验证。     

Design and experiment of onboard laser time transfer in Chinese Beidou navigation satellites

High-precision time synchronization between satellites and ground stations plays the vital role in satellite navigation system. Laser time transfer (LTT) technology is widely recognized as the highest accuracy way to achieve time synchronization derived from satellite laser ranging (SLR) technology. Onboard LTT payload has been designed and developed by Shanghai Astronomical Observatory, and successfully applied to Chinese Beidou navigation satellites. By using the SLR system, with strictly controlling laser firing time and developing LTT data processing system on ground, the high precise onboard laser time transfer experiment has been first performed for satellite navigation system in the world. The clock difference and relative frequency difference between the ground hydrogen maser and space rubidium clocks have been obtained, with the precision of approximately 300 ps and relative frequency stability of 10E−14. This article describes the development of onboard LTT payload, introduces the principle, system composition, applications and LTT measuring results for Chinese satellite navigation system.     

Formation control using μ-synthesis for Inner-Formation Gravity Measurement Satellite System

Inner-Formation Gravity Measurement Satellite System (IFGMSS) is used to map the gravity field of Earth. The IFGMSS consists of two satellites in which one is called “inner satellite” and the other one is named as “outer satellite”. To measure the pure Earth gravity, the inner satellite is located in the cavity of the outer satellite. Because of the shield effect of the cavity, the inner satellite is affected only by the gravitational force, so it can sense Earth gravity precisely. To avoid the collision between the inner satellite and the outer satellite, it is best to perform a real-time control on the outer satellite. In orbit, the mass of the outer satellite decreases with the consumption of its propellant. The orbit angular rate of the inner satellite varies with time due to various disturbing forces. These two parameters’ uncertainties make the C–W function be not so accurate to describe the formation behavior of these two satellites. Furthermore, the thrusters also have some uncertainties due to the unmodelled dynamics. To cancel the effects caused by the above uncertainties, we have studied the robust control method based on the μ-synthesis. This μ-synthesis eliminates the conservativeness and improves the control efficiency comparing with the H_∞ method. Finally, to test the control method, we simulate an IFGMSS mission in which the satellite runs in a sun synchronous circular orbit with an altitude of 300 km. The simulation results show the effectiveness of the robust control method. The performances of the closed-loop system with the μ-controller are tested by the μ-analysis. It has found that the nominal performance, the robust stability and the robust performance are all achieved. The transient simulation results further prove the control response is fast and the accuracy of the relative position meets the demand of the gravity measurement.     

基于对偶四元数的编队飞行卫星相对位姿描述

为统一描述编队飞行卫星中主从星的相对位置和姿态参数,利用对偶四元数,建立编队飞行卫星运动学模型,分析其物理意义,提出了基于对偶四元数的编队飞行卫星相对位姿描述的划船算法,并利用这一算法解算出相对位置和姿态参数,突破了传统方法中将卫星轨道和姿态分而治之的方式。仿真结果表明该算法科学合理,能够有效描述编队飞行卫星间的相对位置和姿态。     

Autonomous satellite navigation using starlight refraction angle measurements

An on-board autonomous navigation capability is required to reduce the operation costs and enhance the navigation performance of future satellites. Autonomous navigation by stellar refraction is a type of autonomous celestial navigation method that uses high-accuracy star sensors instead of Earth sensors to provide information regarding Earth’s horizon. In previous studies, the refraction apparent height has typically been used for such navigation. However, the apparent height cannot be measured directly by a star sensor and can only be calculated by the refraction angle and an atmospheric refraction model. Therefore, additional errors are introduced by the uncertainty and nonlinearity of atmospheric refraction models, which result in reduced navigation accuracy and reliability. A new navigation method based on the direct measurement of the refraction angle is proposed to solve this problem. Techniques for the determination of the refraction angle are introduced, and a measurement model for the refraction angle is established. The method is tested and validated by simulations. When the starlight refraction height ranges from 20 to 50 km, a positioning accuracy of better than 100 m can be achieved for a low-Earth-orbit (LEO) satellite using the refraction angle, while the positioning accuracy of the traditional method using the apparent height is worse than 500 m under the same conditions. Furthermore, an analysis of the factors that affect navigation accuracy, including the measurement accuracy of the refraction angle, the number of visible refracted stars per orbit and the installation azimuth of star sensor, is presented. This method is highly recommended for small satellites in particular, as no additional hardware besides two star sensors is required.     

圆轨道串行卫星编队的相对运动研究

针对圆形轨道串行卫星编队进行研究,推导出满足开普勒轨道假设的相对运动方程,从物理概念上证明了这种描述关系的正确性;并在此基础上利用星间测量信息,设计扩展卡尔曼滤波器进行相对轨道自主确定,仿真结果验证了此相对运动方程与导航方案的有效性。     

Inter-agency comparison of TanDEM-X baseline solutions

TanDEM-X (TerraSAR-X add-on for Digital Elevation Measurement) is the first Synthetic Aperture Radar (SAR) mission using close formation flying for bistatic SAR interferometry. The primary goal of the mission is to generate a global digital elevation model (DEM) with 2 m height precision and 10 m ground resolution from the configurable SAR interferometer with space baselines of a few hundred meters. As a key mission requirement for the interferometric SAR processing, the relative position, or baseline vector, of the two satellites must be determined with an accuracy of 1 mm (1D RMS) from GPS measurements collected by the onboard receivers. The operational baseline products for the TanDEM-X mission are routinely generated by the German Research Center for Geosciences (GFZ) and the German Space Operations Center (DLR/GSOC) using different software packages (EPOS/BSW, GHOST) and analysis strategies. For a further independent performance assessment, TanDEM-X baseline solutions are generated at the Astronomical Institute of the University of Bern (AIUB) on a best effort basis using the Bernese Software (BSW).     

椭圆轨道卫星空间任意位置悬停的方法

对任务星施加持续的控制加速度,使其在飞行过程中相对于目标卫星的空间位置保持不变,即实现任意位置悬停飞行。通过对任务星与目标星的相对运行分析和重力差异补偿分析,给出了在飞行过程中任务星相对于运行在椭圆轨道上的目标星实现任意位置悬停所需的径向、切向和法向控制加速度公式。最后对典型悬停飞行过程进行了动力学仿真,并对不同悬停飞行任务的能量消耗进行了对比分析,表明在一段时间内对任务星进行轨道悬停是可行的。     

基于预设性能控制的超紧密航天器编队防避撞协同控制

研究了考虑具有外界干扰和防避撞约束的近地轨道超紧密航天器构型控制问题,将反步控制技术、预设性能控制相结合,提出了一种基于预设性能鲁棒控制的六自由度编队协同鲁棒控制方法。首先,给出了近地轨道完整的编队航天器相对位置和相对姿态非线性动力学方程,并根据状态约束条件转换了相对位置动力学模型。其次,设计了预设性能函数,通过误差转换,建立系统等效误差模型,基于反步法设计了预设性能鲁棒控制器,进一步应用Lyapunov稳定性定理证明了其闭环系统的一致最终有界性。最后在MATLAB/Simulink平台上进行了仿真验证,结果表明了方法的有效性。     

环火星自主导航系统设计及参数优化研究

当前火星探测器环绕段的导航信息主要依赖地面深空探测网提供,基于光学成像的导航方式尚不能提供较高的导航精度。因此提出一种应用相对测量的探测器实现火星环绕段的自主导航。两颗编队飞行的探测器进行相对测量,观测信息为探测器之间的相对视线矢量(LOS)。同时利用主星的星敏感器确定星体在惯性空间的姿态,将观测信息转换至惯性系下获得简化的观测方程,使用扩展卡尔曼滤波器(EKF)对卫星的轨道进行确定。介绍了具体导航方案的实现方法和技术细节,使用粒子群优化方法(PSO)对模型设计的相关参数进行优化,导航精度得到明显提高。实现位置确定精度10 m,速度确定精度0.01 m/s。为设计最优的编队导航系统参数提供了有效思路。     

Establishment criteria,routing algorithms and probability of use of inter-satellite links in mixed navigation constellations

In this paper, the establishment criteria, routing algorithm and the probability of use of ISLs (inter-satellite links) in the mixed navigation constellation of GEO satellites, IGSO satellites and MEO satellites are analyzed. Firstly, the general criteria of ISL establishment in mixed navigation constellation are proposed from the perspective of geometry, and the influences of these criteria on routing algorithms and the probability of use of ISLs are discussed. Then, from the perspective of autonomous orbit determination, the routing algorithm in mixed navigation constellation is designed. Thirdly, a stochastic study of ISLs load in mixed navigation constellation is proposed, and the formulae of probability of use of ISLs are given. Finally, in the simulation, the establishment criteria, routing algorithm and the probability of use of ISLs in a specific mixed navigation constellation of 3GEO + 3IGSO + 24MEO are discussed in detail. The findings of this paper provide a basis for the ISL establishment and routing algorithm, and offer the quantitative indicators for the use of ISL in the mixed navigation constellation.     

The study of enhanced earth observations on a satellite image chain

The Multi-Spectral Camera (MSC) on the KOrea Multi-Propose SATellite (KOMPSAT)-2 was developed and launched as a main payload to provide a One(1) m panchromatic image and four(4) band four(4) m multi-spectral images at an altitude of 685 km covering a swath width of 15 km. These images, archived around the world, are a useful resource for space applications in agriculture, cartography, geology, forestry, regional planning, surveillance, and national security. The image quality of KOMPSAT-2 depends upon its image chain, which is comprised of an on-board system in the satellite and a processing system at the ground station. Therefore, in this study we determine the factors that have a major impact on the image quality through an investigation of the entire image chain. Consequently, two methods, involving a compression algorithm and a deconvolution technique, were determined as having a significant influence on the KOMPSAT-2 image quality. The compression algorithm of KOMPSAT-2 is rate-controlled JPEG-like algorithm that controls the mismatch between the input and output data rate. The ability to control the input/output data rate may be useful during the operation of the satellite but can also lower the overall image quality. The deconvolution technique may increase the sharpness of images, but it can also amplify the image noise level. Therefore, we propose methods of wavelet-based compression and denoising as an alternative to currently existing algorithms. Satisfactory results were obtained through experimentation with these two algorithms, and they are expected to be successfully implemented into the future KOMPSAT series to yield high-quality images for enhanced earth observation.