Characteristics and accuracies of the GRACE inter-satellite pointing

For almost 10 years, the Gravity Recovery and Climate Experiment (GRACE) has provided information about the Earth gravity field with unprecedented accuracy. Efforts are ongoing to approach the GRACE baseline accuracy as there still remains an order of magnitude between the present error level of the gravity field solutions and the GRACE baseline. At the current level of accuracy, thorough investigation of sensor related effects is necessary as they are one of the potential contributors to the error budget. In the science mode operations, the twin satellites are kept precisely pointed with their KBR antennas towards each other. It is the task of the onboard attitude and orbit control system (AOCS) to keep the satellites in the required formation. We analyzed long time series of the inter-satellite pointing variations as they reflect the AOCS performance and characteristics. We present significant systematic effects in the inter-satellite pointing and discuss their possible sources. Prominent features are especially related to the magnetic torquer characteristics, star cameras’ performance and KBR antenna calibration parameters. The relation between the magnetic torquer attitude control and the Earth magnetic field, impact of the different performance of the two star camera heads on the attitude control and the features due to uncertainties in the calibration parameters relating the star camera frame to K-frame are discussed in detail. Proper understanding of these effects will help to reduce their impact on the science data and subsequently increase the accuracy of the gravity field solutions. Moreover, understanding the complexity of the onboard system is essential not only for increasing the accuracy of the GRACE data but also for the development of the future gravity field satellite missions.     

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.     

精确动力学模型中的行星引力辅助轨道设计

轨道设计分为初步设计和精确模型迭代两步,初步设计基于等效脉冲模型,用圆锥曲线拼接法确定时间窗口和引力辅助产生的速度脉冲。精确模型中引力辅助看作是一个连续的过程,将简化模型得到的引力辅助双曲线轨道化为行星心目标B平面参数,以地心逃逸速度作为设计变量,通过微分修正的方法进行求解。通过算例对比分析了简化模型和精确模型设计结果之间的关系,结果表明,引力辅助脉冲等效模型精度较好。     

Gravity modeling in aerospace applications

The science of inertial navigation has evolved to the point that the traditional gravity model is a principal error source in advanced, precise systems. Specifically, the unmodeled vertical deflections of the earth's gravitational field are a major contributor to CEP (circular error probable) divergence in precise terrestrial inertial navigation systems (INS). Over the years, several studies have been undertaken to the development of advanced techniques for accurate, real-time compensation of gravity disturbance vectors. More complex on-board gravity models which compute vertical deflection components will reduce the CEP divergence rate, but imperfect modeling due to on-board processing limitations will still cause residual vertical deflection errors. In order to eliminate or reduce gravity-induced errors in the INS requires measurement of gravity disturbance values and in-flight compensation to the inertial navigator. It is assumed in this paper that gravity disturbance values have been measured prior to the airborne mission and various techniques for compensation are to be considered. As part of a screening process in this study, several gravity compensation techniques (both deterministic and stochastic models) were investigated. The screening process involved identification of gravity models and algorithms, and developments of selection criteria for subsequent screening of the candidates.     

A numerical model characterizing internal gravity wave propagation into the upper atmosphere

A new two-dimensional, time-dependent and fully nonlinear model is developed to numerically simulate plane wave motions for internal gravity waves in a non-isothermal and windy atmosphere that accounts for the dissipation due to eddy and molecular processes. The atmosphere has been treated as a well mixed total gas with a constant mean molecular weight. The effects of Rayleigh friction and Newtonian cooling are applied near the upper boundary of the model to simulate the radiation conditions as well as to act as a sponge layer; lateral boundaries are periodic over a horizontal wavelength to simulate a horizontally infinite domain. The thermal excitation to initiate upward propagating waves is spatially localized in the troposphere and is a Gaussian function of time. A time-splitting technique is applied to the finite difference equations that are derived from the Navier–Stokes equations. The time integration for these highly coupled equations is performed using an explicit second order Lax–Wendroff scheme and an implicit Newton–Raphson scheme. The wave solutions derived from the model are found to be broadly agreeable with those derived from a Wentzel–Kramers–Brillouin theory.     

A gravity wave analysis near to the Andes Range from GPS radio occultation data and mesoscale numerical simulations: Two case studies

Global maps of potential wave energy per unit mass, recently performed with the Global Positioning System (GPS) Radio Occultation (RO) technique and different satellite missions (CHAMP and SAC-C since 2001, GRACE and COSMIC since 2006) revealed in Argentina, at the eastern side of the highest Andes Mountains, a considerable wave activity (WA) in comparison with other extra-tropical regions. The main gravity wave (GW) sources in this natural laboratory are deep convection (mainly during late Spring and Summer), topographic forcing and geostrophic adjustment.     

Vertical wavenumber spectra of atmospheric ozone measured from ozonesonde observations

Vertical profiles of ozone have been measured at balloon altitudes. Our purpose is to examine the character of vertical wavenumber spectra of ozone fluctuations, to assess the possible roles of gravity wave field in ozone fluctuations, and to determine dominant vertical wavelengths of ozone spectra. Vertical wavenumber spectra of 12 ozone fluctuations obtained during June–August 2003 are presented. Results indicate that mean spectral slopes in the wavenumber range from 4.69 × 10⁻⁴ to 2.50 × 10⁻³ cyc/m are about −2.91 in the troposphere and −2.87 in the lower stratosphere, which is close to the slope of −3 predicted by current gravity wave saturation models. The consistency of the observed spectral slopes with the value of −3 predicted by current gravity wave saturation models suggests that the observed ozone fluctuations are due primarily to atmospheric gravity waves. At m = 1/(1000 m) the mean spectral amplitude is over 30 times larger in the lower stratosphere than in the troposphere. Mean vertical wavenumber spectra in area-preserving form reveal dominant vertical wavelengths of ∼2.6 km in the troposphere and ∼2.7 km in the lower stratosphere, which is consistent with the values varying between 1.5 and 3.0 km estimated from the velocity field and temperature field at these heights.     

Flight performance analysis of GRACE K-band ranging instrument with simulation data

A dual one-way ranging (DOWR) system provides very high accuracy range measurements between two satellites. The GRACE satellite mission implements the DOWR, called KBR (K-band ranging), to measure very small inter-satellite range change in order to map the Earth gravity field. The flight performance of the KBR is analyzed by using a hybrid software simulator that incorporates actual satellite orbit data into a comprehensive KBR simulator, which was earlier used for computing the GRACE baseline accuracy. Three types of experiments were performed. First is the comparison of the flight data with the simulated data in spectral domain. Second is the comparison of double differenced noise level. Third is the comparison of the range-rate difference with GPS clock estimates. The analysis shows a good agreement with the simulation model except some excessive high frequency noise, e.g. 10⁻⁴ m/√Hz at 0.1 Hz. The range-rate difference shows 0.003 cyc/s discrepancy with the clock estimates. These analyses are helpful to refine the DOWR simulation model and can be benefit to future DOWR instrument development.     

空间站基于动量管理的集成能量与姿态控制系统

研究了使用飞轮和变速控制力矩陀螺的空间站基于动量管理的集成能量与姿态控制系 统（Integrated Power and Attitude Control System IPACS）。设计了使用飞轮和变速控 制力矩陀螺的空间站基于动量管理的IPACS框架,通过仿真验证了基于动量管理的IPACS的有 效性,以及相对于单独的IPACS的优越性,同时变速控制力矩陀螺因同时具备飞轮和框架力 矩陀螺的特点更适用于空间站长期在轨的姿态控制和能量存储要求。
     

Impact of the orbital eccentricity on the attitude performance before and after the deorbiting phase for Alsat-1

Due to the presence of periodic forcing terms in the gravity gradient torque, orbit eccentricity may produce large response for the roll, yaw and pitch angles. This paper investigates the influence of the orbit eccentricity on the performance of the attitude determination and control subsystem (ADCS) pointing of passive Low Earth Orbit (LEO) satellites stabilized by a gravity gradient boom or having long appendages before and after the deorbiting operation. The contribution of this work is twofold. First, the satellite attitude dynamics and kinematics are modeled by introducing the orbit eccentricity in the equations of motion of a LEO satellite in order to provide the best scenario in which satellite operators can keep the nominal functionality of LEO satellites with a gravity gradient boom after the deorbiting operation. Second, a Quaternion-based Extended Kalman Filter (EKF) is analyzed when the orbit eccentricity is considered in order to determine the influence of this disturbance on the convergence and stability of the filter. The simulations in this work are based on the true parameters of Alsat-1 which is a typical LEO satellite stabilized by a gravity gradient boom. The results show that the orbit eccentricity has a big influence on the pointing system accuracy causing micro-vibrations that affect the geocentric pointing particularly after the deorbiting phase. In this case, satellites have no orbital correction option. The Quaternion-based Extended Kalman Filter analyzed in this paper, achieved satisfactory results for eccentricity values less than 0.4 with respect to pointing system accuracy. However, singularities were observed for eccentricity values greater than 0.4.