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.     

气动力矩和重力梯度矩实现微小卫星三轴姿态控制

提出运用低轨道两个主要环境力矩 (重力梯度矩和气动力矩 )实现微小卫星三轴姿态被动控制方案。重力梯度矩提供俯仰和滚转恢复力矩 ,气动力矩提供偏航和俯仰恢复力矩 ;通过姿态稳定性分析和姿控过程动态仿真 ,结果表明此卫星具有结构简单、姿态稳定精度高的优点。     

GPS-only gravity field recovery with GOCE,CHAMP, and GRACE

Gravity missions such as the Gravity field and steady-state Ocean Circulation Explorer (GOCE) are equipped with onboard Global Positioning System (GPS) receivers for precise orbit determination (POD), instrument time-tagging, and the extraction of the long wavelength part of the Earth’s gravity field. The very low orbital altitude of the GOCE satellite and the availability of dense 1 s GPS tracking data are ideal characteristics to exploit the contribution of GPS high-low Satellite-to-Satellite Tracking (hl-SST) to gravity field determination. We present gravity field solutions based on about 8 months of GOCE GPS hl-SST data from 2009 and compare the results with those obtained from the CHAllenging Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) missions. The very low orbital altitude of GOCE significantly improves gravity field recovery from GPS hl-SST data above degree 20, but not for the degrees below 20, where the quality of the spherical harmonic coefficients remains essentially unchanged. Despite the limited time span of GOCE data used, the gravity field of the Earth can be resolved up to about degree 115 using GPS data only. Empirically determined phase center variations (PCVs) of the GOCE onboard GPS helix antenna are, however, mandatory to achieve this performance.     

Impact of covariance information of kinematic positions on orbit reconstruction and gravity field recovery

Gravity missions are equipped with onboard Global Positioning System (GPS) receivers for precise orbit determination (POD) and for the extraction of the long wavelength part of the Earth’s gravity field. As positions of low Earth orbiters (LEOs) may be determined from GPS measurements at each observation epoch by geometric means only, it is attractive to derive such kinematic positions in a first step and to use them in a second step as pseudo-observations for gravity field determination. The drawback of not directly using the original GPS measurements is, however, that kinematic positions are correlated due to the ambiguities in the GPS carrier phase observations, which in principle requires covariance information be taken into account. We use GRACE data to show that dynamic or reduced-dynamic orbit parameters are not optimally reconstructed from kinematic positions when only taking epoch-wise covariance information into account, but that essentially the same orbit quality can be achieved as when directly using the GPS measurements, if correlations in time are taken into account over sufficiently long intervals. For orbit reconstruction covariances have to be considered up to one revolution period to avoid ambiguity-induced variations of kinematic positions being erroneously interpreted as orbital variations. For gravity field recovery the advantage is, however, not very pronounced.     

Remote sounding of atmospheric gravity waves with satellite limb and nadir techniques

Recent advances in satellite techniques hold great potential for mapping global gravity wave (GW) processes at various altitudes. Poor understanding of small-scale GWs has been a major limitation to numerical climate and weather models for making reliable forecasts. Observations of short-scale features have important implication for validating and improving future high-resolution numerical models. This paper summarizes recent GW observations and sensitivities from several satellite instruments, including MLS, AMSU-A, AIRS, GPS, and CLAES. It is shown in an example that mountain waves with horizontal wavelengths as short as 30 km now can be observed by AIRS, reflecting the superior horizontal resolution in these modern satellite instruments. Our studies show that MLS, AMSU-A and AIRS observations reveal similar GW characteristics, with the observed variances correlated well with background winds. As a complementary technique, limb sounding instruments like CRISTA, CLAES, and GPS can detect GWs with better vertical but poorer horizontal resolutions. To resolve different parts of the broad GW spectrum, both satellite limb and nadir observing techniques are needed, and a better understanding of GW complexities requires joint analyses of these data and dedicated high-resolution model simulations.     

深空探测重力模拟飞行器方案设想

为解决失重环境对航天员生理健康的影响,在调研国内外重力飞行器研究现状的基础上,结合重力模拟飞行器的原理及人造重力舒适度影响因素,提出了一种通过自旋产生人造重力的深空探测飞行器方案设想。最后给出了重力模拟飞行器建设的实施规划、总体方案、在轨组装流程及技术难点。深空探测重力模拟飞行器稳定运转可为空间工作生活的航天员提供与地面无异的重力环境,将为执行深空探测任务提供必要的环境保障。     

Effect of the seed perturbation amplitude on the equatorial spread F initiation during solar minimum

The contribution of gravity wave (GW) to the initiation/development of spread F during a solar minimum year was investigated through the comparison of the observed precursory parameters and characteristics of the corresponding equatorial spread F (ESF) events. The ionospheric parameters were recorded at the magnetic equatorial station Sao Luis (2.3°S, 44°W, dip latitude 2°S) during March and October 2010. These data were used to estimate the influence of the relative gravity wave amplitude and the ambient ionospheric condition on the diurnal variation of the spread F initiation. The vertical velocity drift indicated a clear control and defines the threshold for the seasonal variability of the ESF occurrence. However, it was insufficient to solely determine or predict the day to day variation of ESF occurrence. Thus, few days with contrasting ambient ionospheric condition and magnitude of GW amplitude were analysed in order to investigate the role of the different precursory factors in the observed diurnal variation of the plasma irregularity development. The density scale length and gravity wave amplitude were shown to immensely contribute to the linear instability growth rate, especially during the days with a low post-sunset rise. Thus, the experimental observations have demonstrated the strong inter-dependence between the precursory factors and they have also highlighted the probable control of the ESF morphology.     

An alternative computation of a gravity field model from GOCE

GOCE is the first satellite with a gravitational gradiometer (SGG). This allows to determine a gravity field model with high spatial resolution and high accuracy. Four of the six independent components of the gravitational gradient tensors (GGT) are measured with high accuracy in the so-called measurement band (MB) from 5 to 100 mHz by the GOCE gradiometer. Based on more than 1 year of GOCE measurements, two gravity field models have been derived. Here, we introduce a strategy for spherical harmonic analysis (SHA) from GOCE measurements, with a bandpass filter applied to the SGG data, combined with orbit analysis based on the integral equation approach, and additional constraints (or stabilization) in the polar areas where no observation is available due to the orbit geometry. In addition, we combined the GOCE SGG part with a set of GRACE normal equations. This improves the accuracy of the gravity field in the long-wavelength parts, due to the complementarity of GOCE and GRACE. Comparison with other models and with external data shows that our results are rather close to the GPS-levelling data in well-selected test regions, with an uncertainty of 4–7 cm, for truncation at degree 200.     

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.