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.     

Autonomous orbit determination using epoch-differenced gravity gradients and starlight refraction

Autonomous orbit determination via integration of epoch-differenced gravity gradients and starlight refraction is proposed in this paper for low-Earth-orbiting satellites operating in GPS-denied environments.Starlight refraction compensates for the significant along-track position error that occurs from only using gravity gradients and benefits from integration in terms of improved accuracy in radial and cross-track position estimates.The between-epoch differencing of gravity gradients is employed to eliminate slowly varying measurement biases and noise near the orbit revolution frequency.The refraction angle measurements are directly used and its Jacobian matrix derived from an implicit observation equation.An information fusion filter based on a sequential extended Kalman filter is developed for the orbit determination.Truth-model simulations are used to test the performance of the algorithm,and the effects of differencing intervals and orbital heights are analyzed.A semi-simulation study using actual gravity gradient data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) combined with simulated starlight refraction measurements is further conducted,and a three-dimensional position accuracy of better than 100 m is achieved.     

单轴旋转捷联惯导系统重力扰动补偿方法研究

随着惯性器件精度的提升以及系统级补偿技术的应用,惯性导航系统精度得到不断提升。原先忽略的一些误差源如重力扰动,成为制约惯导精度进一步提升的关键。针对该问题,研究了单轴旋转捷联惯导系统重力扰动补偿,补偿所需重力扰动信息通过德国波尔茨坦GFZ研制的EIGEN-6C4计算得到。仿真结果表明,经重力扰动补偿后,单轴旋转捷联惯导系统精度有显著提升。     

飞机主动重心控制系统设计及应用

以我国先进飞机需求牵引为背景,研究了主动重心控制系统方案和设计方法.首先,构建了一种飞机主动重心控制系统结构方案,用于协调纵向重心与气动焦点之间的关系;其次,基于平衡输油系统建立了重心位移模型,提出了最佳重心位置设计准则,在此基础上设计了基于干扰观测器补偿的主动重心控制器,并将其应用到某型飞机超声速巡航中.仿真结果表明,该主动重心控制系统合理地协调了飞机的纵向稳定性和操纵性,并有效地减小了巡航阻力,提高了巡航的效率和航程.     

A Modified Karhunen-Loeve Model of Gravity Disturbance Vector

A modified anisotropic Karhunen-Loeve (KL) model for the gravity disturbing potential is proposed. This model, unlike the previous KL model of Bose, does not vanish on the boundaries of a local region. Laplace's equation for the gravity disturbing potential and flatearth Vening-Meinesz relationships of the gravity disturbance vectorcomponents (?,?,?g) when the model is isotropic, are exploited to determine the unknown parameters of the model. The resulting model, in addition to having random boundary values, has three more parameters than those found in Bose's KL model. This should provide extra flexibility in fitting the model to the noisy data available in a local finite region.     

Error Covariance Analysis of a Karhunen-Loeve Collocation Estimator

An error covariance analysis of a two-dimensional gravity compensation technique (KLC) employing a Karhunen-Loeve gravity disturbance model and the linear least-square collocation algorithm for its estimation is presented, without actually using any data. Its performance is compared with another gravity compensation technique (KLE), whose error covariance analysis was previously presented by Gupta. From the mismodeling analysis, KLC appears to be superior to KLE.     

New concepts for airborne gravity measurement

A fundamental survey of vehicle mounted gravimeters shows the superposition from the gravity and the kinematical acceleration due to item modification. The particular problems of airborne gravimetry lie in the presence of relatively strong disturbances due to air turbulence. The vehicle acceleration caused in this manner is from high dynamics and up to a factor of 10⁶ greater than the anomaly signal (local changes of acceleration due to the earth's gravitation). Thus, the technically scientific problem of utilizing gravimeters in airplanes lies in a suitable compensation for the vehicle's acceleration. The measurement methods applied reduce the high frequency disturbance signal with the aid of a low-pass filter. These methods are restricted only for the localization of very large anomalies. The required resolution for an air gravimeter cannot be reached only through a direct low-pass or band-pass filtering, since the frequency ranges of the disturbance and the anomaly overlap. A clear improvement of the resolution requires completely new concepts. For separating gravity and kinematical acceleration, there must be further sensors that are not influenced by gravity, e.g. altimeter and the Global Positioning System (GPS). An overall system, into which the individual sensors are integrated and associated via suitable complementary filtering with each other, allows it to register gravity with a higher resolution than is presently possible.     

量子重力梯度仪研究进展

重力梯度是重力位的二阶微分,对地球密度扰动具有更高的分辨率,能够更加精细、全面地反映重力位在空间上的变化.高精度重力梯度测量在地质调查、地球重力场测绘、惯性导航以及基础科学研究等方面发挥着重要作用.量子重力梯度仪是近年来快速发展的一种基于激光操控原子技术的新型高精度重力梯度测量设备,具有测量精度高、长期稳定性好等特点,...     

Balloon gravimetry using GPS and INS

Measurement of the horizontal components of gravity at altitude using balloon-borne instrumentation consisting of a Global Positioning System (GPS) receiver and a strapdown inertial navigation system (INS) is discussed. GPS data are to be used primarily to determine the total inertial acceleration of the balloon, while the INS accelerometers sense all nongravitational accelerations. A covariance analysis based on the Kalman filter shows that conventional gravity estimation from GPS-aided INS data is possible only if external attitude updates are also available. An alternative technique is explored that attempts to estimate at least part of the gravitational spectrum without modeling the gravity disturbance as a state variable or relying on external attitude updates, while, at the same time, admitting uncorrected (long-wavelength) attitude errors. Simulations based on a model for typical balloon motion are used to discuss this possibility     

加油机尾流场建模与仿真分析

提出了等效气动效应法,建立了加油机尾流场的等效扰动模型。等效气动效应法采用逐点积分方法和加权平均方法,将尾流的影响等效为受油机运动方程直接可用的平均风速度和风梯度。对不同状态下受油机所受尾流的扰动作用进行了仿真。结果表明,扰动模型与实际情况比较符合。     

A Modified Discrete Karhunen-Loeve Random Field Estimator

Based upon the modified Karhunen-Loeve model of the gravity disturbance vector proposed by us recently, a corresponding Karhunen-Loeve random field estimator is developed in this paper for a two-dimensional grid of gravity data in a local finite region.The new eigenvectors obey the "required" orthogonality relations on the chosen grid provided the KL expansion is now separated into odd and even integers. The closed-form solution of the estimator isthen obtained under the "diagonal" assumption for the gain coefficients. It is shown that this assumption, without which nosolution is possible, enables the estimator to reproduce the data atgrid points when the noise in the data is absent and the number of terms in the Karhunen-Loeve expansion are equal to the number of grid points.     

Macroscopic Transport Large-scale advection, turbulent diffusion, wave transport

While the solar convection zone is very well mixed by its turbulent motions, chemical composition gradients build up in the radiative interior due to microscopic diffusion and settling, and to nuclear burning. Standard models, which ignore any type of macroscopic transport, cannot explain the depletion of lithium in solar-type stars, as they evolve; neither do they account for the observed profile of molecular weight at the base of the solar convection zone. Such macroscopic transport can be achieved through thermally driven meridian currents, through turbulent diffusion generated by differential rotation and possibly through gravity waves. These processes transport also angular momentum, and therefore the internal rotation profile of the Sun provides a crucial test for their relative importance. So does also the behavior of tidally locked binaries, which appear to destroy less lithium than single stars of the same mass. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Dawn Gravity Investigation at Vesta and Ceres

The objective of the Dawn gravity investigation is to use high precision X-band Doppler tracking and landmark tracking from optical images to measure the gravity fields of Vesta and Ceres to a half-wavelength surface resolution better than 90-km and 300-km, respectively. Depending on the Doppler tracking assumptions, the gravity field will be determined to somewhere between harmonic degrees 15 and 25 for Vesta and about degree 10 for Ceres. The gravity fields together with shape models determined from Dawn??s framing camera constrain models of the interior from the core to the crust. The gravity field is determined jointly with the spin pole location. The second degree harmonics together with assumptions on obliquity or hydrostatic equilibrium may determine the moments of inertia.     

Polar magnetic disturbances and field-aligned currents

The results of research of the morphology and physics of polar magnetic disturbances and their connection with three-dimensional magnetospheric currents are reviewed. Magnetic disturbance current systems are examined, also their relation to solar wind parameters and magnetic activity level and their seasonal dependence. On the basis of numerical model calculations it is shown that magnetospheric field-aligned currents observed by the TRIAD and ISIS-2 satellites are the main generation mechanism of high-latitude magnetic disturbances. Plasma pressure gradients are examined as a source of energy for driving field-aligned currents in the closed magnetosphere.     

月球重力场及低轨环月卫星轨道保持仿真分析

为了在满足精度要求的前提下节省月球重力场模型的计算时间,依据Kaula准则分析了目前国际上公认的最精确的两个重力场模型GLGM-2和LP165P,提出了在一定阶次截断重力场模型的问题.通过仿真不同阶次重力场模型作用下轨道高度为50 km的圆形极轨道环月卫星轨道特征的变化,验证了50 km以上高度卫星非球形摄动分析时可以将重力场模型截断至一定阶次的结论,并利用截断至70阶次的重力场模型仿真分析200 km圆轨道卫星一年内轨道下降程度.最后在仿真结果的基础上得到了200 km高度环月卫星需要每50天进行一次轨道保持控制的结论并完成一次轨道保持控制仿真.研究结论可以为我国低轨环月卫星轨道保持提供参考.     

Effects of Geodetic Uncertainties on a Damped Inertial Navigation System

Gravity uncertainties are an inexorable source of error in all inertial navigation systems and are particularly important in high-quality inertial navigation systems. In this paper the steady-state rms errors that are excited in a damped inertial navigation system are analytically determined for four gravity uncertainty models and two vehicle maneuver models. The statistical approach used in this paper is compared with an alternate scheme (?direct simulation?) that does not require statistical models for gravity uncertainties.     

Polar ionospheric disturbance effects on NNSS satellite positioning

From the analysis of the United States Navy navigation satellite system (NNSS) positioning data of about 10000 passes, it is clearly found that polar ionospheric disturbance affects the positioning. The positioning error increases with increasing geomagnetic disturbance level (local K-index), and the pass number of position fixes decreases by one or two per day when the K-index is large. These effects may arise from the spatial gradients of electron density and/or the radio wave scattering due to well-developed ionospheric irregularities inherent to the disturbed auroral ionosphere     

风洞虚拟飞行模型机与原型机动力学特性分析

在低速风洞虚拟飞行试验系统中,采用三自由度（3-DOF）球铰支撑动力学相似缩比飞机模型,在气动力矩作用下试验模型可绕质心自由转动。这种带约束的运动与具有六自由度（6-DOF）的真实大气飞行存在差别,鉴于此,对各影响因素逐个剖离并进行了数值模拟和对比分析。结果表明：位移约束使两者间的动力学特性产生较明显的差异,缩比的影响符合相似准则规律,机构摩擦、模型重心与支撑点不重合影响较小,常值干扰力矩对模型的初始响应有一定影响。对比分析结果可以用于指导风洞虚拟飞行试验的开展,并有助于完善风洞虚拟飞行试验技术及其拓展应用。     

Tidal Models in a New Era of Satellite Gravimetry

The high precision gravity measurements to be made by recently launched (and recently approved) satellites place new demands on models of Earth, atmospheric, and oceanic tides. The latter is the most problematic. The ocean tides induce variations in the Earth's geoid by amounts that far exceed the new satellite sensitivities, and tidal models must be used to correct for this. Two methods are used here to determine the standard errors in current ocean tide models. At long wavelengths these errors exceed the sensitivity of the GRACE mission. Tidal errors will not prevent the new satellite missions from improving our knowledge of the geopotential by orders of magnitude, but the errors may well contaminate GRACE estimates of temporal variations in gravity. Solar tides are especially problematic because of their long alias periods. The satellite data may be used to improve tidal models once a sufficiently long time series is obtained. Improvements in the long-wavelength components of lunar tides are especially promising. This revised version was published online in August 2006 with corrections to the Cover Date.     

导弹飞控系统可靠性仿真研究

提出了在几种主要因素影响下进行飞控系统性能和可靠性一体化分析的方法。建立了风、结构误差(包括弹体质量分布不对称、弹体不同轴、翼面安装角误差和舵面机械零位误差)、推力偏心和硬件故障等因素的扰动模型,给出了可靠性仿真的方法、实施步骤、具体算法流程和相关可靠性指标的计算公式。以某型导弹飞控系统作为案例,进行了大量仿真,分析了风等因素对该系统可靠性的影响。通过算例证明,所建立的扰动模型和可靠性分析方法是正确的。