捷联式航空重力测量算法比较

捷联式航空重力测量系统与平台式系统相比具有体积小、重量轻、功耗低等许多优点,近些年来取得了显著的研究进展.本文给出了捷联式航空重力测量的两种算法模型:捷联式惯性标量重力测量(SISG)和旋转不变式标量重力测量(RISG)模型,并对其误差模型作了初步讨论.利用我国首套捷联式航空重力仪SGA-WZ01在某海域的部分试验数据,对两种算法模型进行了比较分析,表明其差值之标准差对于200s的滤波长度小于0.5mGal.同时,利用两组重复测线数据估算了不同滤波尺度下的两种算法的内符合精度,表明SISG算法略优于RISG算法.对于200s和300s的滤波长度,SISG的内符合精度分别为1.06mGal和0.80mGal.     

Absolute airborne gravimetry: a feasibility study

We report here the results obtained during a feasibility study that was pursued in order to evaluate the performances of absolute airborne gravimetry. In contrast to relative systems, which use spring‐type gravimeters, each measurement acquired by absolute systems is independent from the others and the instrument is not suffering from problems like instrumental drift, frequency response of the spring and variation of the calibration factor. After a validation of the dynamic performance of the experimental setup in a moving truck, a comparison between the experimental airborne data retrieved over the Swiss Alps and those obtained by ground upward continuation at flight altitude allow us to state that airborne absolute gravimetry is feasible. The first test flight shows a spatial resolution comparable to those obtained by relative airborne gravimetry. For a wavelength on the order of 12 km the absolute value of gravity can be evaluated with an uncertainty of 6.9 mGal.     

Improving airborne strapdown vector gravimetry using stabilized horizontal components

Integrating the deflections of the vertical along the flight line can yield geoid profiles which are valuable in the study of geodesy and geophysics, fortunately, the deflections can be measured directly by vector gravimetry. Airborne vector gravimetry using a Strapdown Inertial Navigation System and the Global Navigation Satellite System (SINS/GNSS) has shown promising results in previous studies. However, the quality of the SINS and GNSS is a major limitation; in particular, the attitude errors induced by the gyros will result in large measurement errors to the horizontal components of the gravity disturbance, and these measurement errors represent the behavior of low-frequency trend. An airborne vector gravimetry method used to remove the bias and low-frequency trends in the gravity disturbance estimated for each survey line has been developed. This method uses the horizontal components of the gravity disturbance computed from EGM2008 (Earth Gravitational Model 2008) as a reference. Firstly, the horizontal measurement results obtained from the gravimeter are divided into high- and low-frequency components according to the resolution of the EGM2008, and then, the bias and low-frequency trends of the low-frequency components are corrected using a linear fit to the EGM2008 reference data. Finally, the ultimate results can be acquired after combining the high-frequency components and the corrected low-frequency components. The data used was obtained from the SGA-WZ, which is the first strapdown airborne gravimeter developed in China. The results of this method are promising. The internal accuracy of the gravity disturbance's horizontal components for repeated survey lines exceeds 3.5 mGal, and the corresponding resolution is approximately 4.8 km based on 160-s data smoothing and an airplane averaging speed of approximately 216 km/h. After applying the WCF (Wavenumber Correlation Filter), the internal accuracy of the horizontal components exceeds 2 mGal. This can satisfy the requirement of the application in geodesy and solid earth geophysics.     

航空重力测量中载体运动加速度的确定

航空重力测量是使用重力仪、GPS及其他传感器测定地球重力场的一种新型技术，其基本原理是利用重力仪测定包括重力加速度、载体运动加速度以及其他一些加速度在内的总加速度，从观测值中减去利用GPS确定的载体运动加速度，再加上一些改正，得到了重力加速度. 本文推导了确定载体运动加速度的直接解算法的公式，利用某次航空重力测量数据，分别在静态、动态两种情况下，分析了确定载体运动加速度精度. 结果表明：在静态、60s的平滑间隔条件下，载体加速度的确定精度是0.4—0.9mGal；在动态、90s的平滑间隔条件下，整个飞行测段载体运动加速度的确定精度是1—3mGal.     

引入最优自适应因子的状态模型法航空重力测量

引入最优自适应比例因子以改善状态模型法航空重力测量的精度,并尝试将其应用到我国困难地区的重力测量.把重力扰动当作状态量引入Kalman滤波进行最优估计,并引入最优自适应因子调节状态信息的权阵,提高重力扰动的最终解算精度.利用新疆地区不同航次和航高的实测数据,计算了垂直向下方向上的重力扰动.与全球重力场模型EGM2008的对比分析表明,差值中误差在10mGal左右,接近国家在困难地区重力测量精度的限差要求.     

Airborne gravimetry using a strapped-down LaCoste and Romberg air/sea gravity meter system: a feasibility study

Marine gravimeters mounted on stabilized platforms are commonly used in aircraft to perform airborne gravity measurements. The role of the stabilized platform is to level the sensor mechanically, whatever the aircraft attitude. However, this compensation is generally insufficient due to the sensitivity of modern gravity sensors. Correcting the offlevel error requires that an offlevel correction calculated from positioning data be added to gravimeter measurements, which complicates not only the processing, but also the assessment of precision and resolution. This paper is a feasibility study describing the levelling of a completely strapped‐down LaCoste and Romberg gravimeter for airborne gravimetry operation, by means of GPS positioning data. It focuses on the calculation of the sensor offlevel correction needed for the complete gravity data processing. The precision of the offlevel correction that can be achieved, in terms of GPS data precision and gravity wavelengths, is theoretically studied and estimated using the gravity and GPS data acquired during the Alpine Swiss French airborne gravity survey carried out in 1998 over the French Western Alps. While a 1 cm precision of GPS‐determined baseline coordinates is sufficient to achieve a 5 mGal precision of the offlevel correction, we maintain that this precision has to reach 1 mm to ensure a 1 mGal precision of the offlevel correction at any wavelength. Without a stabilized platform, the onboard instrumentation becomes significantly lighter. Furthermore, the correction for the offlevel error is straightforward and calculated only from GPS data. Thus, the precision and the resolution of airborne gravity surveys should be estimated with a better accuracy.     

航空重力测量研究进展

近十几年来,航空重力测量技术的研究和应用日趋活跃,业已成为地球重力场研究中最为热门的领域之一．航空重力测量可分为航空标量重力测量、航空矢量重力测量和航空梯度重力测量．本文概述了航空标量重力测量的研究现状及发展动态,传统航空重力测量系统的改进,新型系统方案的研究,从GPS中导出加速度的理论和方法．滤波和估算方法及航空重力数据的应用等五个方面的重要研究成果．文中最后介绍了我国自行研制的航空重力测量系统的概况。     

自适应卡尔曼滤波在航空重力异常解算的应用研究

依据航空重力测量基本原理,构建了航空重力异常解算的卡尔曼滤波模型,将新息自适应卡尔曼滤波器(IAE,Innovation based Adaptive Estimation)应用于量测噪声未知的航空重力异常解算.针对IAE滤波器滑动窗口宽度难以准确确定的问题,通过对多个不同滑动窗口新息协方差估计的加权平均,获得改进的IAE滤波器,该IAE滤波器不仅具有量测噪声自适应估计能力,还能实现滑动采样窗口的优化选取.试验结果表明,IAE滤波器可以降低因量测噪声统计信息不明引起的解算误差,改进IAE解算的重力异常误差约为1mGal.     

Reconstructing the gravity gradient anomaly field from surveys with wide line spacing using equivalent source processing: an error analysis

When anomalous gravity gradient signals provide a large signal‐to‐noise ratio, airborne and marine surveys can be considered with wide line spacing. In these cases, spatial resolution and sampling requirements become the limiting factors for specifying the line spacing, rather than anomaly detectability. This situation is analysed by generating known signals from a geological model and then sub‐sampling them using a simulated airborne gravity gradient survey with a line spacing much wider than the characteristic anomaly size. The data are processed using an equivalent source inversion, which is used subsequently to predict and grid the field in‐between the survey lines by means of forward calculations. Spatial and spectral error analysis is used to quantify the accuracy and resolution of the processed data and the advantages of acquiring multiple gravity gradient components are demonstrated. With measurements of the full tensor along survey lines spaced at 4 × 4 km, it is shown that the vertical gravity gradient can be reconstructed accurately over a bandwidth of 2 km with spatial root‐mean square errors less than 30%. A real airborne full‐tensor gravity gradient survey is presented to confirm the synthetic analysis in a practical situation.     

航空重力重复线测试数据质量评价方法研究

为了量化评估航空重力系统的性能指标,通常采用多次往返的重复线测量方式来测试航空重力仪动态测量的重复性和一致性,但现有规范中没有明确针对航空重力重复线测试数据质量的评估准则,本文研究总结了航空重力重复线测试数据均方差精度计算方法,依据重复线测试数据均方差内、外符合精度的计算结果,可以更为客观地评估仪器的动态测量精度指标和工作状态.     

EGM2008地球重力模型数据在中国大陆地区的精度分析

本文介绍了5′×5 ′的EGM2008地球重力模型及其在全球的精度评价.按照地形变化规律,将中国大陆大致分为7个区域,在10 km网度上,将EGM2008地球重力模型数据与中国地面实测空间重力网格数据进行了对比.由于数据源的问题,中国大陆的模型数据精度普遍低于北美和欧洲.二种数据在地形平坦的东部地区差别较小,向西随着地形复杂程度的增加,二种数据之间的标准差从小于10 mGal增大到50多mGal.畸变点分析表明精度极低的网格点均分布在地形起伏大的地区.总体而言,5′×5′的EGM2008地球重力模型数据在中国大陆将近80％的面积上的精度可达10 mGal之内,可用于小比例尺重力编图和构造研究.在地形起伏较大的中国西部以青藏高原为例进一步比较了EGM2008重力模型和重力测点数据,结果表明在重力点分布稀疏不均匀的地区,平面网格数据难以准确表达重力场信息.由于缺少地面重力数据控制,EGM2008重力模型数据在中国西部精度较低,但模型数据依然在很大程度上提高了空间重力异常信息的丰富程度.将中国区域重力调查成果数据应用于地球模型的构建是一项有意义的工作.     

Numerical Studies on the Harmonic Downward Continuation of Band-Limited Airborne Gravity

In this paper, the numerical stability and efficiency of methods of harmonic downward continuation from flying altitudes are treated for sampled gravity field data. The problem is first formulated in its continuous form, i.e. as the inverse solution of the spherical Dirichlet problem, and is then approximated by Gaussian quadrature to yield a finite system of linear equations. The numerical stability of this system is investigated for both error-free gravity data and for the noisy and band-limited gravity measurements usually obtained from airborne gravity surveys. It can be shown that the system becomes ill-conditioned, once the ratio between flying altitude and data sampling rate exceeds a certain limit. It can also be shown that noisy measurements tend to generate a solution that is practically useless, long before the system becomes ill-conditioned. Therefore, instead of treating the general solution of the discrete downward continuation problem, the more modest question is studied, for which range of flying altitudes and sampling rates, the numerical solution of the discrete linear system can be considered as practically useful. Practically useful will be defined heuristically as of sufficient accuracy and stability to satisfy the requirements of the user. The question will be investigated for the specific application of geoid computation from gravity data sampled at flying altitudes. In this case, a stable solution with a standard deviation of a few centimeters is required. Typical flight parameters are heights of 2–6 km, a minimum half-wavelength resolution of 2 km, and data noise between 0.5 and 1.5 mGal. Different methods of geoid determination, different solution techniques for the resulting systems of linear equations, and different minimization principles will be compared. As a result operational parameters will be defined which, for a given noise level, will result in a geoid accuracy of a few centimeters for the estimated band-limited gravity field spectrum.     

一种新的基于局部重力图逼近的组合匹配算法

惯性导航系统定位误差随时间积累发散,利用重力场辅助惯性导航已成为组合导航领域的新方向,该技术对实现潜艇无源定位意义重大.首先利用二维高斯基函数对局部离散格网重力异常基准图进行逼近获取其解析表达式,在此基础上对传统相关极值匹配算法进行重新建模,采用拟牛顿BFGS非线性寻优方法对该模型进行解算,最终完成基于连续解析形式重力异常基准图的相关极值匹配算法设计.为进一步提高算法性能进行以下两点改进:(1)采用TERCOM算法进行预匹配以缩小寻优范围提高寻优速度;(2)采用差分法减小实测过程中Eötvös效应对重力匹配的影响.最后在2'×2'卫星测高反演重力异常数据库基础上进行了三组对比仿真实验,从实验结果可以看出,在重力测量误差、系统误差及初始定位误差较大的情况下,通过该组合匹配算法获得的匹配定位仍能以较高的精度跟踪真实航迹,且其性能较传统单一匹配算法有较大提高.     

空间分辨率和空间差分精度对水平网格性能的影响

为了说明在物理空间中空间差分精度和空间分辨率对Arakawa A-D网格性能的影响程度,将线性浅水方程组采用二阶中央差和四阶中央差格距分别取100 km、10 km和1 km在Arakawa A-D网格上进行离散和120 min的模拟预报,模拟结果和解析解进行比较,结果表明：当网格距是1 km时,不论采用二阶中央差分方案还是四阶中央差分方案,重力惯性波在4种网格上模拟的结果相同,即变量配置的影响是可以忽略的;当网格距增加到10 km或100 km时,不同的变量配置模拟的结果是不同的.但是,不论对二阶中央差还是四阶中央差,当网格距相同的情况下,在C网格上模拟得到的结果均方根误差最小,在D网格上模拟得到的结果均方根误差最大.同时也表明：当差分精度从二阶增加到四阶后,模拟结果的误差并非一致减少,并和群速相对误差的变化一致,因此对于初值为混合波的多变量方程组而言,增加差分精度不能改进模拟的结果.并且缩小网格距比增加差分精度对减少在Arakawa A-D 网格上离散产生的误差更明显.     

融合多源数据构建区域航空重力梯度扰动全张量

通过联合全球重力位模型(EGM2008)、航空重力扰动数据和剩余地形模型(RTM)数据,基于频谱域(二维FFT变换)和空间域(Stokes数值积分)算法对毛乌素测区GT-2A航空重力测量系统采集的空中测线后处理重力扰动数据进行解算,构建了该地区的航空重力梯度扰动全张量.(1)残余航空重力扰动延拓结果表明:残余航空重力扰动经向下延拓至大地水准面,再向上延拓至航空高度后与原数据差值的标准差为1.0078 mGal,考虑边缘效应后,内缩计算范围得到的差值标准差减小至0.1269 mGal.(2)基于残余重力扰动数据(原航空高度数据及向下延拓数据),通过不同方案解算得到的梯度扰动结果表明:两种方案得到的研究区域重力梯度扰动各分量之差的最大标准差为6.4798E(Γ_(yz)分量),最小标准差为2.6968E(Γ_(xy)分量),内缩计算范围后得到的差值标准差最大值为1.8307E(Γ_(zz)分量),最小值为0.7223E(Γ_(yz)分量).本文的思路和方法可为未来我国自主构建航空重力梯度标定场提供参考.     

Optimal Model for Geoid Determination from Airborne Gravity

Two different approaches for transformation of airborne gravity disturbances, derived from gravity observations at low-elevation flying platforms, into geoidal undulations are formulated, tested and discussed in this contribution. Their mathematical models are based on Green's integral equations. They are in these two approaches defined at two different levels and also applied in a mutually reversed order. While one of these approaches corresponds to the classical method commonly applied in processing of ground gravity data, the other approach represents a new method for processing of gravity data in geoid determination that is unique to airborne gravimetry. Although theoretically equivalent in the continuous sense, both approaches are tested numerically for possible numerical advantages, especially due to the inverse of discretized Fredholm's integral equation of the first kind applied on different data. High-frequency synthetic gravity data burdened by the 2-mGal random noise, that are expected from current airborne gravity systems, are used for numerical testing. The results show that both approaches can deliver for the given data a comparable cm-level accuracy of the geoidal undulations. The new approach has, however, significantly higher computational efficiency. It would be thus recommended for real life geoid computations. Additional errors related to regularization of gravity data and the geoid, and to accuracy of the reference field, that would further deteriorate the quality of estimated geoidal undulations, are not considered in this study.     

一种新型重力测量卫星系统确定全球重力场的性能分析

本文设计了一种高-低卫星跟踪卫星、低-低卫星跟踪卫星和卫星重力梯度测量相结合的新型重力测量卫星系统,其可在一定程度上发挥卫星重力梯度和低低卫星跟踪卫星两种测量模式各自的优势.基于重力卫星系统指标设计的半解析法,深入分析了不同重力测量卫星系统配置和不同观测量及其不同白噪声水平情况下,新型卫星重力测量模式反演重力场模型的能力.数值模拟分析结果表明：在观测值精度和星间距离相同的条件下,轨道高度是影响重力场反演精度的关键因素;随着星间距离的增大,高频重力场信号反演精度会先提高后降低,轨道高度在200~350 km之间时,星间距离在150~180 km之间时反演精度最优;星间距离变率和卫星重力梯度两类观测值仅在某些精度配置时可达到优势互补,如果某一类观测值精度很高,则另一类观测值在联合解算时贡献非常小或者没有贡献.在300 km轨道高度,若以GRACE和GOCE任务的设计指标1 μm·s^-1/√Hz和5 mE/√Hz来配置新型重力测量卫星系统中星间距离变率和引力梯度观测值的精度,联合两类观测值解算200阶次模型大地水准面的精度比独立解算分别提高1.2倍和2.8倍.如果以实现100 km空间分辨率1~2 cm精度大地水准面为科学目标,考虑卫星在轨寿命,建议轨道高度选择300 km,星间距离变率和卫星重力梯度的精度分别为0.1 μm·s^-1/√Hz和1 mE/√Hz.本文的研究成果可为中国研制自主的重力测量卫星系统提供参考依据.     

The NAFE’06 data set: Towards soil moisture retrieval at intermediate resolution

The National Airborne Field Experiment 2006 (NAFE’06) was conducted during a three week period of November 2006 in the Murrumbidgee River catchment, located in southeastern Australia. One objective of NAFE’06 was to explore the suitability of the area for SMOS (Soil Moisture and Ocean Salinity) calibration/validation and develop downscaling and assimilation techniques for when SMOS does come on line. Airborne L-band brightness temperature was mapped at 1 km resolution 11 times (every 1–3 days) over a 40 by 55 km area in the Yanco region and 3 times over a 40 by 50 km area that includes Kyeamba Creek catchment. Moreover, multi-resolution, multi-angle and multi-spectral airborne data including surface temperature, surface reflectance (green, read and near infrared), lidar data and aerial photos were acquired over selected areas to develop downscaling algorithms and test multi-angle and multi-spectral retrieval approaches. The near-surface soil moisture was measured extensively on the ground in eight sampling areas concurrently with aircraft flights, and the soil moisture profile was continuously monitored at 41 sites. Preliminary analyses indicate that (i) the uncertainty of a single ground measurement was typically less than 5% vol. (ii) the spatial variability of ground measurements at 1 km resolution was up to 10% vol. and (iii) the validation of 1 km resolution L-band data is facilitated by selecting pixels with a spatial soil moisture variability lower than the point-scale uncertainty. The sensitivity of passive microwave and thermal data is also compared at 1 km resolution to illustrate the multi-spectral synergy for soil moisture monitoring at improved accuracy and resolution. The data described in this paper are available at www.nafe.unimelb.edu.au.     

武汉九峰地震台超导重力仪观测分析研究

连续重力观测和GPS的技术结合能够监测到物质迁移和地壳垂直形变之间的量化关系.和相对重力测量以及绝对重力测量技术相比,其避免了时间分辨率和观测精度低,无法精细描述观测周期内的物质迁移过程问题.本文利用武汉九峰地震台超导重力仪SGC053超过13000 h连续重力观测数据;同址观测的绝对重力仪观测结果;气压数据;周边GPS观测结果;GRACE卫星的时变重力场;全球水储量模型等资料,采用同址观测技术、调和分析法、相关分析方法在扣除九峰地震台潮汐、气压、极移和仪器漂移的基础上,利用重力残差时间序列和GPS垂直位移研究物质迁移和地壳垂直形变之间的量化关系.结果表明:在改正连续重力观测数据的潮汐、气压、极移的影响后,不仅准确观测到2009年的夏秋两季由于水负荷引起的约(6~8)×10^-8m·s^-2短期的重力变化.而且在扣除2.18×10^-8(m·s^-2)/a仪器漂移和水负荷的影响后,验证了本地区长短趋势垂直形变和重力变化之间具有一致的负相关性规律.同时长趋势表明该地区地壳处于下沉,重力处于增大过程,增加速率约为1.79×10^-8(m·s^-2)/a.武汉地区重力梯度关系约为-354×10^-8(m·s^-2)/m.     

基于改进A*算法的水下重力匹配导航路径规划

水下重力匹配导航作为辅助手段,能够有效克服惯性导航系统在水下长时间航行产生的误差积累.重力场的不规则性,使得不同海域重力场适配性存在差异,重力特征变化显著的海域匹配精度较高,反之精度较低.在适配性评价基础上,对导航路径进行规划有助于提高作业任务可行性,合理规避不利因素.本文采用重力异常标准差、粗糙度等特征参数对海域重力场适配性进行评价,形成重力场适配格网参考图,引入A^*算法规划起始点和目标点间路径,达到了有效规避非适配区、提高航路设计合理性的目的.传统A^*算法存在的问题是,规划路径折线较多、线路总弯曲度大,本文设计了一种改进方法,通过前后向对比分析,对单个路径节点逐个进行筛选过滤,有效减少了冗余航向调整,实现了路径的平滑优化.