航空重力测量中基准站与测线的距离对精度的影响

简要介绍了航空重力测量中基准站的布设原则,结合2010年某地区的实际测量数据分析了基准站与测线的距离对航空重力测量的精度的影响。实际数据验证表明,基准站距离测线360km时,其交叉点重力异常不符值标准差可以达到±2．0816mGal,其精度符合规范要求,所以在GPS基准站布设困难的地区,可以依据测区的具体情况适当地放宽GPS的布设位置和距离。     

海岸带航空重力测量的初步结果及分析

2008年4月至7月，利用航空重力测量系统CHAGS对某海岸地区200km×200km区域进行了重力测量。本文概述了测量情况，介绍了航空重力测量数据处理方法。数据处理结果表明，在中等湍流条件下，交叉点重力异常不符值的标准差为3．0mGal；与卫星测高反演结果相比，5’×5’格网平均重力异常的精度为4．6mGal。     

渤海湾航空重力及其在海域大地水准面精化中的应用

近海航空重力数据在陆海大地水准面统一中起着重要作用。近3年来,利用我国首套航空重力测量系统(CHAGS)完成了渤海湾地区近20万平方千米的5′×5′格网平均重力异常数据的获取。本文首先介绍了渤海湾地区航空重力测量的概况,给出航空重力测量数据的处理要点;然后,详细讨论了航空重力测量的精度评估方法,其中针对该区域的测线布设特点,提出了"重叠格网比较法"以评估格网平均重力异常的内符合精度。结果表明,对于5′的波长分辨率,交叉点重力异常不符值在抗差后的中误差约为1.5 mGal,重叠格网法获得的5′×5′格网平均重力异常的中误差约为1.6 mGal;5′×5′格网重力异常与卫星测高和船测重力的比较精度优于3.0mGal;由航空重力测量获得的1°×1°格网平均重力异常与GOCE卫星重力位模型的计算值相比较,其系统性差异小于0.5 mGal、中误差约为2.7 mGal。利用航空重力数据后,渤海湾区域大地水准面与16个GPS水准点的比较精度由EGM2008模型的约23 cm提高到约12 cm。     

平原地区航空重力测量的精度分析

为检验我国首套航空重力测量系统(CHAGS)在平原地区的测量精度以及验证其在严寒气候条件下的作业性能,2003年11月以国产某新型航测机为载体在我国东北某地区进行试验。概述试验情况,介绍航空重力测量数据处理方法。试验结果表明,CHAGS在严寒气候条件下工作稳定、性能可靠,半波长分辨率为9km时,交叉点重力异常不符值的标准差为2.0mGal,5′×5′格网平均重力异常的外部精度为1.7mGal。     

航空重力测量数学模型及其测量精度分析

基于数学和分析力学角度分别推导了航空矢量重力测量的数学模型,得到了一致的模型公式;给出了矢量模型的3个分量形式,其中垂直方向的分量就是标量重力测量的数学模型;简要介绍了我国研制成功的航空标量重力测量系统CHAGS的数据处理的过程,分析了标量重力测量中测线交叉点和重复测线的重力异常的精度;根据实测数据计算的结果表明:测线交叉点重力异常不符值的标准差约为5×10-5ms-2左右,重复测线的内符合精度优于5×10-5ms-2,达到了预期的要求。     

LaCoste＆Romberg航空重力仪的交叉耦合改正

基于最小二乘原理．分别利用地面重力测量数据、交叉点重力异常不符值对CC（cross—coupling）监视项系数进行了重新标定，同时给出了CC监视项系数和摆杆尺度因子的联合标定方法。试验结果表明，采用新系数显著地降低了空中重力异常估值的系统误差，对于大同航空重力测量，系统误差从4．8mGal减小至1．8mGal。     

航空重力测量数学模型及其测量精度分析

基于数学和分析力学角度分别推导了航空矢量重力测量的数学模型,得到了一致的模型公式;给出了矢量模型的3个分量形式,其中垂直方向的分量就是标量重力测量的数学模型;简要介绍了我国研制成功的航空标量重力测量系统CHAGS的数据处理的过程,分析了标量重力测量中测线交叉点和重复测线的重力异常的精度;根据实测数据计算的结果表明:测线交叉点重力异常不符值的标准差约为5×10-5ms-2左右,重复测线的内符合精度优于5×10-5ms-2,达到了预期的要求.     

船载重力测量数据不同测区系统偏差纠正方法研究

分析了我国近海海域船载重力测量数据特征,并提出了消除不同测区之间重力测线上重力异常存在系统偏差的方案。提出了参考线的选择标准,利用参考测线上交叉点处的残差重力异常不符值,纠正其他测线重力异常的新思路。结果表明,对测线重力进行纠正后,不同测区的重力值不存在系统偏差,交叉点处不符值明显改善,测线上纠正后重力异常明显优于纠正前的重力异常。     

航空重力向上延拓的外部精度评估

分别采用基于梯度、基于泊松积分和基于快速傅里叶变换（FFT）的地面重力向上延拓方案,并提出交叉检验方法估计地面重力数据误差及其空中误差传播,对毛乌素测区GT-2A航空重力测量系统采集的空中测线数据进行外符合精度评价。对比结果表明：地面重力格网插值误差和代表性误差对空中点的影响达到0.66~0.92 mGal（1 Gal=1×10^-2 m/s²）,航空重力数据误差估计必须扣除这一影响;基于泊松积分和基于FFT的地面重力向上延拓方法能够客观评价航空重力观测值的外符合精度,二者表现相当;扣除地面重力误差影响后,在包含残余边界效应的情况下,毛乌素测区GT-2A航空重力空中测线重力扰动的外符合精度优于1.42 mGal。     

单站GPS确定航空重力测量载体运动加速度的方法与结果分析

飞机运动加速度的测量精度是制约航空重力测量技术发展的主要障碍之一。相较于传统动态差分GPS（differential GPS，DGPS）技术，所提方法采用单站测量模式，无需布设地面基准站。首先通过相位历元间差分解得高精度历元间位移序列，然后结合泰勒一阶中心差分获得载体加速度，重点分析了卫星轨道和卫星钟差对加速度估计的影响，结果表明，不同卫星轨道产品对加速度估计影响较小，而卫星钟差采样率对加速度估计的影响很大。结合中国陕西省境内的GT-2A航空重力测量系统飞行实测数据，利用单站法解算的加速度联合重力和姿态数据解算重力扰动结果与DGPS解算的重力扰动符合较好，当滤波长度为100 s时，两者互差优于1.0 mGal。重力扰动交叉点不符值网平差后，均方根（root mean square，RMS）为1.13 mGal。与地面重力实测值比较的结果表明，所提方法与DGPS方法在精度上基本一致，说明单站法标量航空重力测量是可行的。     

Flight test results from a strapdown airborne gravity system

In June 1995, a flight test was carried out over the Rocky Mountains to assess the accuracy of airborne gravity for geoid determination. The gravity system consisted of a strapdown inertial navigation system (INS), two GPS receivers with zero baseline on the airplane and multiple GPS master stations on the ground, and a data logging system. To the best of our knowledge, this was the first time that a strapdown INS has been used for airborne gravimetry. The test was designed to assess repeatability as well as accuracy of airborne gravimetry in a highly variable gravity field. An east-west profile of 250 km across the Rocky Mountains was chosen and four flights over the same ground track were made. The flying altitude was about 5.5km, i.e., between 2.5 and 5.0km above ground, and the average flying speed was about 430km/h. This corresponds to a spatial resolution (half wavelength of cutoff frequency) of 5.07.0km when using filter lengths between 90 and 120s. This resolution is sufficient for geoid determination, but may not satisfy other applications of airborne gravimetry. The evaluation of the internal and external accuracy is based on repeated flights and comparison with upward continued ground gravity using a detailed terrain model. Gravity results from repeated flight lines show that the standard deviation between flights is about 2mGal for a single profile and a filter length of 120s, and about 3mGal for a filter length of 90s. The standard deviation of the difference between airborne gravity upward continued ground gravity is about 3mGal for both filter lengths. A critical discussion of these results and how they relate to the different transfer functions applied, is given in the paper. Two different mathematical approaches to airborne scalar gravimetry are applied and compared, namely strapdown inertial scalar gravimetry (SISG) and rotation invariant scalar gravimetry (RISG). Results show a significantly better performance of the SISG approach for a strapdown INS of this accuracy class. Because of major differences in the error model of the two approaches, the RISG method can be used as an effective reliability check of the SISG method. A spectral analysis of the residual errors of the flight profiles indicates that a relative geoid accuracy of 23cm over distances of 200km (0.1 ppm) can be achieved by this method. Since these results present a first data analysis, it is expected that further improvements are possible as more refined modelling is applied. Received: 19 August 1996 / Accepted: 12 May 1997     

New results in airborne vector gravimetry using strapdown INS/DGPS

A method for airborne vector gravimetry has been developed. The method is based on developing the error dynamics equations of the INS in the inertial frame where the INS system errors are estimated in a wave estimator using inertial GPS position as update. Then using the error-corrected INS acceleration and the GPS acceleration in the inertial frame, the gravity disturbance vector is extracted. In the paper, the focus is on the improvement of accuracy for the horizontal components of the airborne gravity vector. This is achieved by using a decoupled model in the wave estimator and decorrelating the gravity disturbance from the INS system errors through the estimation process. The results of this method on the real strapdown INS/DGPS data are promising. The internal accuracy of the horizontal components of the estimated gravity disturbance for repeated airborne lines is comparable with the accuracy of the down component and is about 4–8 mGal. Better accuracy (2–4 mGal) is achieved after applying a wave-number correlation filter (WCF) to the parallel lines of the estimated airborne gravity disturbances.     

Downward continuation and geoid determination based on band-limited airborne gravity data

 The downward continuation of the harmonic disturbing gravity potential, derived at flight level from discrete observations of airborne gravity by the spherical Hotine integral, to the geoid is discussed. The initial-boundary-value approach, based on both the direct and inverse solution to Dirichlet's problem of potential theory, is used. Evaluation of the discretized Fredholm integral equation of the first kind and its inverse is numerically tested using synthetic airborne gravity data. Characteristics of the synthetic gravity data correspond to typical airborne data used for geoid determination today and in the foreseeable future: discrete gravity observations at a mean flight height of 2 to 6 km above mean sea level with minimum spatial resolution of 2.5 arcmin and a noise level of 1.5 mGal. Numerical results for both approaches are presented and discussed. The direct approach can successfully be used for the downward continuation of airborne potential without any numerical instabilities associated with the inverse approach. In addition to these two-step approaches, a one-step procedure is also discussed. This procedure is based on a direct relationship between gravity disturbances at flight level and the disturbing gravity potential at sea level. This procedure provided the best results in terms of accuracy, stability and numerical efficiency. As a general result, numerically stable downward continuation of airborne gravity data can be seen as another advantage of airborne gravimetry in the field of geoid determination. Received: 6 June 2001 / Accepted: 3 January 2002     

航空重力测量数据向下延拓的改进Poisson积分迭代法

目前,航空重力测量是快速获取陆地和近海区域高精度、高分辨率重力场信息的非常有效的技术手段,向下延拓则是其数据处理中的关键环节,直接影响到测量结果的进一步应用。本文在对传统最小二乘法、改进最小二乘法、Tikhonov正则化法等延拓模型进行数值分析的基础上,根据调和函数的基本特性,提出并建立了Poisson积分迭代法和改进Poisson积分迭代法延拓模型。实测航空和地面重力测量数据的试验结果表明,本文新建的Poisson积分迭代法和改进Poisson积分迭代法延拓模型精度相当,比传统最小二乘法延拓模型精度提高了15.26 mGal,比改进最小二乘法延拓模型精度提高了0.21 mGal,比Tikhonov正则化法延拓模型精度略低0.13 mGal,从而证明了本文所建模型的正确性和有效性。     

国产零长弹簧原理动态重力仪首次飞行试验及精度评估

CHZ-Ⅱ重力仪是首套完全国产零长弹簧原理航空重力仪,2018年4月在陕西渭南地区进行了首次飞行试验,共完成4个架次24条测线的有效飞行,标志着我国航空重力仪在自主研发的道路上又取得了长足的进步。利用飞行地区地面重力数据对CHZ-Ⅱ重力仪的测线扰动重力和格网扰动重力数据进行精度评估,其中空中测线在10 km分辨率条件下,精度达到1 mGal。采用地形辅助法对测量形成的5'测格网重力数据进行向下延拓,经延拓至地面后精度优于5 mGal,基本满足平原地区的测量需求。     

海空重力测量及应用技术研究若干进展

总结分析评述了海军重力研究团队在海空重力测量及应用技术研究领域取得的一些有理论意义和实用价值的研究成果,主要涵盖需求论证与顶层设计、观测数据归算与精度评估、测量误差分析处理与分离补偿、地表观测重力向上延拓、航空观测重力向下延拓、海域重力数据模型构建、地球外部重力场逼近和大地水准面精化等8个研究方向,重点从各项关键技术的研究背景、研究思路、难点突破、成果应用前景等几个方面进行了分析和总结,回答了该研究领域涉及理论方法和工程应用的一系列科学问题,为该领域未来发展提供借鉴和参考。     

卫星测高与船载重力测量数据融合的点质量拟合法

以拟合方差最小为准则,通过点质量法拟合船载重力测量数据,得到点质量大小、埋深等参数。回避点质量法数值求解的不稳定性问题,借鉴移去-恢复技术的思路,利用该参数计算船载重力测量点上的重力异常,并将其在测线上的重力异常中扣除,计算出船载重力残差值。以点质量大小、埋深等参数计算卫星测高重力格网点上重力异常,同样得到测高重力残差值。采用加权最小曲率格网化方法,将船载重力残差值与测高重力残差值格网化,进而恢复由点质量大小、埋深等参数计算格网点处的重力异常,实现卫星测高与船载重力测量数据融合。经国际船载重力测量数据检核,融合后的模型较国际船载重力测量数据的平均偏差在1~2 mGal（1 Gal=1×10^-2 m/s²）,标准差约为4 mGal。本文的研究方法可为陆地、海岸带区域的多种重力数据的融合、航空重力及卫星重力的向下延拓等问题提供参考。     

Cross-Coupling Correction for LaCoste ＆ Romberg Airborne Gravimeter

Abstract The cross-coupling corrections for the LaCoste ＆ Romberg airborne gravimeter are computed as a linear combination of 5 so-called cross-coupling monitors. The weight factors （coefficients） determined from marine gravity data by the factory are obviously not optimal for airborne application. These coefficients are recalibrated by minimizing the difference between airborne data and upward continued surface data （external calibration） and by minimizing the errors at line crossings （internal calibration） respectively. An integrating method to recalibrate the above-mentioned coefficients and the beam scale factor simultaneously is also presented. Experimental results show that the systemic errors in the airborne gravity anomalies can be greatly reduced by using any of the recalibrated coefficients. For example, the systemic error is reduced from 4.8 mGal to 1.8 mGal in Datong test.     

航空重力测量的滤波处理及最佳波长分辨率的探讨

根据航空重力测量的数据性质，对其滤波处理中最佳滤长分辨率的确定，提出了一种采用静态飞行数据进行检测的方法－即利用静态飞行数据处理后的重力异常误差平方和最小的原则。并对其在航空重力测量中的必要性做了检验和说明。