A comparison and analysis of airborne gravimetry results from two strapdown inertial/DGPS systems

In September 1996 the University of Calgary tested a combination of strapdown inertial navigation systems and differential global positioning system (DGPS) receivers for their suitability to determine gravity at aircraft flying altitudes. The purpose of this test was to investigate the long-term accuracy and repeatability of the system, as well as its potential for geoid and vertical gradient of gravity determination. The test took place during a 3-day period in the Canadian Rocky Mountains over a single 100 × 100 km area which was flown with 10-km line spacing. Two flights were done at 4350 m in E–W and N–S profile directions, respectively, and one at 7300 m with E–W profiles. Two strapdown inertial systems, the Honeywell LASEREF III and the Litton-101 Flagship, were flown side by side. Comparison of the system estimates with an upward-continued reference showed root-mean-square (RMS) agreement at the level of 3.5 mGal for 90- and 120-s filter lengths. The LASEREF III, however, performed significantly better than the Litton 101 for shorter filtering periods of 30 and 60 s. A comparison between the two systems results in an RMS agreement of 2.8 and 2.3 mGal for the 90- and 120-s filters. The better agreement between the two systems is mainly due to the fact that the upward-continued reference has not been filtered identically to the system gravity disturbance estimates. Additional low-frequency differences seem to point to an error in the upward-continued reference. Finally, an analysis of crossover points between flight days for the LASEREF III shows a standard deviation of 1.6 mGal, which is near the noise level of the INS and GPS data. Further improvements to the system are possible, and some ideas for future work are briefly presented. Received: 17 March 1998 / Accepted: 1 February 1999     

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     

A comparison of methods for the inversion of airborne gravity data

Four integral-based methods for the inversion of gravity disturbances, derived from airborne gravity measurements, into the disturbing potential on the Bjerhammar sphere and the Earths surface are investigated and compared with least-squares (LS) collocation. The performance of the methods is numerically investigated using noise-free and noisy observations, which have been generated using a synthetic gravity field model. It is found that advanced interpolation of gravity disturbances at the nodes of higher-order numerical integration formulas significantly improves the performance of the integral-based methods. This is preferable to the commonly used one-point composed Newton–Cotes integration formulas, which intrinsically imply a piecewise constant interpolation over a patch centered at the observation point. It is shown that the investigated methods behave similarly for noise-free observations, but differently for noisy observations. The best results in terms of root-mean-square (RMS) height-anomaly errors are obtained when the gravity disturbances are first downward continued (inverse Poisson integral) and then transformed into potential values (Hotine integral). The latter has a strong smoothing effect, which damps high-frequency errors inherent in the downward-continued gravity disturbances. An integral method based on the single-layer representation of the disturbing potential shows a similar performance. This representation has the advantage that it can be used directly on surfaces with non-spherical geometry, whereas classical integral-based methods require an additional step if gravity field functionals have to be computed on non-spherical geometries. It is shown that defining the single-layer density on the Bjerhammar sphere gives results with the same quality as obtained when using the Earths topography as support for the single-layer density. A comparison of the four integral-based methods with LS collocation shows that the latter method performs slightly better in terms of RMS height-anomaly errors.     

A new approach for airborne vector gravimetry using GPS/INS

A new method for airborne vector gravimetry using GPS/INS has been developed and the results are presented. The new algorithm uses kinematic accelerations as updates instead of positions or velocities, and all calculations are performed in the inertial frame. Therefore, it is conceptually simpler, easier, more straightforward and computationally less expensive compared to the traditional approach in which the complex navigation equations should be integrated. Moreover, it is a unified approach for determining all three vector components, and no stochastic gravity modeling is required. This approach is based on analyzing the residuals from the Kalman filter of sensor errors, and further processing with wavenumber coefficient filterings is applied in case closely parallel tracks of data are available. An application to actual test-flight data is performed to test the validity of the new algorithm. The results yield an accuracy in the down component of about 3–4 mGal. Also, comparable results are obtained for the horizontal components with accuracies of about 6 mGal. The gravity modeling issue is discussed and alternative methods are presented, none of which improves on the original approach. Received: 18 April 2000 / Accepted: 14 August 2000     

Assessment of long-range kinematic GPS positioning errors by comparison with airborne laser altimetry and satellite altimetry

Long-range airborne laser altimetry and laser scanning (LIDAR) or airborne gravity surveys in, for example, polar or oceanic areas require airborne kinematic GPS baselines of many hundreds of kilometers in length. In such instances, with the complications of ionospheric biases, it can be a real challenge for traditional differential kinematic GPS software to obtain reasonable solutions. In this paper, we will describe attempts to validate an implementation of the precise point positioning (PPP) technique on an aircraft without the use of a local GPS reference station. We will compare PPP solutions with other conventional GPS solutions, as well as with independent data by comparison of airborne laser data with “ground truth” heights. The comparisons involve two flights: A July 5, 2003, airborne laser flight line across the North Atlantic from Iceland to Scotland, and a May 24, 2004, flight in an area of the Arctic Ocean north of Greenland, near-coincident in time and space with the ICESat satellite laser altimeter. Both of these flights were more than 800 km long. Comparisons between different GPS methods and four different software packages do not suggest a clear preference for any one, with the heights generally showing decimeter-level agreement. For the comparison with the independent ICESat- and LIDAR-derived “ground truth” of ocean or sea-ice heights, the statistics of comparison show a typical fit of around 10 cm RMS in the North Atlantic, and 30 cm in the sea-ice region north of Greenland. Part of the latter 30 cm error is likely due to errors in the airborne LIDAR measurement and calibration, as well as errors in the “ground truth” ocean surfaces due to drifting sea-ice. Nevertheless, the potential of the PPP method for generating 10 cm level kinematic height positioning over long baselines is illustrated.     

重力异常向上延拓严密改化模型及向下延拓应用

重力异常向上延拓全球积分模型在航空重力测量数据质量评估和向下延拓迭代计算等领域具有广泛的应用。为了消除积分核函数奇异性影响,需要对该模型进行基于积分恒等式的移去-恢复转换及全球积分域的分区改化处理。在此过程中,传统改化处理方法往往忽略了全球积分过渡到局域积分引起的积分恒等式偏差影响,从而导致不必要的计算模型误差,最终影响向上延拓计算结果的可靠性,甚至影响向下延拓迭代解算结果的稳定性。针对此问题,本文开展了重力异常向上延拓积分模型改化及向下延拓应用分析研究,依据实测数据保障条件和积分恒等式适用条件要求,导出了重力异常向上延拓积分模型的分步改化公式,提出了补偿传统改化模型缺陷的修正公式,并将最终的严密改化模型应用于重力异常向下延拓迭代解算。使用超高阶地球位模型EGM2008作为标准位场开展数值计算检验,分别对重力异常向上延拓分步改化模型的计算精度及在向下延拓迭代解算中的应用效果进行了检核评估,验证了采用严密改化模型的必要性和有效性。     

Analyses and Solutions of Errors on GPS／GLONASS Positioning

This paper focuses mainly on the major errors and their reduction approaches pertaining to combined GPS/GLONASS positioning.To determine thd difference in the time reference systems,different receiver clock offsets are introduced with respect to GPS and GLONASS system time.A more desirable method for introducing a independent unknown parameter of fifth receiver,which can be canceled out when forming difference measurements,is discussed.The error of orbit integration and the error of transformation parameters are addressed in detail.Results of numerical integration are give.To deal with the influence of ionospheric delay,a method for forming dual-frequency ionospheric free carrier phase measurements is detailed.     

油田地面工程地理信息系统的设计与开发

根据油田地面集输数据的分布特点,采用SuperMap空间数据处理技术和二三维一体化技术,并紧密结合数字油田和物联网理念,探索与研究基于数据层、服务层和应用层的Browse/Servre模式油田地面工程地理信息系统,旨在为油田集输管理提供基础依据,提高油田事故预警、投资决策的科学性。     

基于多智能体与GIS集成的体育场人群疏散模拟方法

研究了基于多智能体与GIS集成的体育场所人群疏散模拟的方法,推演、提出了模拟模型的总体框架与数学表达式,讨论了移动人群智能体移动决策的表达与实现技术,设计并开发了模拟原型系统。以上海体育场主体育中心为案例实现了对观众离场的全过程模拟,为应急情况下的决策处理提供了一个有用的可参考范例。