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.     

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 stable platform and strapdown airborne gravity

To date, operational airborne gravity results have been obtained using either a damped two-axis stable platform gravimeter system such as the LaCoste and Romberg (LCR) S-model marine gravimeter or a strapdown inertial navigation system (INS), showing comparable accuracies. In June 1998 three flight tests were undertaken which tested an LCR gravimeter and a strapdown INS gravity system side by side. To the authors' knowledge, this was the first time such a comparison flight was undertaken. The flights occurred in Disko Bay, off the west coast of Greenland. Several of the flight lines were partly flown along existing shipborne gravity profiles to allow for an independent source of comparison of the results. The results and analysis of these flight tests are presented. The measurement method and error models for both the stable platform and strapdown INS gravity systems are presented and contrasted. An intercomparison of gravity estimates from both systems is given, along with a comparison of the individual estimates with existing shipborne gravity profiles. The results of the flight tests show that the gravity estimates from the two systems agree at the 2–3 mGal level, after the removal of a linear bias. This is near the combined noise level of the two systems. It appears that a combination of both systems would provide an ideal airborne gravity survey system, combining the excellent bias stability of the LCR gravimeter with the higher dynamic range and increased spatial resolution of the strapdown INS. Received: 3 June 1999 / Accepted: 30 November 1999     

用SINS／GPS进行动态重力矢量测量的理论与方法

ＳＩＮＳ／ＧＰＳ组合导航技术为研究地球重力场开辟了一条崭新的探索途径。可以在运动过程中同时测定重力异常和垂线偏差，从而实现真正的动态矢量重力测量。本文研究了这种新理论方法的数学模型及实现方法，并针对重力扰动矢量的确定探讨了这种新技术的分辨率。     

Vector gravimetry using GPS in free-fall and in an Earth-fixed frame

The Global Positioning System (GPS) is considered in conjunction with a strapdown Inertial Measurement Unit (IMU) for measuring the gravity vector. A comparison of this system in space and on an airborne platform shows the relative importance of each system element in these two different acceleration environments. With currently available instrumentation, the acceleration measurement accuracy is the deciding factor in space, while on an Earth-bound (including airborne) platform, the attitude error of the IMU is most critical. A simulation shows that GPS-derived accelerations in space can be accurate to better than 0.1mgal for a 30s integration time, leading to estimates of 1° mean gravity anomalies on the Earth's surface with an accuracy of 4–5 mgal. On an airborne platform, the horizontal gravity estimation error is tightly coupled to the attitude error of the platform, which can only be bounded by external attitude updates. Horizontal gravity errors of 5mgal are achievable if the attitude is maintained to an accuracy of 1arcsec.     

Deriving Acceleration from DGPS: Toward Higher Resolution Applications of Airborne Gravimetry

Although airborne gravimetry is now considered a fully operational technique, errors due to motion compensation using differential GPS (DGPS) continue to influence both its accuracy and the range of applications in which it can be used. In typical medium-resolution applications such as airborne geoid mapping, errors due to DGPS contribute considerably to the error budget of an airborne gravity system. At the same time, efforts to increase the resolution of such systems for demanding applications such as resource exploration remain impedded by errors in DGPS. This article has three objectives. The first one is to compare eight industrially relevant DGPS software packages for the determination of aircraft acceleration. The second objective is to analyze and quantify the effect that each relevant portion of the DGPS error budget has on the determination of acceleration. Using data sets that represent a wide range of operational conditions, this is done in the frequency domain over a range of frequencies corresponding to spatial resolution as high as 450 m. The third objective is to use that information to recommend and demonstrate approaches that optimize the estimation of aircraft acceleration for determining the geoid and for resource exploration. It is shown, for example, that the time of day in which the survey is carried out and the dynamic characteristics of the aircraft being used are two of the most crucial parameters for very high-resolution gravity field estimation. It is demonstrated that when following the above-mentioned recommendations, agreements with ground daa of better than 1.5 and 2.5 mGal can be achieved for spatial resolutions (half-wavelengths) of 2.0 and 1.4 km, respectively. ? 2002 Wiley Periodicals, Inc.     

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     

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。     

GPS/INS navigation precision and its effect on airborne radio occultation retrieval accuracy

An airborne radio occultation (RO) system has been developed to retrieve atmospheric profiles of refractivity, moisture, and temperature. The long-term objective of such a system is deployment on commercial aircraft to increase the quantity of moisture observations in flight corridors in order to improve weather forecast accuracy. However, there are several factors important to operational feasibility that have an impact on the accuracy of the airborne RO results. We investigate the effects of different types of navigation system noise on the precision of the retrieved atmospheric profiles using recordings from the GNSS Instrument System for Multistatic and Occultation Sensing (GISMOS) test flights, which used an Applanix POS/AV 510 Global Positioning System (GPS)/Inertial Navigation System (INS). The data were processed using a carrier phase differential GPS technique, and then the GPS position and inertial measurement unit data were combined in a loosely coupled integrated inertial navigation solution. This study quantifies the velocity precision as a function of distance from GPS reference network sites, the velocity precision with or without an inertial measurement unit, the impact of the quality of the inertial measurement unit, and the compromise in precision resulting from the use of real-time autonomous GPS positioning. We find that using reference stations with baseline lengths of up to 760?km from the survey area has a negligible impact on the retrieved refractivity precision. We also find that only a small bias (less than 0.5% in refractivity) results from the use of an autonomous GPS solution rather than a post-processed differential solution when used in an integrated GPS/INS system. This greatly expands the potential range of an operational airborne radio occultation system, particularly over the oceans, where observations are sparse.     

机载SAR影像主动定位的数学模型研究

本文基于差分GPS(Differential Global Positioning System,DGPS)和惯性导航系统(Inertial Navigation System,INS)数据,在无控制点的情况下,导出了一种进行机载SAR影像主动定位的数学模型。此模型包括DGPS/INS数据进行坐标系转换、天线动态偏心改正、雷达天线相位中心插值和距离-多普勒(Range-Doppler,R-D)模型及解算。根据距离-多普勒(Range-Doppler,R-D)模型和数字高程模型(Digital Elevation Model,DEM)数据,获得机载SAR影像上每点所对应的地理坐标,重采样生成正射影像图。本文通过成都测区1m分辨率的机载SAR影像主动定位试验,验证了此数学模型的正确性,分析了主要系统误差源及系统误差的改正方法。     

Differentiation for High-Precision GPS Velocity and Acceleration Determination

Accurate estimates of the velocity and acceleration of a platform are often needed in high dynamic positioning, airborne gravimetry, and geophysics. In turn, differentiation of GPS signals is a crucial process for obtaining these estimates. It is important in the measurement domain where, for example, the phase measurements are used along with their instantaneous derivative (Doppler) to estimate position and velocity. It is also important in postprocessing, where acceleration is usually estimated by differentiating estimates of position and velocity. Various methods of differentiating a signal can have very different effects on the resulting derivative, and their suitability varies from situation to situation. These comments set the stage for the investigations in this article. The objective is twofold: (1) to carry out a comprehensive study of possible differentiation methods, characterizing each in the frequency domain; and (2) to use real data to demonstrate each of these methods in both of the measurement and position domains, in conditions of variable, high, or unknown dynamics. Examples are given using real GPS data in both the measurement domain and in the position and velocity domain. The appropriate differentiator is used in several cases of varying dynamics to derive a Doppler signal from carrier phase measurements (rather than using the raw Doppler generated by the receiver). In the statistic case, it is seen that the accuracy of velocity estimates can be improved from 4.0 mm/s to 0.7 mm/s by using the correct filter. In conditions of medium dynamics experienced in an airborne gravity survey, it is demonstrated that accelerations as the 2–4 mGal level (1 mGal = 0.00001 m/s²) can be obtained at the required filtering periods. Finally, a precision motion table is used to show that when using the correct filter, velocity estimates under high dynamics can be improved by an order of magnitude to 27.0 mm/s. ? 1999 John Wiley & Sons, Inc.     

机载POS系统对地定位方法初探

高精度定位定向系统(Position&;OrientationSystem,简称POS系统)能够获取机载传感器的空间位置和三轴姿态信息,从而定量化反演遥感信息获取过程,实现机载遥感直接对地定位(DirectGeoreferencing)。本文首先介绍POS与航空摄影系统的集成方法与工作原理;然后初步分析了POS系统的主要误差来源,在此基础上,研究了POS系统数据处理及误差控制方法;最后,结合河南安阳飞行试验数据的分析处理结果,进行了精度和可行性分析。     

GPS单点测速的误差分析及精度评价 (英文)

Error sources which decrease the accuracy of GPS in absolute velocity determination have been changed since SA was turned off. Firstly, quantities of all kinds of error sources that influence velocity determination are analyzed. The potential accuracy of GPS absolute velocity determination is derived from both theory and field GPS data simulation. After that, two tests were carried out to evaluate the performance of GPS absolute velocity determination in the case of a static and an airborne GPS receiver and INS （Inertial Navigation System） instrument in kinematic mode. In static mode, the receiver velocity has been estimated to be several mm/s with the carrier-phase derived Doppler measurements, and several cm/s with the receiver generated Doppler measurements. In kinematic mode, GPS absolute velocity estimates are compared with the synchronized measurements from the high accuracy INS. The root mean square statistics of the velocity discrepancies between GPS and INS come up to dm/s. Moreover, it has a strong correlation with the acceleration or jerk of the aircraft.     

一种低动态高抖动环境下的GPS/INS紧组合方法

针对低动态高抖动环境下,影响GPS/INS紧组合精度的重要因素——惯性测量单元(IMU)数据中的噪声,该文提出利用小波降噪方法分离IMU数据中的噪声和有用信号以提高GPS/INS紧组合的精度。首先对IMU数据进行小波分解后得到的高频系数进行阈值量化处理,然后将GPS观测数据与降噪后的IMU数据进行GPS/INS紧组合解算,最终得到载体的导航信息。实例结果表明,该方法可以大幅提升GPS/INS紧组合的精度和稳定可靠性。     

A combined algorithm of improving INS error modeling and sensor measurements for accurate INS/GPS navigation

Although the integrated system of a differential global positioning system (DGPS) and an inertial navigation system (INS) had been widely used in many geodetic navigation applications, it has sometimes a major limitation. This limitation is associated with the frequent occurrence of DGPS outages caused by GPS signal blockages in certain situations (urban areas, high trees, tunnels, etc.). In the standard mechanization of INS/DGPS navigation, the DGPS is used for positioning while the INS is used for attitude determination. In case of GPS signal blockages, positioning is provided using the INS instead of the GPS until satellite signals are obtained again with sufficient accuracy. Since the INS has a very short-time accuracy, the accuracy of the provided INS navigation parameters during these periods decreases with time. However, the obtained accuracy in these cases is totally dependent on the INS error model and on the quality of the INS sensor data. Therefore, enhanced navigation parameters could be obtained during DGPS outages if better inertial error models are implemented and better quality inertial measurements are used. In this paper, it will be shown that better INS error models are obtained using autoregressive processes for modeling inertial sensor errors instead of Gauss–Markov processes that are implemented in most of the current inertial systems and, on the other hand, that the quality of inertial data is improved using wavelet multi-resolution techniques. The above two methods are discussed and then a combined algorithm of both techniques is applied. The performance of each method as well as of the combined algorithm is analyzed using land-vehicle INS/DGPS data with induced DGPS outage periods. In addition to the considerable navigation accuracy improvement obtained from each single method, the results showed that the combined algorithm is better than both methods by more than 30%.     

Geoid undulation modelling and interpretation at Ladak, NW Himalaya using GPS and levelling data

Fast and accurate relative positioning for baselines less than 20 km in length is possible using dual-frequency Global Positioning System (GPS) receivers. By measuring orthometric heights of a few GPS stations by differential levelling techniques, the geoid undulation can be modelled, which enables GPS to be used for orthometric height determination in a much faster and more economical way than terrestrial methods. The geoid undulation anomaly can be very useful for studying tectonic structure. GPS, levelling and gravity measurements were carried out along a 200-km-long highly undulating profile, at an average elevation of 4000 m, in the Ladak region of NW Himalaya, India. The geoid undulation and gravity anomaly were measured at 28 common GPS-levelling and 67 GPS-gravity stations. A regional geoid low of nearly −4 m coincident with a steep negative gravity gradient is compatible with very recent findings from other geophysical studies of a low-velocity layer 20–30 km thick to the north of the India–Tibet plate boundary, within the Tibetan plate. Topographic, gravity and geoid data possibly indicate that the actual plate boundary is situated further north of what is geologically known as the Indus Tsangpo Suture Zone, the traditionally supposed location of the plate boundary. Comparison of the measured geoid with that computed from OSU91 and EGM96 gravity models indicates that GPS alone can be used for orthometric height determination over the Higher Himalaya with 1–2 m accuracy. Received: 10 April 1997 / Accepted: 9 October 1998     

重力异常阶方差模型精度及其截断误差分析

在评估重力场模型计算空间扰动引力精度时,对模型截断误差常采用阶方差方法。文中将6种经典的重力异常阶方差模型与现有超高阶重力场模型的阶方差进行比较,TSD模型与重力场模型的差值最小。根据重力异常阶方差模型TSD,文中分析不同高度、不同阶次利用重力场模型计算空中扰动引力时截断误差的影响。实验结果表明:36阶模型截断误差最大径向和水平方向分别为26.455 1mGal、25.946 3mGal;360阶模型截断误差最大径向和水平方向分别为9.969 0mGal、9.960 9 mGal;2160阶模型截断误差最大径向和水平方向分别为2.538 5 mGal、2.538 1mGal;2160阶模型计算空中扰动引力时,即使在低空附近,截断误差在2.5mGal以内,计算高度超过5km,截断误差可以忽略;超过400km的高度,都可以用36阶模型计算,截断误差在1mGal以内。     

扰动重力水平分量对惯导系统的位置误差影响

研究了不同运动状态下扰动重力水平分量（HDG）对高精度惯导系统（inertial navigation system,INS）的位置误差影响。首先推导了HDG对INS误差影响的状态空间方程,进而推导出3种运动条件下INS位置误差与HDG之间的解析关系式,设计了基于惯导解算求解上述影响的方法。在匀速运动条件下,分别通过解析式与惯导解算两种方法计算了相同HDG引起的INS位置误差。解析式计算结果表明,±80 mGal（1 mGal=10-5 m/s2）范围内变化的HDG约可引起最大约3 000 m的INS位置误差;对两种方法计算结果的比较显示,所得INS位置误差的量级与变化情况基本一致,两组结果验证了各自方法的有效性。