航空重力测量理论、方法及应用研究
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摘要
本文以我国首套航空重力测量系统(CHAGS)的研制为背景，基于CHAGS在汉中、大同和哈尔滨的三次实测数据，重点研究了观测数据滤波、航空重力仪观测数据处理、垂直加速度精密确定及空中重力扰动矢量估算等四方面的理论和方法；侧重探讨了航空重力测量数据在确定局部大地水准面中的应用。本文的主要工作和创新点概括如下。
1．基于牛顿第二运动定律，建立了平台式、捷联式矢量重力测量以及捷联式、旋转不变式和平台式标量重力测量的数学模型。
2．针对重力仪与GPS观测数据的空间同步，建立了位置、速度和加速度的偏心改正公式；实测数据分析表明，实用中仅需顾及空间改正和垂直加速度的偏心改正。
3．提出了参照不同滤波尺度下的内部精度，依据航空重力测量的频谱窗口，在兼顾分辨率的同时确定滤波器截止频率的新观点，有效地解决了滤波器设计的关键问题。
4．摒弃了传统使用的6×20sRC滤波器和300s高斯滤波器，设计了适用于不同作业环境的FIR滤波器和级联式巴特沃思滤波器。针对FIR滤波器阶数过高之不足，提出了航空重力测量数据的FIR级联滤波法，即两步滤波法。
5．研究了稳定平台倾斜角和水平加速度改正的频谱特性，确定了水平加速度改正的预滤波尺度，有效地减弱了水平加速度改正不完善引起的系统性误差。
6．研究了K因子与滤波尺度的相关性，提出了K因子的四种标定方法。结果表明，利用重新标定的K因子计算的空中重力异常，精度提高了约0.2～0.4mGal。
7．提出了交叉耦合系数的外部、内部标定法以及与K因子的联合标定方法，采用新系数显著地降低了系统误差的影响，对于大同航空重力测量，系统误差从约4mGal减小至约1mGal。内部标定法仅需在测区内构成一定数目的交叉点，无需其它外部信息，且其标定结果与外部标定结果非常一致，因此，这种方法有着更广的应用面和实际应用价值。
8．从频域上研究分析了GPS大气误差、星历误差、多路径效应、测量误差和卫星几何结构变化对垂直加速度精密确定的影响，结果表明：多路径效应、测量噪声和卫星几何结构变化对垂直加速度的确定具有较大影响。
9．从理论和实测数据两方面，对利用GPS测定加速度的三种常用方法即位置差分法、多普勒频移法和相位时序差分法进行了比较和分析，对于200s的滤波尺度，静态测量精度分别为0.7、7.5和0.3mGal，动态测量的精度分别为1.6、4.8和0.5mGal。
10．设计了航空重力测量数据处理流程，优化处理了汉中、大同和哈尔滨三次试验的观
信息工程大学博士学位论文
测数据。精度估算表明，波长分辨率约为10km时，交叉点不符值的标准差分别为smGal、
5.smGal和2.OmGal，空中5‘xs’格网平均重力异常的精度对于大同地区和哈尔滨地区分别
为3 .6mGal和1 .7mGal。
H.建立了当地水平坐标系和惯性坐标系下的INs/GPS误差状态方程，分别构建了利
用GPS位置作为状态更新的重力扰动矢量水平分量的传统卡尔曼滤波估算模型和利用
GPS加速度作为状态更新的重力扰动全矢量的新型卡尔曼滤波估算模型;首次利用航空标
量重力测量数据计算了空中和地面格网的垂线偏差，其与地面重力测量数据计算结果之差
的标准偏差，对于子午分量和卯酉分量分别为0.5”和0.4，。
12.首次研究了空中数据向下延拓方法和滤波尺度对大地水准面精密确定的影响，结果
表明:利用直接代表法、点质量法和正则化算法均可获得约3cm的精度，直接代表法由于
不受测区形状及范围大小限制且无边界效应成为最合适的向下延拓方法;就滤波尺度而
言，1005一2505的滤波尺度均适用于大地水准面的确定，顾及滤波器边界效应的影响，宜
采用小一些的滤波尺度如1005。与地面重力测量数据计算的参考大地水准面相比，利用航
空重力测量数据确定的大地水准面的精度可以达到3cm。
关键词:航空重力测量;FIR低通滤波器;巴特沃思滤波器;摆杆尺度因子;垂直加速度;
水平加速度改正;交叉祸合改正;重力扰动矢量;大地水准面;GPS
第ii页
In this dissertation the theories and methods for the airborne gravimetry are investigated in detail with the emphasis on four aspects, on the basis of three groups of real data from Hanzhong, Datong and Harbin tests using the first Chinese Airborne Gravimetry System (CHAGS). They are the data filtering, airborne gravimeter observation processing, the precise determination of the vertical acceleration and the estimation of the airborne gravity disturbance vector. Furthermore, we also focus on the precise determination of the local geoid by using airborne gravity data. The main works and contributions are summarized as follows.1. On the basis of the Newton's second law of motion, the gravity equations relevant to the stabilized systems and the strapdown systems for the airborne vector gravimetry and those related to the stabilized systems, the rotation invariant system and the strapdown systems for the airborne scalar gravimetry are established.2. For the local coordination of the airborne gravimeter and the GPS antenna phase center, the lever arm corrections with respect to the GPS position, velocity and acceleration are formulated. The test results indicate that only the lever arm corrections for the free-air corrections and the vertical accelerations are required to be taken into account in reality.3. In view of the dependence of the accuracy and resolution for the airborne gravimetry, one new concept to determine the cutoff frequency of the lowpass filter that based on the spectral windows for the airborne gravimetry and the internal accuracy (e.g. crossover errors) under different filter length is advanced.4. Instead of using the traditional filters in airborne gravimetry, viz. the 6x20s resistor-capacitor (RC) filter and the 300s Gaussian filter, we design the Finite Impulse Response (FIR) filter and the cascaded Butterworth filter that can be suited for various operation conditions. Aiming to reduce the length of the FIR filter, a technique involved in a cascaded FIR filter is suggested to filter the raw airborne gravity.5. The spectral properties of the stabilized platform tilt angle and the horizontal acceleration correction are investigated and analyzed. The amount of the pre-filtering of the horizontal acceleration correction is derived, which matches the platform period. With this amount the potentially systemic biases due to the imperfection of the horizontal acceleration correction can be reduced significantly.6. The dependence of the beam scale factor (K-factor) on the amount of the filtering applied to the data is discussed. Four methods for calibrating the K-factor are developed, and the results show that the accuracy of the airborne gravity anomalies is improved about 0.2~0.4mGal by using of the new K-factor.7. The cross-coupling corrections for the L&R gravimeter are computed as a linear combination of 5 so-called cross-coupling monitors, the weight factors (coefficients) determined from marine data by factory may not be optimal for airborne application. In this paper, these coefficients are recalibrated to minimize the difference between airborne data and upward continued surface data (external calibration) and to minimize the errors at line crossings (internal calibration) respectively. An integrating method to simultaneously recalibrate the above mentioned coefficients and the K-factor is also presented. Numerical results show that the systemic errors in the airborne gravity anomalies can be greatly reduced using any of the recalibrated coefficients.
The systemic error is reduced from 4mGal to 1mGal in Datong test. Since the internal calibration requires only the survey to be well structured, with a large and well-distributed number of line crossings, and it doesn't require any of external information, it will be useful and valuable.8. The main factors that impact on the precise determination of the vertical acceleration using GPS are the residual atmospheric and orbit errors, multipath errors, measurement noise and the errors due to changes in the satellite cons
1．基于牛顿第二运动定律，建立了平台式、捷联式矢量重力测量以及捷联式、旋转不变式和平台式标量重力测量的数学模型。
2．针对重力仪与GPS观测数据的空间同步，建立了位置、速度和加速度的偏心改正公式；实测数据分析表明，实用中仅需顾及空间改正和垂直加速度的偏心改正。
3．提出了参照不同滤波尺度下的内部精度，依据航空重力测量的频谱窗口，在兼顾分辨率的同时确定滤波器截止频率的新观点，有效地解决了滤波器设计的关键问题。
4．摒弃了传统使用的6×20sRC滤波器和300s高斯滤波器，设计了适用于不同作业环境的FIR滤波器和级联式巴特沃思滤波器。针对FIR滤波器阶数过高之不足，提出了航空重力测量数据的FIR级联滤波法，即两步滤波法。
5．研究了稳定平台倾斜角和水平加速度改正的频谱特性，确定了水平加速度改正的预滤波尺度，有效地减弱了水平加速度改正不完善引起的系统性误差。
6．研究了K因子与滤波尺度的相关性，提出了K因子的四种标定方法。结果表明，利用重新标定的K因子计算的空中重力异常，精度提高了约0.2～0.4mGal。
7．提出了交叉耦合系数的外部、内部标定法以及与K因子的联合标定方法，采用新系数显著地降低了系统误差的影响，对于大同航空重力测量，系统误差从约4mGal减小至约1mGal。内部标定法仅需在测区内构成一定数目的交叉点，无需其它外部信息，且其标定结果与外部标定结果非常一致，因此，这种方法有着更广的应用面和实际应用价值。
8．从频域上研究分析了GPS大气误差、星历误差、多路径效应、测量误差和卫星几何结构变化对垂直加速度精密确定的影响，结果表明：多路径效应、测量噪声和卫星几何结构变化对垂直加速度的确定具有较大影响。
9．从理论和实测数据两方面，对利用GPS测定加速度的三种常用方法即位置差分法、多普勒频移法和相位时序差分法进行了比较和分析，对于200s的滤波尺度，静态测量精度分别为0.7、7.5和0.3mGal，动态测量的精度分别为1.6、4.8和0.5mGal。
10．设计了航空重力测量数据处理流程，优化处理了汉中、大同和哈尔滨三次试验的观
信息工程大学博士学位论文
测数据。精度估算表明，波长分辨率约为10km时，交叉点不符值的标准差分别为smGal、
5.smGal和2.OmGal，空中5‘xs’格网平均重力异常的精度对于大同地区和哈尔滨地区分别
为3 .6mGal和1 .7mGal。
H.建立了当地水平坐标系和惯性坐标系下的INs/GPS误差状态方程，分别构建了利
用GPS位置作为状态更新的重力扰动矢量水平分量的传统卡尔曼滤波估算模型和利用
GPS加速度作为状态更新的重力扰动全矢量的新型卡尔曼滤波估算模型;首次利用航空标
量重力测量数据计算了空中和地面格网的垂线偏差，其与地面重力测量数据计算结果之差
的标准偏差，对于子午分量和卯酉分量分别为0.5”和0.4，。
12.首次研究了空中数据向下延拓方法和滤波尺度对大地水准面精密确定的影响，结果
表明:利用直接代表法、点质量法和正则化算法均可获得约3cm的精度，直接代表法由于
不受测区形状及范围大小限制且无边界效应成为最合适的向下延拓方法;就滤波尺度而
言，1005一2505的滤波尺度均适用于大地水准面的确定，顾及滤波器边界效应的影响，宜
采用小一些的滤波尺度如1005。与地面重力测量数据计算的参考大地水准面相比，利用航
空重力测量数据确定的大地水准面的精度可以达到3cm。
关键词:航空重力测量;FIR低通滤波器;巴特沃思滤波器;摆杆尺度因子;垂直加速度;
水平加速度改正;交叉祸合改正;重力扰动矢量;大地水准面;GPS
第ii页
In this dissertation the theories and methods for the airborne gravimetry are investigated in detail with the emphasis on four aspects, on the basis of three groups of real data from Hanzhong, Datong and Harbin tests using the first Chinese Airborne Gravimetry System (CHAGS). They are the data filtering, airborne gravimeter observation processing, the precise determination of the vertical acceleration and the estimation of the airborne gravity disturbance vector. Furthermore, we also focus on the precise determination of the local geoid by using airborne gravity data. The main works and contributions are summarized as follows.1. On the basis of the Newton's second law of motion, the gravity equations relevant to the stabilized systems and the strapdown systems for the airborne vector gravimetry and those related to the stabilized systems, the rotation invariant system and the strapdown systems for the airborne scalar gravimetry are established.2. For the local coordination of the airborne gravimeter and the GPS antenna phase center, the lever arm corrections with respect to the GPS position, velocity and acceleration are formulated. The test results indicate that only the lever arm corrections for the free-air corrections and the vertical accelerations are required to be taken into account in reality.3. In view of the dependence of the accuracy and resolution for the airborne gravimetry, one new concept to determine the cutoff frequency of the lowpass filter that based on the spectral windows for the airborne gravimetry and the internal accuracy (e.g. crossover errors) under different filter length is advanced.4. Instead of using the traditional filters in airborne gravimetry, viz. the 6x20s resistor-capacitor (RC) filter and the 300s Gaussian filter, we design the Finite Impulse Response (FIR) filter and the cascaded Butterworth filter that can be suited for various operation conditions. Aiming to reduce the length of the FIR filter, a technique involved in a cascaded FIR filter is suggested to filter the raw airborne gravity.5. The spectral properties of the stabilized platform tilt angle and the horizontal acceleration correction are investigated and analyzed. The amount of the pre-filtering of the horizontal acceleration correction is derived, which matches the platform period. With this amount the potentially systemic biases due to the imperfection of the horizontal acceleration correction can be reduced significantly.6. The dependence of the beam scale factor (K-factor) on the amount of the filtering applied to the data is discussed. Four methods for calibrating the K-factor are developed, and the results show that the accuracy of the airborne gravity anomalies is improved about 0.2~0.4mGal by using of the new K-factor.7. The cross-coupling corrections for the L&R gravimeter are computed as a linear combination of 5 so-called cross-coupling monitors, the weight factors (coefficients) determined from marine data by factory may not be optimal for airborne application. In this paper, these coefficients are recalibrated to minimize the difference between airborne data and upward continued surface data (external calibration) and to minimize the errors at line crossings (internal calibration) respectively. An integrating method to simultaneously recalibrate the above mentioned coefficients and the K-factor is also presented. Numerical results show that the systemic errors in the airborne gravity anomalies can be greatly reduced using any of the recalibrated coefficients.
The systemic error is reduced from 4mGal to 1mGal in Datong test. Since the internal calibration requires only the survey to be well structured, with a large and well-distributed number of line crossings, and it doesn't require any of external information, it will be useful and valuable.8. The main factors that impact on the precise determination of the vertical acceleration using GPS are the residual atmospheric and orbit errors, multipath errors, measurement noise and the errors due to changes in the satellite cons
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