【作者】 王峥；

【导师】 李建成；

【作者基本信息】 武汉大学 ， 大地测量学与测量工程， 2016， 博士

【摘要】 航空重力测量技术是以飞机为载体,快速测定近地空中重力加速度的重力测量方法。经过数十年的沉淀与发展,航空重力测量技术已成为高效测定中高频地球重力场信息的主要手段。航空矢量重力测量技术相较于航空标量重力测量技术,不仅能获取重力扰动矢量的垂直分量,而且也能获取重力扰动矢量的水平分量(即垂线偏差)。因此,航空矢量重力测量技术是目前大地测量领域的研究热点之一。目前国内还没有独立的航空矢量重力测量系统,数据处理方面也尚处于起步阶段。因此,本文在充分吸收国内外研究成果基础上,深入研究了联合捷联式惯导系统与全球导航卫星系统的航空矢量重力测量原理与数据处理方法,并编写了一套完整的航空矢量重力测量数据处理软件,不仅为航空矢量实测数据处理和相关应用奠定基础,也对我国航空矢量重力测量技术的发展具有重要的科学意义和应用价值。本文的主要研究工作及贡献如下:1)根据牛顿第二定律详细推导了航空矢量重力测量数学模型。根据航空矢量重力测量的误差模型分析了对GNSS定位、测速、载体运动加速度确定以及SINS惯导比力测量、姿态确定的精度要求。2)对SINS随机误差进行了系统的分析和处理。详细介绍了用于分析和处理惯性元件随机误差的几种方法:Allan方差法、ARMA模型、ARIMA模型以及Kalman滤波法,给出了这几种方法的原理及用途;利用Allan方差法详细分析了惯性元件随机误差中的量化噪声、角度随机游走、零偏不稳定性、角速率随机游走、速率斜坡、指数相关噪声以及正弦噪声七种误差源,并比较了它们不同的Allan方差特性及表现形式。3)深入研究了时间序列法在SINS随机误差建模中的应用。利用SINS随机信号的自相关系数和偏自相关系数的截尾性和拖尾性,建立了 SINS随机误差的ARIMA模型。并利用Kalman滤波对其进行了实时的在线补偿。4)对捷联惯导姿态更新算法进行了深入研究。详细分析了欧拉角法、方向余弦法、四元数法、等效旋转矢量法和锥运动下的等效旋转矢量优化算法的优缺点,得出等效旋转矢量优化算法最适合高精度的捷联惯导姿态更新。并对姿态更新中的圆锥误差开展了详细研究,研究结果表明圆锥振动频率f对姿态解算精度影响最大,采样间隔h次之,圆锥角α最小。5)在划桨运动条件下对捷联惯导速度更新算法进行了深入研究。研究结果表明,载体振动频率f对速度更新算法精度影响最大,采样间隔h次之,角振动幅度Aθ和线振动幅度Ap最小。接着对涡卷误差中的位置算法进行了详细研究,研究表明相比于圆锥误差、划桨误差的影响,涡卷误差最小。但涡卷误差的解算过程却最复杂、计算量也最大。针对这个问题,文中推荐使用一种简化的位置更新算法,该方法既满足解算精度要求又减少了计算量。6)在详细分析了圆锥误差、划桨误差和涡卷误差的机理和补偿算法后,文中给出了一套完整的捷联惯导更新算法。在姿态更新算法中考虑了圆锥误差的影响,在速度更新算法中考虑了划桨误差的影响。根据这些算法,程序设计者能够很容易设计出一套实用的、高精度的捷联惯导解算程序。7)为了验证捷联惯导更新算法的正确性与有效性。根据飞行动力学,设计了一套飞行轨迹仿真程序,该程序可自由组合各种机动动作,并能给出惯性器件的输出测量值及载体的真实飞行数据。通过惯导解算结果与真实轨迹的差值,来检核惯导更新算法的正确性。8)对捷联式惯性导航系统的误差特性以及传播规律进行了深入研究。研究结果表明:捷联式惯性导航系统中主要存在三种不同周期的振荡型误差,周期为84.4min的舒勒振荡,周期为24h的地球振荡和角频率随纬度变化的傅科振荡,并且舒勒振荡总是伴随着傅科振荡的调制。陀螺漂移是最严重的误差源,北向及方位陀螺漂移将引起累积性的位置误差,东向陀螺漂移将引起常值性的纬度误差及方位误差;加速度计偏置主要引起水平姿态误差;初始条件误差主要引起振荡型系统误差。9)对捷联式惯导初始对准展开了详细的研究。经过对两种粗对准方式的理论分析和数值计算结果可知,改进式粗对准比传统式粗对准具有更好的水平对准精度。在判断初始对准系统可观测性时,提出了一种可观测矩阵和奇异值SVD相结合的方法,该方法能快速判定系统的可观性、最佳不可观测状态以及可观测状态变量的可观测度。经可观测性分析结果可知,初始对准后得到的三个姿态误差角估值是姿态误差角和不可观测状态的线性组合。水平姿态误差角的精度由加速计偏置误差决定,方位误差角的精度由东向陀螺漂移精度决定。因此,估计和补偿惯性器件误差是提高初始对准精度的最有效措施。10)从理论和实测数据两方面对GNSS确定载体运动加速度的位置差分法和载波相位直接法进行了比较分析。在静态条件下经过120s低通滤波,位置差分法和载波相位直接法获取的载体运动加速度精度均在1mGal以内,载波相位直接法略优。在动态条件下,由于载体运动加速度未知,比较了两种算法的内符合精度,经120s低通滤波后水平加速度误差在1mGal以内,垂直加速度误差在2mGal以内。11)从窗函数类型和滤波器长度选择两方面研究了滤波器参数对载体运动加速度确定精度的影响。研究结果表明,在静态情况下经120s低通滤波后,哈明窗、汉宁窗、布莱克曼窗和凯泽窗四种滤波器可获得1～2mGa1精度的载体运动加速度。在动态情况下经120s低通滤波后,五种窗函数的滤波精度均可满足1～2mGal的载体运动加速度确定精度要求。综合考虑滤波器幅频响应精度和边界效应影响,在实测数据量较大时,滤波器的长度N可选为201-451;当实测数据量较少时,滤波器长度N可选为101-251。12)详细研究了联合SINS/GNSS的航空矢量重力测量解算方法。根据SINS/GNSS卡尔曼滤波状态方程中是否包含重力扰动随机误差模型,可分为直接求差法和基于模型法两种方法。对两种方法的数学模型及其特点进行了详细研究。研究结果表明,基于模型法虽然理论上最优但实际解算精度却远低于直接求差法,原因是基于模型法受测区先验重力场统计信息精度限制,而在实际测量中先验重力场统计信息获取是一件非常困难的事情。故,本文采用直接求差法来求解重力扰动矢量。13)基于可观测矩阵和奇异值SVD相结合的方法研究了直接求差法的可观性。研究结果表明,虽然在匀速直线运动条件下由SINS/GNSS组合形成的15阶卡尔曼滤波系统不完全可观,但用于比力修正的误差组合状态-fUφN+baE、fUφE+bN和baU却是完全可观的,这说明基于直接求差法的SINS/GNSS航空矢量重力测量系统是可观的。最后,利用数值分析结果验证了该结论的正确性与合理性。14)深入研究了 SINS惯导误差对重力扰动矢量解算精度的影响。研究结果表明,在加速度计噪声水平相同的情况下,垂向重力扰动矢量解算精度不受陀螺仪精度水平的影响;低精度的惯性器件会在重力扰动矢量的估值中引入系统性误差;惯性器件误差是限制重力扰动矢量低频部分解算精度的关键因素。15)深入研究了 GNSS定位测速精度及采样率对重力扰动矢量解算精度的影响。通过对比不同GNSS定位测速的精度对重力扰动矢量解算精度影响发现:在GNSS位置更新率为1Hz的条件下,实现1mGal的重力扰动矢量解算精度,GNSS的测速精度应小于等于3cm/s。在GNSS同等的测速定位精度下,10Hz采样率解算得到的重力扰动矢量精度相较采样率为1Hz解算得到的重力扰动精度有很大的提高。说明,GNSS数据采样率的提高是获取高精度重力扰动矢量的一个新的途径。另外研究发现,GNSS定位测速精度是限制重力扰动矢量高频部分解算精度的关键因素。更多还原

【Abstract】 Airborne gravimetry is an efficient way for gravity measurement in the air.After decades of development,it has been the main way to measure medium-high frequency information of the earth gravity field.Compared to airborne scalar gravimetry,airborne vector gravimetry can obtain not only the vertical component of the gravity disturbance vector,but also the horizontal ones,i.e.,deflection of the vertical.Thus,airborne vector gravimetry is being one of the research hotspots in geodesy.So far,there has no technical independent airborne vector gravimetry system in China and the data processing of airborne vector gravimetry is still in the start stage.On the basis of all the related research results in this field,the principles and methods of airborne vector gravimetry based on SINS and GNSS are studied thoroughly in this dissertation.And the corresponding data processing software are developed.The ultimate purpose is not only to establish the foundation of the airborne vector gravimetry practical data processing and related application research,but also to accumulate experiences for the development of our country’s airborne vector gravimetry system in the future.The main word and contributions in this dissertation are as following:1)The mathematical model of airborne vector gravimetry is derived base on Newton’s second law and mechanics of rigid bodies.On the basis of error model of airborne vector gravimetry,the accuracy requirements of GNSS position,velocity,acceleration and SINS specific force,attitude are analyzed.2)The stochastic errors of SINS are analyzed and processed systematically.Several methods for analyzing and processing the stochastic errors of SINS are introduced in detail,including Allan Variance,ARMA model,ARIMA model and kalman filter.The principles and applications are given.Seven noise terms in SINS,i.e.,quantization noise,angle random walk,bias instability,rate random walk,drift rate ramp,exponentially correlated(Markov)noise and sinusoidal noise are analyzed in detail with Allan Variance,and their different characteristics and forms in Allan Variance are compared.3)The application of Time Series Model in SINS stochastic error modeling is studied intensively.Base on the truncation and trailing property of autocorrelation and partial correlation coefficients,the ARIMA model of SINS stochastic error is established and kalman filter is adopted to implement online compensationin real time.4)The attitude update algorithm of SINS is studied intensively.The advantages and disadvantages of Euler angle algorithm,direction cosine algorithm,quaternion algorithm,rotation vector algorithm and optimized rotation vector algorithm under conic motion are analyzed.Base on the analysis,the conclusion that rotation vector algorithm is the best-fit algorithm for high accuracy attitude update of SINS is drawn.The coning error in attitude update is studied in detail,which shows that coning frequency f affects accuracy the most,sampling interval h less and coning angle a the least.5)The velocity update algorithm of SINS under sculling motion is studied intensively.The result shows that the vibrational frequency f affects accuracy the most,sampling interval h less,angular vibration amplitude Aθ and linear vibration amplitude Ap the least.Then,the position update algorithm of SINS under scrolling motion is studied intensively.The result shows that,compared to coning error and sculling error,the scrolling error affects accuracy the least while the computation of it is the most complicated and hugest.In this regard,a simplified position update algorithm is recommended,which not only satisfies the accuracy requirement but also reduces the computation burden.6)With the intensive research of the mechanism and compensation algorithm of coning error,sculling error and curlingerror,a complete updating algorithm for SINS is presented in this paper.The impact of coning error is eliminated in the updating algorithm for attitude,as well as the impact of sculling error in the updating algorithm for velocity.Based on the methods above,a practical and high-precision software package for SINS is easy to achieve.7)In order to validate the correctness and effectiveness of the update algorithm of SINS,a set oftrajectory simulation programs are designed,which can implement free combination of various maneuvers and output the measurements of SINS and the real flight data.Through comparison of the calculated result and the real ones,the correctness of SINS update algorithm is checked.8)The error characteristics and their propagation pattern of SINS are researched in this paper.The experiments show that there mainly are three oscillation errors of different periods,which are Schuler oscillation with the period of 84.4 minutes,Earth oscillation with the period of 24 hours and Foucault oscillation whose angular frequency varies with the latitude.Generally,Schuler oscillation appears along with Foucault oscillation.The results are also shown that gyro drift is the dominant error in SINS applications.The cumulative error of position would be induced by north and azimuth gyro drift.East gyro drift could result in constant bias for latitude and azimuth.Offsets of accelerometer always influence the horizontal attitude,while oscillation errors usually originate from initial condition errors.9)The initial alignment of SINS is studied in detail.Through theoretical analysis and numerical computation of two coarse alignments,the modified one outperforms the traditional one in horizontal accuracy.As to the system observability analysis of initial alignment,a method combining observability matrix and SVD is proposed,which can determine the system observability,the least observable state and the observable degrees efficiently.The observability analysis shows that the estimates of three attitude errors after initial alignment are linear combinations of the real ones and the unobservable states.Moreover,the horizontal angle estimation accuracies are determined by the accelerometer biases and the azimuth angle estimation accuracy is determined by the east gyroscope drift.Therefore,estimation and compensation of SINS error are the most effective measure to improve the accuracy of initial alignment.10)Two different acceleration determination methods with GNSS,i.e.position differentiation method and carrier phase direct method,are compared and analyzed from theoretical and experimental aspects.In the static case,the acceleration accuracy are both better than 1mGral after 120s Low-Pass filtering while the carrier phase direct method performs slightly better.In the dynamic case,the internal agreement of these two methodsis adopted to assess the accuracy because the real value is unknown.After 120s Low-Pass filtering,the horizontal acceleration accuracy is better than 1mGal while the vertical one is better than 2mGal.11)The impact of filter parameters on acceleration accuracy is discussed from two aspects,i.e.the type of window function and the length of filter.The results show that,in both static and dynamic case,four kinds of filter,which adopt Hamming Window,Hanning Window,Blackman Window and Kaiser Window,can all meet the 1-2 mGal accuracy requirement of acceleration.Considering both the amplitude-frequency response and the boundary effect of filter,the length of filter can be 201-451 when the data length is long and be 101-251 when the data length is short.12)The computing methods of airborne vector gravimetry based on SINS and GNSS are studied in detail.According to whether the gravity disturbance vector is included in the state vector of SINS/GNSS kalman filter,the methods are divided into two methods:direct difference methods and state model method.The mathematical model and characteristic of these two methods are studied in detail.The results show that,although the state model method is optimal in theory,its practical accuracy is far below the one of direct difference method.The reason is that,the state model method is limited by the stochastically accuracy of a prior gravity field which is very difficult to obtain in practice.Therefore,the direct difference method is adopted to compute the gravity disturbance vector in this dissertation.13)The system observability of the direct difference method is studied based on observability matrix and SVD.The result shows that,although the 15-order kalman filter model of SINS/GNSS integration is not completely observable,the state combinations-fUφN+baE,fUφE and baU for specific force correction are observable,which indicates that the direct difference method in airborne vector gravimetry based on SINS/GNSS is observable.Then,the correctness and rationality of the algorithm are demonstrated with simulated data.14)The impact of SINS errors on gravity disturbance vector is studied intensively.The result shows that,with the same accuracy level of accelerometers,the vertical component of gravity disturbance vector is not influenced by the gyroscope accuracy;low accuracy SINS will introduce systematic errors in the estimates of gravity disturbance vector;SINS errors are the key factor on the low frequency part of gravity disturbance vector.15)The impact of GNSS position,velocity accuracy and sampling rate on gravity disturbance vector is studied intensively.Gravity disturbance vector results with different GNSS position,velocity accuracy are compared,which shows that,with the GNSS sampling rate being 1 Hz,the GNSS velocity accuracy should equal or less than 3 cm/s in order to achieve 1mGal accuracy gravity disturbance vector.Besides,with the same GNSS position,velocity accuracy,the gravity disturbance vector results with the GNSS sampling rate being 10 Hz has a great improvement compared to that with the GNSS sampling rate being 1 Hz,which indicates that improvement in GNSS data sampling rate is a new way for obtain high accuracy gravity disturbance vector.Moreover,the GNSS position,velocity accuracy is found to be the key factor on the high frequency part of the gravity disturbance vector.更多还原