实时重力梯度补偿的惯性导航方法研究

发布时间：2018-05-22 12:50

本文选题：惯性导航 + 重力梯度　；参考：《武汉大学》2014年博士论文

【摘要】：惯性导航在军用和民用领域都有着广泛的应用,是载体实现高精度导航定位的重要技术手段。以惯性导航定位系统为基础,结合GPS、重力观测、磁场、星象等其它观测手段,可以实现多种多样、不同精度和应用目的的组合导航模式。重力梯度辅助惯性导航技术就是一项能够实现高精度自主导航定位的新型组合导航模式,在军事上有着重要作用。随着惯性元件的精度不断地提高,对于高精度惯性导航来说,由重力引起的误差已经到了不可忽略的地步,是进一步提高导航精度必须考虑的一项因素。重力梯度对地球重力场的高频信号比较敏感,可以很好地反映地球表面的重力变化,是描述扰动重力场的理想物理量。利用实时观测的重力梯度值来消除惯性导航中的扰动重力误差,得到更高精度的实时重力矢量,而后实现惯性导航中重力矢量和惯性力的分离,进而获得高精度的载体速度和位置信息是重力梯度辅助惯性导航的发展趋势。早在上个世纪六七十年代,美国军方就开始了这项技术的研究,但是限于当时的技术水平,这些研究主要停留在理论探讨阶段。相关资料显示,在上世纪末,有些机构对这项技术进行了一些初步的实验。进入本世纪以来,随着惯性导航精度的不断提高和重力梯度移动测量平台技术的逐渐成熟,这项技术又得到了人们的重视,开始重新活跃起来。目前来说,国内的高精度惯性导航产品的精度已经与国外相差不多,只是实用上的稳定性稍逊,而国内的重力梯度测量技术由于起步较晚,与国外还有一定的差距。就目前的相关文献来看,国内对这项技术的研究主要还停留在理论探讨阶段。由于这项技术的重要性,国内的许多科研机构已经开始了重力梯度仪的研发,取得了一些初步成果。本文的主要工作和研究成果如下： 1.总结和介绍了惯性导航和重力梯度测量的国内外现状,讨论了当前重力梯度仪的性能指标。根据重力梯度仪的设计原理的不同,分别讨论了几种重力梯度仪的测量原理,并分析了各自的优缺点,探讨了未来的梯度仪发展趋势,讨论了原子/量子干涉重力梯度仪的发展前景。 2.分析和研究了重力梯度的特性。定量计算和分析了质量与距离对重力梯度值的影响,并模拟了一个简单的均匀密度山峰,计算了固定高度的一条直线轨迹上的重力矢量和重力梯度各分量的值。结果表明垂直重力梯度分量E：要大于其它分量,对于一个高度为2000m的高斯形山峰,其最大值约为400E。 3.分析了地球重力场以及地形对重力梯度值的贡献。利用EGM96模型,计算了1°×1°格网的重力梯度值。根据Jekeli给出的地形计算重力梯度值的公式,使用SRTM地形数据,计算了一个1°×1°格网内某条直线上的重力梯度值,并验证了地形与计算得到的重力梯度值的相关性。计算结果显示,在经度范围为东经108°～109°,纬度范围为33°～34°的格网内的地表附近,EGM96对扰动重力的贡献约为-20～20E,而地形的影响大约为-100～100E。 4.从基本的导航方程开始,系统总结了惯性导航的基本原理、惯性导航中的坐标转换、误差方程、观测单元以及惯性导航中常用的数值方法。 5.介绍了旋转平台式重力梯度仪的测量原理,利用模拟的12-轴重力梯度仪模型,分别推导了其在捷联式和平台式移动平台下的误差方程。 6.分析了高精度惯性导航对重力场模型的要求。采用由距离倒数模型描述的扰动重力位模型,计算了各向同性的空间频率和时间频率上的重力梯度功率谱密度,并由得到的功率谱密度值计算了对惯性导航速度误差和位置误差的影响。由给定的高精度惯性导航位置误差要求,分析了其对重力场模型的阶数和分辨率的要求。结果表明,在载体速度分别为50km/h,400km/h,1000km/h时受到重力扰动影响的重力误差的功率谱密度的最大值分别为10.4mGal2,1.3mGal2,0.52mGal2.如果要满足一小时内5m精度的下一代高精度惯性导航目标,则重力场阶数至少要达到3600阶。 7.建立了一个多传感器的重力梯度辅助惯性导航测量平台,进行了重力和重力测量移动平台误差分析。根据移动平台上的加速度计、陀螺仪、重力梯度仪、GPS等传感器,分别给出了各自适用的误差模型。根据给出的传感器精度指标,计算了各自本身的空间和时间分辨率上的功率谱密度。根据给出的不同误差之间耦合误差计算公式,分析了不同传感器之间的耦合误差。 8.根据模拟的重力扰动位模型,计算并分析了对地表附近扰动重力梯度值进行观测所需的重力梯度仪灵敏度。结果表明,一个灵敏度为30E/(?)的重力梯度仪可以感应到波长约为7km到17km的梯度信号。但是,由于信号的衰减,实际上我们需要灵敏度更高的重力梯度仪。如果其灵敏度为1E/(?),则可以感应到波长约为1.4km到2.3km的梯度信号。 9.针对短航时、高精度重力梯度补偿的惯性导航系统,设计并实现了惯性仪器精度指标与扰动重力梯度误差指标的组合分析模型,对利用重力梯度测量辅助惯性导航平台的误差进行了数值分析。给出了测量平台的卡尔曼滤波状态方程和观测方程,并根据高精度惯性导航要求的惯导元件精度指标,以及由距离倒数扰动重力位模型计算的扰动重力梯度值,计算了不同精度指标组合的最终位置误差影响。结果表明,采用10E精度的重力梯度观测,则惯导精度可控制在5km左右,而1E精度的重力梯度观测则最高可达到4～6m的导航精度。
[Abstract]:Inertial navigation is widely used in military and civil fields. It is an important technical means to realize high precision navigation and positioning. Based on inertial navigation and positioning system, combined with other observation means such as GPS, gravity observation, magnetic field and star image, a variety of integrated navigation modes, different precision and application purpose, can be realized. The degree aided inertial navigation technology is a new integrated navigation mode which can realize high precision autonomous navigation and positioning. It plays an important role in the military. With the continuous improvement of the precision of the inertial components, the error caused by gravity has reached the point which can not be ignored for the high precision inertial navigation system, and it is to further improve the navigation precision. The gravity gradient is more sensitive to the high frequency signal of the earth's gravity field. It can well reflect the gravity variation on the earth's surface, and it is an ideal physical quantity to describe the disturbed gravity field. Then, the separation of the gravity vector and the inertia force in the inertial navigation system, and then obtain the high precision information of the carrier velocity and position is the trend of the gravity gradient auxiliary inertial navigation.
As early as the 60s and 70s of the last century, the US military began the study of the technology, but limited to the level of technology at that time. These studies were mainly at the stage of theoretical discussion. At present, the precision of the high precision inertial navigation products in China is a little different from that of the foreign countries, but the practical stability is a little worse than the domestic gravity gradient measurement technology. In the current relevant literature, the domestic research on this technology is still at the stage of theoretical discussion. Because of the importance of this technology, many research institutions in China have begun the research and development of gravity gradiometer, and some preliminary results have been obtained.
The main work and research results of this paper are as follows:
1. summarize and introduce the current situation at home and abroad of inertial navigation and gravity gradient measurement, discuss the performance indexes of gravity gradiometer. According to the different design principles of gravity gradiometer, the measuring principles of several gravity gradients are discussed respectively, their advantages and disadvantages are analyzed, the development trend of the gradiometer in the future is discussed, and the original method is discussed. The development prospect of sub / quantum interference gravity gradiometer.
2. the characteristics of gravity gradient are analyzed and studied. The effects of mass and distance on the gravity gradient are calculated and analyzed. A simple uniform density mountain is simulated and the values of the gravity vector and the gravity gradient components on a straight line track are calculated. The results show that the vertical gravity gradient component E is greater than that of it. Its component, for a Gauss shaped mountain with a height of 2000m, is about 400E..
3. analysis the contribution of earth gravity field and terrain to gravity gradient. Using the EGM96 model, the gravity gradient value of the 1 * 1 degree grid is calculated. According to the formula of gravity gradient calculated by the topographic calculation given by the Jekeli, the gravity gradient value of a straight line in a 1 * 1 degree grid is calculated by using the topographic data of SRTM, and the terrain and the meter are verified. The calculated results show that the contribution of EGM96 to the disturbed gravity is about -20 to 20E, and the effect of the terrain is about -100 to 100E. in the range of 108 degrees to 109 degrees and the latitude range from 33 to 34 degrees.
4. starting from the basic navigation equation, the system summarizes the basic principle of inertial navigation, the coordinate transformation in inertial navigation, the error equation, the observation unit and the common numerical methods in the inertial navigation.
5. the measuring principle of the rotating platform gravity gradiometer is introduced, and the error equations of the 12- axis gravity gradiometer model are derived respectively in the strapdown peace platform mobile platform.
6. the requirement of the gravity field model with high precision inertial navigation is analyzed. The gravity gradient model is used to calculate the gravity gradient power spectral density of the isotropic space frequency and time frequency. The influence of the velocity error and position error on the inertial navigation velocity error and the position error is calculated by the obtained power spectral density value. The requirements for the order and resolution of the gravity field model are analyzed by the requirement of the position error of a given high precision inertial navigation system. The results show that the maximum power spectral density of gravity error affected by gravity disturbance at the velocity of 50km/h, 400km/h and 1000km/h, respectively, is 10.4mGal2,1.3mGal2,0.52mGal2. if the maximum value of the gravity error is satisfied. For the next generation of high-precision inertial navigation targets with 5m accuracy within one hour, the order of gravity field should be at least 3600 orders.
7. a multi-sensor gravity gradient auxiliary inertial navigation measurement platform is set up, and the error analysis of the moving platform for gravity and gravity measurement is carried out. According to the accelerometers, gyroscopes, gravity gradiometer, GPS and other sensors on the mobile platform, the applicable error models are given respectively. According to the precision index of the proposed sensor, the calculation is calculated. The power spectral density of the space and time resolution in each of its own space and time resolution. The coupling error between different sensors is analyzed based on the calculation formula of the coupling error between different errors.
8. according to the simulated gravity disturbance position model, the sensitivity of gravity gradiometer required to observe the disturbed gravity gradient near the surface is calculated and analyzed. The results show that a gradient instrument with a sensitivity of 30E/ (?) can induce a gradient signal with a wavelength of about 7km to 17km. However, the attenuation of the signal is actually necessary. If the sensitivity is 1E/ (?), the gradient signal with a wavelength of about 1.4km to 2.3km can be induced.
9. for the inertial navigation system with high precision gravity gradient compensation in short navigation, the combined analysis model of the inertial instrument precision index and the disturbance gravity gradient error index is designed and realized. The numerical analysis of the error of the auxiliary inertial navigation platform by gravity gradient measurement is carried out. The Calman filtering state equation of the measuring platform is given out. According to the precision index of inertial navigation elements required by high precision inertial navigation and the value of gravity gradient calculated by the gravity position model of the distance reciprocal disturbance gravity model, the influence of the final position error of the combination of different precision indexes is calculated. The result shows that the inertial navigation precision can be controlled in the left 5km by the gravity gradient observation of 10E precision. Right, and the 1E accuracy of gravity gradient observation can reach up to 4 ~ 6m navigation accuracy.
【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：P223;TN96

【参考文献】