解算大地测量主题正算问题的两种数值方法

大地测量主题正算问题是一个古老的课题。采用贝塞尔方法时,解算中对椭圆积分方程的求解,一般均采用简单迭代法,且未给出该方程近似解的误差估计公式。针对以上问题,本文提出两种算法,并给出其误差估计公式。又在DJS030计算机上通过实际计算验证了方法及其误差估算公式的正确性。两种算法在长距离大地测量主题解算时,计算效率较简单迭代法均有所提高。     

自适应抗差Kalman滤波在多天线原始观测值瞬时姿态确定中的应用

由载波相位观测值直接解算姿态能实现观测及姿态约束信息的最优利用。本文推导了基于失准角及乘性误差四元数的载波相位观测模型,分别建立了有外部角速度传感器和无外部传感器辅助下姿态参数估计的状态模型;利用自适应抗差滤波估计姿态误差,借鉴分类自适应因子的思想,分别确定模糊度和姿态误差参数的自适应因子,其中姿态自适应因子由Ratio值构造的三段函数确定。自适应抗差滤波能够充分利用约束信息和历史信息,将其融合在浮点解计算过程中,极大提高模糊度浮点解精度及其协方差的结构,在此基础上使用整数最小二乘模糊度降相关平差法(least-squares ambiguity decorrelation adjustment,LAMBDA)方法即能快速搜索出固定解,满足实时性需求。采用实测舰载GNSS 3天线测姿算例对方法进行了验证,结果表明,基于自适应抗差滤波的观测值直接定姿方法效率高、可靠性好。     

外空扰动引力分量核函数的改化

Ｍｏｌｏｄｅｎｓｋｙ最早提出了利用最小平方逼近的方法对Ｓｔｏｋｅｓ积分核进行改化以减小外区积分的截断误差，基迂个思想，许厚泽在文献中把截断系数的解算归结为解一组ｍ次一代数方程组。本文将此方法推广到扰动引力分量的计算中，并分析了改化积分核的作用，理论分析的结果与实算结果相一致。通过改化后扰动引力分量截断系数Ｑ１ｎＲ１ｎ的量级大大减小，说明截断误差大为降低，同时也表明引逼近方法对扰动引力分量来说明样是     

基于整体最小二乘法的线性回归建模和解法

对基于自变量和因变量误差的回归问题进行了进一步研究,证明了两种方法的实质并未解决同时考虑自变量和因变量的误差问题,其解算结果和不考虑自变量误差的解算结果完全相同.给出了能同时顾及自变量和因变量误差的新的回归模型,并推导了具体的解算方法.算例结果和基于矩阵分解的整体最小二乘法解算方法的结果相同,说明了本文方法的正确性.     

一种基于加表零偏稳定性的GNSS/SINS组合导航异常探测方法

在地面车载组合导航中,全球导航卫星系统（global navigation satellite system,GNSS）的观测值容易受地面复杂环境的干扰,导致其定位结果出现异常,严重影响GNSS/捷联惯性导航系统（strap-down inertial navigation system,SINS）组合的滤波解算。从惯导系统误差特性的角度,研究了一种基于加表零偏稳定性的组合导航异常探测新方法。该方法从加表零偏解算的异常来发现GNSS位置、速度等观测值中的粗差,并采取剔除和降权的抗差方法抵御粗差影响。通过一组车载数据的分析表明,观测粗差对加表零偏解算的影响十分显著,以此为判别条件能够准确地发现观测粗差。采用该方法后,位置误差、速度误差和姿态误差的均方根分别减小了70.8%、87.9%和77.7%,显著提高了组合导航的解算精度和鲁棒性,为组合导航数据的抗差处理提供了一种新思路。     

广播星历下多系统卫星位置、速度计算及精度分析

目前GNSS空间部分主要由GPS、GLONASS、Galileo、BDS 4系统构成,在利用广播星历进行多星组合导航时,需要根据不同卫星星座广播星历精度信息实现多系统定位信息的组合。现有研究对GPS、GLONASS广播星历精度进行了充分分析,但对由Galileo、BDS广播星历计算卫星位置、速度及其精度的研究相对较少。本文利用精密星历对GNSS广播星历计算的卫星位置、速度精度进行了分析。结果表明,GPS广播星历解算的卫星位置误差小于2 m,GLONASS广播星历解算的卫星位置误差最大在4 m左右,Galileo广播星历解算的卫星位置误差最大在3 m左右,BDS广播星历解算的GEO卫星位置误差最大在40 m左右,IGSO卫星位置误差最大在9 m左右,MEO卫星位置误差最大在5 m左右。GPS、Galileo、BDS速度误差在1 mm/s内,GLONASS速度误差在2 mm/s内。     

顾及地形效应的重力向下延拓模型分析与检验

向下延拓是航空重力测量数据实际应用中必不可少的技术环节。向下延拓属于不适定反问题,其解算过程具有较大的不确定性,故该问题一直是大地测量领域国内外学者的研究热点。本文深入分析研究了当前国内外最具代表性的3种向下延拓计算模型的技术特点和适用条件,提出了应用超高阶位模型、局部地形改正和移去—恢复技术顾及地形效应,以及位场延拓结果球面化曲面的工程化方法,重点探讨了计算模型的稳定性及数据观测误差对延拓计算结果的影响。通过理论分析、数值仿真和实测数据计算等手段,定量评估了不同向下延拓模型的解算精度及其可靠性。其主要结论是:传统逆Poisson积分模型解严重受制于输入数据观测噪声的干扰,在现有作业条件下,该模型至多只能用于1km以下高度的延拓解算;频谱截断积分和位模型加地改两种延拓新模型具有良好的计算稳定性,完全适用于2′分辨率和5km飞行高度条件下的航空重力测量数据向下延拓解算,其延拓计算精度可达2×10~(-5) m/s~2,可满足各方面实际应用需求。     

隧道洞内导线加测陀螺方位角最佳位置的研究

根据误差传播定律及条件平差法求得直线型洞内导线加测陀螺方位角后贯通点的横向中误差;并运用多元函数求条件极值的方法,确定加测陀螺方位角的最佳位置;而后在贯通误差满足规范要求的前提下,计算了单向开挖长度分别为6 km和9 km的隧道需加测陀螺方位角的数量。     

利用LP多普勒数据解算月球重力场模型的分析

利用GSFC/NASA提供的GEODYNII/SOLVE软件处理月球探测器LP(Lunar Prospector)扩展任务阶段最后3个月的测速和测距跟踪数据,解算月球重力场模型,比较分析全部位系数解算和部分中高阶次位系数解算2种方法,并对2种方法解算得到的模型进行阶方差分析.同时通过轨道残差、重复轨道误差以及模型大地水准面等几个方面对基于部分中高阶次住系数解算的有效性和得到的模型进行精度评估.结果表明基于部分中高阶次位系数解算的方法进行恢复月球重力场是可行的.该方法将用于"嫦娥工程"中月球重力场的解析.     

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。     

基于惯性导航系统的轨道检查仪双位置对准方法

为提高轨道检查仪惯性导航系统对准精度,提出适用于轨道检查仪的惯性导航系统双位置对准方法。该方法利用轨道检查仪掉头方式,实现惯导系统加速度计常值零偏补偿。选用0.1°/h光纤陀螺仪和200 μg石英挠性加速度计组成惯性导航系统,在一铁路路段进行轨道检测试验。试验结果表明,双位置对准方法能够有效去除惯性器件零偏误差导致的轨道参数检测误差,在轨检仪连续工作300 m的情况下,铁路轨道水平检测精度明显提高。     

基于MEMS的室内定位误差修正方法研究

根据室内惯性定位存在误差累积的特点,建立广义似然比检测的方法进行零速度检测,利用Kalman滤波对检测到的"零速度"时刻进行零速修正(zero velocity update,ZUPT),从而有效降低系统累积误差。但行人行走过程中存在的无效振动,导致测得的加速度和角速度数据中出现明显的噪声,这对长时间定位精度产生较大的影响。文中提出在利用Kalman滤波进行误差校正之前首先采用Butterworth低通滤波滤除加速度和角速度数据中由无效振动引起的高频部分,即噪声部分,从而消除行人运动过程中的无效振动对定位精度的影响。     

Enhanced MEMS-IMU/odometer/GPS integration using mixture particle filter

Dead reckoning techniques such as inertial navigation and odometry are integrated with GPS to avoid interruption of navigation solutions due to lack of visible satellites. A common method to achieve a low-cost navigation solution for land vehicles is to use a MEMS-based inertial measurement unit (IMU) for integration with GPS. This integration is traditionally accomplished by means of a Kalman filter (KF). Due to the significant inherent errors of MEMS inertial sensors and their time-varying changes, which are difficult to model, severe position error growth happens during GPS outages. The positional accuracy provided by the KF is limited by its linearized models. A Particle filter (PF), being a nonlinear technique, can accommodate for arbitrary inertial sensor characteristics and motion dynamics. An enhanced version of the PF, called Mixture PF, is employed in this paper. It samples from both the prior importance density and the observation likelihood, leading to an improved performance. Furthermore, in order to enhance the performance of MEMS-based IMU/GPS integration during GPS outages, the use of pitch and roll calculated from the longitudinal and transversal accelerometers together with the odometer data as a measurement update is proposed in this paper. These updates aid the IMU and limit the positional error growth caused by two horizontal gyroscopes, which are a major source of error during GPS outages. The performance of the proposed method is examined on road trajectories, and results are compared to the three different KF-based solutions. The proposed Mixture PF with velocity, pitch, and roll updates outperformed all the other solutions and exhibited an average improvement of approximately 64% over KF with the same updates, about 85% over KF with velocity updates only, and around 95% over KF without any updates during GPS outages.     

Use of a reduced IMU to aid a GPS receiver with adaptive tracking loops for land vehicle navigation

A reduced inertial measurement unit (IMU) consisting of only one vertical gyro and two horizontal accelerometers or three orthogonal accelerometers can be used in land vehicle navigation systems to reduce volume and cost. In this paper, a reduced IMU is integrated with a Global Positioning System (GPS) receiver whose phase lock loops (PLLs) are aided with the Doppler shift from the integrated system. This approach is called tight integration with loop aiding (TLA). With Doppler aiding, the noise bandwidth of the PLL loop filters can be narrowed more than in the GPS-only case, which results in improved noise suppression within the receiver. In this paper, first the formulae to calculate the PLL noise bandwidth in a TLA GPS/reduced IMU are derived and used to design an adaptive PLL loop filter. Using a series of vehicle tests, results show that the noise bandwidth calculation formulae are valid and the adaptive loop filter can improve the performance of the TLA GPS/reduced IMU in both navigation performance and PLL tracking ability.     

Low-cost attitude estimation with MIMU and two-antenna GPS for Satcom-on-the-move

We detail a low-cost method to estimate vehicle attitude for Satcom-on-the-move (SOTM) using micro inertial measurement unit and two-antenna global positioning system (GPS). The attitude is calculated by integrating gyros, while accelerometers and GPS are used as an aiding system to calibrate the gyro biases. In order to accurately eliminate the accelerometer errors induced by maneuvering accelerations, a sideslip compensation is proposed to calibrate the acceleration estimation derived from the GPS-measured velocity. An adaptive unscented Kalman filter is then developed to deal with the failure of the two-antenna GPS to provide the yaw and sideslip angles. When the yaw angle is unavailable and the vehicle is in straight motion, the yaw angle observation is substituted by velocity heading. During turning, the yaw angle observation is turned off and the yaw angle estimates are obtained from integrating gyros only. Meanwhile, the sideslip angle is estimated by differencing the yaw angle estimate and the velocity heading. The performance of the proposed method is demonstrated with driving tests, suggesting that this technique is a viable candidate for low-cost SOTM.     

New jump trajectory determination method using low-cost MEMS sensor fusion and augmented observations for GPS/INS integration

Objective information on athletic maneuvers for performance evaluation has become highly desired in sports such as skiing, snowboarding, and mountain biking. Body-mounted devices, incorporating low-cost microelectromechanical, inertial navigation units, and global positioning system (GPS) receivers, to calculate sport-specific key performance variables (KPVs) and provide real-time feedback, are now commercially available. However, algorithms implemented for such purposes still lack accuracy and power efficiency. A new GPS/INS (inertial navigation system) integration algorithm is proposed to determine the trajectory of an athlete executing jumps while skiing, snowboarding, mountain biking etc. KPVs, such as jump horizontal distance, vertical height, and drop, are calculated from the trajectory. A new sensor error compensation scheme is developed using sensor fusion and linear Kalman filters (LKF). The LKF parameters are varied to address the fluctuating dynamics of the athlete during a jump. The extended Kalman filter used for GPS/INS integration has an observation vector augmented with sensor error measurements derived from sensor fusion. The performance of the proposed algorithm is evaluated through experimental field tests. For the determination of jump horizontal distance, height, and drop, the proposed algorithm has errors of 14.3 cm (5.5 %), 1.6 cm (38 %), and 6.7 cm (9.4 %), respectively. Errors in KPVs for a set of jumps were first determined with respect to the true KPVs, and then the errors for all the jumps were averaged to calculate the absolute and percentage errors. The accuracy achieved is deemed to fulfill the expectations of both recreational and professional athletes.     

CNS+GNSS+INS船载高精度实时定位定姿算法改进研究

天文导航(CNS)、卫星导航(GNSS)和惯性导航(INS) 3种系统组合可提供高精度的定位定姿结果。实际工程中因INS长时间误差累积,以及系统硬件传输存在不可忽略的时间延迟,导致INS提供给CNS的预报粗姿态误差较大,恶劣海况下难以保障快速搜星,造成天文导航可靠性下降、姿态测量精度较低的问题。为此,本文提出了一种CNS+GNSS+INS高精度信息融合实时定位定姿框架,引入了等角速度外推措施,有效地解决了惯导信息延迟问题。通过高精度转台模拟恶劣海况下载体大角速度摇摆,验证了本文提出的改进算法的有效性。试验结果表明,该算法架构简单,性能可靠,显著提高了恶劣环境下星敏感器的快速、准确搜星能力,保障了三组合姿态测量的精度和可用性。     

GOCE gradiometer: estimation of biases and scale factors of all six individual accelerometers by precise orbit determination

A method has been implemented and tested for estimating bias and scale factor parameters for all six individual accelerometers that will fly on-board of GOCE and together form the so-called gradiometer. The method is based on inclusion of the individual accelerometer observations in precise orbit determinations, opposed to the baseline method where so-called common-mode accelerometer observations are used. The method was tested using simulated data from a detailed GOCE system simulator. It was found that the observations taken by individual accelerometers need to be corrected for (1) local satellite gravity gradient (SGG), and (2) rotational terms caused by centrifugal and angular accelerations, due to the fact that they are not located in the satellite’s center of mass. For these corrections, use is made of a reference gravity field model. In addition, the rotational terms are derived from on-board star tracker observations. With a perfect a priori gravity field model and with the estimation of not only accelerometer biases but also accelerometer drifts, scale factors can be determined with an accuracy and stability better than 0.01 for two of the three axes of each accelerometer, the exception being the axis pointing along the long axis of the satellite (more or less coinciding with the flight direction) for which the scale factor estimates are unreliable. This axis coincides with the axis of drag-free control, which results in a small variance of the signal to be calibrated and thus an inaccurate determination of its scale factor in the presence of relatively large (colored) accelerometer observation errors. In the presence of gravity field model errors, it was found that still an accuracy and stability of about 0.015 can be obtained for the accelerometer scale factors by simultaneously estimating empirical accelerations.     

基于微惯性技术的室内定位理论及应用

室内定位方法的可行性及准确性成为位置信息服务体系的研究热点,针对移动智能终端普及率的提高,提出了基于内置微惯性传感器的定位理念。通过采用Allan方差分析惯性器件误差参数,并基于频谱分析采用滤波降噪方案提高器件输出信噪比,结合人体运动特征准确判定步态,为零速修正算法的实现提供依据,通过建立局部区域的地磁信息数据库,实现磁匹配零速修正卡尔曼组合误差修正。实验结果验证了基于微惯性技术的室内定位方法的可行性。     

捷联惯导系统四元数转换误差分析

捷联惯性导航系统中,根据四元数与直余弦矩阵的关系可以得到3种转换矩阵。充分分析了这3种转换方案所产生的误差。并在恒定角速率下对3种不同转换矩阵中漂移误差、不对称误差和刻度误差进行评估,最后通过仿真验证了分析结果。