Deterministic and stochastic parameters in inertial survey adjustment

In the adjustment of inertial position surveys the additional parameters describing the systematic errors of individual traverses can be considered as deterministic or stochastic. The paper deals with various aspects of the deterministic or stochastic approach by way of a standard functional model. If purely deterministic parameters are set up, the solvability of the least squares problem depends on redundant observations like coordinate discrepancies of forward and backward runs or coordinate differences at cross-over points of traverse networks. Inequalities are presented to handle the configuration problem for any net and for several ways of introducing parameter sets. Also condition equations being geometrically explainable are developed solving the datum problem in free adjustment applications. Based on the Ebersberger Forst campaigns with a large amount of Ferranti, Honeywell and Litton data, numerical investigations into the stochastic properties of the additional parameters and the observations follow. It turns out that additional parameters for Honeywell and Litton data can be considered as stochastic parameters while for Ferranti data significant azimuth and time dependent effects can be found. The investigations of true errors show that in case of the deterministic adjustment approach a diagonal covariance matrix can be introduced and in case of stochastic additional parameters a first order Gauss-Markov process serves as a good approximation for the stochastic behaviour of the observations.     

Analysis of the heading sensitivity in the Litton inertial survey system

The straight line concept which has developed as a practical design restriction in intertial surveys with the Litton System is not only cumbersome in the planning stage but also often affects the economy of the survey adversely. A more flexible use of the system is therefore desirable. The analysis of test data taken along a well-controlledL-shaped traverse near Ottawa indicates that software modifications can eliminate a large part of the errors the to heading sensitivity. The paper discusses the design of an appropriate smoother and ways to find its model structure and its weighting from a series of test runs. Results show that the maximum standard deviation along anL-shaped traverse of100 km length is about half a metre. Further improvements are envisaged by changes in the survey procedures and a more effective use of the filter output. Optimal smoothing is not possible at present and would require a redesign of the filter output.     

Experience with the ULISS-30 inertial survey system for local geodetic and cadastral network control

The capability of the recently developed SAGEM ULISS-30 inertial survey system for performing local surveys at high accuracies have been tested in a field campaign carried out November 1989 on the island of Fyn, Denmark, in cooperation with the Swedish National Land Survey. In the test a number of lines between existing national geodetic control points were surveyed, along with points in the less reliably determined cadastral network, forming an irregular network pattern of 10–15 km extent. The survey involved frequent offset measurements (up to 50–100 m) with an ISS-integrated total station. The profile geometries were not particularly suited for inertial surveys, with narrow and rather winding roads, necessitating frequent vehicle turns. In addition to the pure inertial surveys a kinematic GPS/inertial test was also carried out, using a pair of Ashtech L-XII receivers. The inertial survey results, analyzed with a smoothing algoritm utilizing common points on forward/backward runs, indicate that 5-cm accuracies are possible on reasonably straight profiles of 5 km length, corresponding to a 10 ppm best-case accuracy for double-run traverses. On longer, more winding traverses error levels of 10–20 cm are typical. To handle the inertial data optimally, proper network adjustments are required. A discussion of suitable adjustment models of both conventional and collocation type is included in the paper.     

Integral transformations of gradiometric data onto a GRACE type of observable

Integral transformations of gravitational gradients onto a Gravity Recovery And Climate Experiment (GRACE) type of observable are derived in this article. The gravitational gradients represent components of the gravitational tensor in the local north-oriented frame. The GRACE type of observable corresponds to a difference between two gravitational vectors as projected onto the line of sight between the two GRACE satellites. In total, three integral transformations relating vertical–vertical, vertical–horizontal and horizontal–horizontal gravitational gradients with the GRACE type of observable are provided. Spectral and closed forms of corresponding isotropic kernels are derived for each transformation. Special cases show that the integral transformations are general and relate gravitational gradients to many other quantities of the gravitational field, such as the gravitational vector, and its radial and tangential components. Correctness of the mathematical derivations is validated in a closed-loop simulation using synthetic data.     

Real time estimation of position and the gravity vector with an inertial survey system

Based on sine functions for fitting horizontal velocity errors in an inertial survey system and a step or slope function approximation of the vertical deflection between stops, a positioning accuracy of 10 m (CEP) can be achieved with a car-borne system – a modified -21 aircraft navigation system, with a 10 min travel period between Zero Velocity Update Times (ZUPTs) and a total 1.5 hour survey time. A rough estimation of the vertical deflection can also be expected in real time out of the approach. Also a forward-backward-forward run is presented which demonstrates determination of the gravity anomaly. Received 10 March 1995; Accepted 8 July 1996     

原子钟辅助GPS定位的研究

铷钟可以用来预测接收机的时钟偏差,通过对时钟偏差估计的改善就可以提高定位的精度,特别是可以改善垂直精度。由于铷钟的漂移非常缓慢,基于自适应低通滤波器,设计了一种导航算法用于铷钟约束的GPS。通过一个例子对所提出的算法进行的验证。     

Integral transformations of deflections of the vertical onto satellite-to-satellite tracking and gradiometric data

With the advent of geodetic satellite missions mapping almost globally the Earth’s gravitational field, new methods and theoretical approaches have been developed and investigated to fully exploit the potential of their new observables. Besides estimating values of numerical coefficients in harmonic series of the gravitational potential, new applications emerged such as data validation and combination. In this contribution, new integral transformations are presented which transform principal components of the terrestrial deflection of the vertical onto disturbing satellite-to-satellite tracking and gradiometric data at altitude. Using spherical approximation, necessary integral kernel functions are derived in both spectral and closed forms. The behaviour of isotropic kernel functions is studied and the new integral transformations are tested in a closed-loop simulation using synthetic terrestrial and satellite data synthesized from a global gravitational model. New integral transformations can be used for data validation and combination purposes.     

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     

Comparative study of the Ferranti,Honeywell and Litton inertial surveying systems testnet Ebersberger Forst

In order to assess the accuracy, reliability and efficiency of current inertial surveying systems a joint project has been started at the University of the Bundeswehr Munich. As a part of this project the testnet Ebersberger Forst has been established. It consists of 60 monumented points located at cross-roads in a flat area and it makes up a grid pattern of6 N-S and9 E-W traverses with a spacing of1–2 km. The points are determined by classical surveying techniques with a standard deviation of less than1 cm forE, N andH. Observation campaigns were carried through with a Ferranti, a Honeywell and a Litton system. Each campaign consisted of three independent missions performed under identical observation schemes. The preliminary evaluation of the data sets leads to standard deviations of between8 and16 cm for each coordinate if determined in a single mission with a Honeywell or Litton system. The correlations along a traverse follow approximately the series ρ, ρ², ρ³, ... with ρ⋟0.9. Cross correlation is only present betweenE orN, respectively, andH. The positions observed with the Ferranti system are less accurate, which might be explainable by the applied software and by two gross input errors during the missions. A rigorous post-mission adjustment of the data considerably improved the results.     

Inertial survey systems in the geodetic arsenal

After reviewing the overall goals of geodesy, the paper focuses on the unique properties of inertial survey systems in the geodetic arsenal: three-dimensionality; ability to determine relative positions and changes in the anomalous components of the earth’s gravity field; and independence of line-of-sight observations and the effects of refraction, both traditional antagonists in geodetic operations. Inertial survey systems, including field and office computational procedures, are briefly reviewed. Their short-comings are pointed out and certain remedies offered. Future possible improvements in hardware and software, as well as the development of hybrid systems (e.g., with gravity gradiometers), are discussed. “Apart from the refinement of existing techniques through the use of computers and the introduction of electromagnetic and optical distance measurement devices, instrumental research and development has been conducted by scientists and engineers outside the geodetic profession. This separateness of geodetic instrument research and development is seen as a deficiency by some, because of the reduced interaction between measurement techniques and the problems to which they apply. However, geodesy does not seem extraordinarily different from other environmentally oriented sciences in this respect and certainly has been quick to adopt new techniques once the benefits become evident.” (NAS 1978, p. 6) From the Keynote Address presented at Second International Symposium on Inertial Technology for Surveying and Geodesy, June 1–5, 1981, Banff, Alberta, Canada.     

Design of survey systems using nonlinear programming methods

This paper discusses theory and results of an attempt to use non-linear programming methods to arrive at an optimal, in the sense of least cost, solution to the design of a survey system to meet specified accuracy. In other words, the method determines the combination of various types of observations which will yield the required accuracy of control points for a minimum cost. The theoretical background of the procedure is discussed, and methods of extension to photo-grammetry and other sciences are presented. Much of the paper is concerned with discussing results of numerical solutions for the optimal design of several small, but typical, mapping problems. It is believed that this research is original with the author, as extensive literature searches and correspondence has produced no knowledge of prior research into this application of nonlinear programming. The method at its current state of development appears to be capable of yielding significant improvements to the present concepts of survey network design.     

Testing a small inertial navigation system for surveying applications

Summary A small and light-weight military land navigation system (Litton LLN-83 strapdown inertial unit with Litef IBAG control unit) was tested for its suitability for inertial surveying applications with moderate accuracy requirements. Field tests with a minivan were carried out on linear test courses of 1 km and 7 km length. The performance of the system was assessed on the basis of double-run accuracy (against true coordinates, after simple adjustment of measured data onto end points). On the 1-km course (sealed road, average spacing of points: 118 m) an accuracy of 0.4 m in E and N and 0.25 m in elevation was achieved. On two 7-km courses (unsealed roads, average spacing of points: 1.0 km) a pooled accuracy of 1.2 m in E and N and 0.4 m in elevation was obtained. The system proved extremely reliable. Susceptibility to rough roads (likely due to the lack of a rigid attachment of the system to the host vehicle) led to the abortion of two missions.     

铁路工程测量中几种平面坐标系的建立

在工程测量中,根据测图和施工放样的要求选择投影面和投影带,确立工程平面控制网的坐标系。针对铁路工程不同特点,从控制投影变形、计算方便和施工放样等方面优化测量方案,确保测量精度。     

消费级惯性传感器动态系统误差分析与建模

针对传统的系统误差转台标定方法耗时耗力且受限于实验地点的问题,该文从载体运动特征的角度,使用高精度战术级惯性导航设备作为参考,采集车载动态数据,通过传统传感器信号误差模型对消费级低成本惯性导航设备在线标定后,对标定后的观测值残差分别与载体运动角速度、角加速度、角冲击(加速度导数)、线性加速度、线性加速度冲击进行相关性分...     

手机视觉与惯性融合的松耦合滤波算法

在智能手机和互联网的普及状态下,对高精度定位技术的需求也更加显著,精确定位服务已渗透到各个领域,如物联网、无人驾驶、机器快递员、应急救援等。在室外环境下,这些服务大多由全球卫星导航系统提供;然而,在深山丛林、矿井隧道、地下室等室内环境下,由于信号衰减及多径效应的影响,GPS无法正常工作。本文针对一些特殊的室内场景,研究了基于松耦合滤波的视觉惯性融合导航方法,设计了一个面向智能手机平台的室内行人定位系统。该方法视觉前端采用了快速、稳健的稀疏直接法,后端采用了扩展卡尔曼滤波器来融合惯性信息,能够有效融合视觉和惯性信息,达到恢复单目视觉尺度、提高稳健性的效果,实现了高精度的室内行人定位。     

陀螺灵敏部运动轨迹参数测定

高精度悬挂式陀螺仪在研制、生产和调试中仍存在无法精确测定和调整陀螺惯性灵敏部静平衡残余量的问题,研究发现含有静平衡残余量和静平衡状态良好的陀螺运动轨迹存在明显的差异,因此精确测定陀螺灵敏部运动轨迹参数可为精确测定陀螺灵敏部静平衡残余量提供有效途径。文中研制利用激光、高清相机、显微放大镜头等部件,结合计算机视觉和图像处理等方法,采用质心跟踪的方式精确测定陀螺灵敏部摆动(未启动马达)轨迹的装置;利用最小二乘方法拟合陀螺摆动轨迹,推导求取陀螺摆动周期、振幅、衰减系数、摆动中心、抖动振幅等参数的方法。最后用文中装置测定JT15陀螺悬挂系统在未启动马达下的运动轨迹参数,验证装置与方法的有效性。     

视觉惯导紧耦合的行人室内自主定位方法

针对行人在大型复杂建筑环境中的高精度和高可靠性室内定位需求,传统的基于视觉点特征方法易受环境纹理缺失、相机快速运动导致图像模糊而定位失效问题,提出了一种基于视觉点线特征与IMU紧耦合的行人室内 自主定位方法.在视觉惯导融合导航系统框架下,前端部分,在点特征基础上引入结构化建筑环境中丰富的线特征,并采取基于梯度密度过滤机制的改进线特征提取策略,剔除局部线特征密集区域;利用点线特征与IMU紧耦合优化机制提高行人位姿估计及定位的准确性和稳定性.通过利用EuRoC数据集和在实际楼道场景下的实验,特别是在弱纹理、光照变化等条件下实验,验证了所提方法进行行人室内定位的准确性和可行性.     

A comparison of models in inertial surveying

The output of an inertial measuring unit contains the combined effect of vehicle acceleration, accelerations due to the reference system, gravitational attraction, calibration and alignment errors, and measuring noise. The separation of individual effects from the total output is the task of modelling. Differences in the existing models are mainly due to the treatment of system errors and of the anomalous gravity field. The paper discusses the state space formulation as a general approach to represent errors of a dynamic system and describes its application to the modelling of an inertial system. Complications due to the effects of the anomalous gravity field are discussed and possible solutions are indicated. Finally, the models in the existing inertial survey systems are compared and implementation requirements for survey applications are outlined.

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Sommaire Les mesures effectuées par l’unité de mesure inertielle continnent les effets de l’accélération du véhicule et de celle due au système de référence, de l’attraction gravitationnelle, des erreurs de calibrage et d’alignement, et finalement du bruit de fond. La séparation de chacun de ces effets sur les mesures est le sujet de la modélisation. Les différences dans les modèles existant sont principalement dues au traitement du système d’erreurs et des anomalies du champ de gravité. La communication discute de la formulation du vector d’erreurs comme approche générale pour la représentation d’erreurs dans un système dynamique et décrit son application dans la modélisation d’un système inertiel. Les complications dues aux effets des anomalies du champ de gravité sont discutées et des solutions possibles sont indiquées. Enfin, les modèles dans les présents systèmes inertiels d’arpentage sont comparés et les exigences pour les applications en arpentage sont soulignées.

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Presented at the 2nd International Symposium on Inertial Technology for Surveying and Geodesy, Banff, Canada, June 1–5, 1981.