DUALITY IN BI-PROJECTIVE CORRESPONDENCE

Abstract

Bi-projection connotes the method of constructing plastic models of an object by projecting two photographs taken from different stations. The variables representing the relative orientation of the two plates and others representing the direction of the base are shown to satisfy symmetrical bi-linear equations, from which it follows that solutions always occur in pairs, and when one solution of a pair is known the other can be written down immediately. It is unlikely that any doubt will ever arise in practice on which solution should be taken. The equations are well suited for the numerical solution of the biprojective problem using the cartesian coordinates of corresponding points on the plates.     

A PROJECTION METHOD OF MAPPING FROM AIR PHOTOGRAPHS

Abstract

An instrument was previously described in the Transactions of the Royal Society of S. Africa for the setting of pairs of photographs, taken from air stations, in correspondence; that is, in the same relative positions that the camera occupied in space at the moments of exposure. The principle of the instrument may be recalled.     

单应性几何下的后方交会直接解法

传统的后方交会最小二乘解法需要良好的外方位元素初值。在无初值或者初值不够精确的情况下,最小二乘迭代不容易收敛。在近景摄影测量或者计算机视觉等领域,往往不提供良好的初值,无法适用传统的后方交会解法。针对上述情况,本文提出了一种基于单应性矩阵的后方交会直接解法,在不需要初值的情况下,获取外方位元素的直接解。该方法根据单应性矩阵所描述的平面几何关系,利用单应性矩阵内在的约束条件,将后方交会问题转换为一个二元二次方程组的求解问题。该方法受舍入误差影响小,在无偶然误差的情况下,解算精度能达到10–9量级,能够避免传统直接解法计算复杂的问题,为传统的平差迭代解法提供良好的初值。此外,在多个控制点共面的情况下,该方法能够直接获得外方位元素的精确解。实验结果表明:在各种不同倾角拍摄的情况下,该方法均能够获得稳定的外方位元素,为后续的后方交会最小二乘算法提供良好的初值。采用本文方法计算的初值参与平差,能够达到与人工给定初值平差一致的精度,且迭代收敛速度是人工给定初值平差的2倍以上。在控制点共面的情况下,该方法的反投影精度能够达到亚像素级,且精度优于大部分主流的直接解法。     

THE APPLICATION OF TRANSFORMATION FACTORS TO THE ADJUSTMENT OF AIR PHOTOGRAPHS COVERING NARROW LAND AREAS AND COASTLINES

Abstract

1. This new method of adjusting air photographs numerically to a uniform scale on a final map grid has already been described by the writert, where it concerns a large block-adjustment. The method to be described in this paper is the application of the same principle to the adjustment of photographic strips, covering narrow land areas and coastlines.     

Non-linear station motions in epoch and multi-year reference frames

In the conventions of the International Earth Rotation and Reference Systems Service (e.g. IERS Conventions 2010), it is recommended that the instantaneous station position, which is fixed to the Earth’s crust, is described by a regularized station position and conventional correction models. Current realizations of the International Terrestrial Reference Frame use a station position at a reference epoch and a constant velocity to describe the motion of the regularized station position in time. An advantage of this parameterization is the possibility to provide station coordinates of high accuracy over a long time span. Various publications have shown that residual non-linear station motions can reach a magnitude of a few centimeters due to not considered loading effects. Consistently estimated parameters like the Earth Orientation Parameters (EOP) may be affected if these non-linear station motions are neglected. In this paper, we investigate a new approach, which is based on a frequent (e.g. weekly) estimation of station positions and EOP from a combination of epoch normal equations of the space geodetic techniques Global Positioning System (GPS), Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI). The resulting time series of epoch reference frames are studied in detail and are compared with the conventional secular approach. It is shown that both approaches have specific advantages and disadvantages, which are discussed in the paper. A major advantage of the frequently estimated epoch reference frames is that the non-linear station motions are implicitly taken into account, which is a major limiting factor for the accuracy of the secular frames. Various test computations and comparisons between the epoch and secular approach are performed. The authors found that the consistently estimated EOP are systematically affected by the two different combination approaches. The differences between the epoch and secular frames reach magnitudes of $23.6~\upmu \hbox {as}$ (0.73 mm) and $39.8~\upmu \hbox {as}$ (1.23 mm) for the x-pole and y-pole, respectively, in case of the combined solutions. For the SLR-only solutions, significant differences with amplitudes of $77.3~\upmu \hbox {as}$ (2.39 mm) can be found.     

Contributions to reference systems from Lunar Laser Ranging using the IfE analysis model

Lunar Laser Ranging (LLR) provides various quantities related to reference frames like Earth orientation parameters, coordinates and velocities of ground stations in the Earth-fixed frame and selenocentric coordinates of the lunar retro-reflectors. This paper presents the recent results from LLR data analysis at the Institut für Erdmessung, Leibniz Universität Hannover, based on all LLR data up to the end of 2016. The estimates of long-periodic nutation coefficients with periods between 13.6 days and 18.6 years are obtained with an accuracy in the order of 0.05–0.7 milliarcseconds (mas). Estimations of the Earth rotation phase \(\Delta \)UT are accurate at the level of 0.032 ms if more than 14 normal points per night are included. The tie between the dynamical ephemeris frame to the kinematic celestial frame is estimated from pure LLR observations by two angles and their rates with an accuracy of 0.25 and 0.02 mas per year. The estimated station coordinates and velocities are compared to the ITRF2014 solution and the geometry of the retro-reflector network with the DE430 solution. The given accuracies represent 3 times formal errors of the parameter fit. The accuracy for \(\Delta \)UT is based on the standard deviation of the estimates with respect to the reference C04 solution.     

以重心坐标为基准的空间后方交会非迭代法

为解决基于迭代的空间后方交会算法在倾斜摄影中可能出现的不收敛现象,提出了一种以重心坐标为基准的非迭代解算方法。首先将控制点物方空间坐标描述成重心坐标,并基于其坐标参考无关性,采用总体最小二乘方法求出对应像方空间坐标,然后通过正交矩阵方法进行绝对定向并优化。试验结果表明,该方法几乎对任意影像姿态均能正确解算,并且精度达到甚至优于基于迭代的空间后方交会方法。     

Investigation of tidal effects in lunar laser ranging

 The analysis of lunar laser ranging (LLR) data enables the determination of many parameters of the Earth–Moon system, such as lunar gravity coefficients, reflector and station coordinates which contribute to the realisation of the International Terrestrial Reference Frame 2000 (ITRF 2000), Earth orientation parameters [EOPs, which contribute to the global EOP solutions at the International Earth Rotation Service (IERS)] or quantities which parameterise relativistic effects in the solar system. The big advantage of LLR is the long time span of lunar observations (1970–2000). The accuracy of the normal points nowadays is about 1 cm.  The capability of LLR to determine tidal parameters is investigated. In principle, it could be assumed that LLR would contribute greatly to the investigation of tidal effects, because the Moon is the most important tide-generating body. In this respect some special topics such as treatment of the permanent tide and the effect of atmospheric loading are addressed and results for the tidal parameters h ₂ and l ₂ as well as values for the eight main tides are given. Received: 14 August 2000 / Accepted: 15 October 2001     

A MATHEMATICAL APPROACH TO PROBLEMS IN PHOTOGRAMMETRY

Abstract

Many have tried their hands at one time or another at developing practical methods in respect to the solutions of the four fundamental problems viz., (1) space resection, (2) orientation of photograph in space and relative to one another, (3) space intersection, and (4) photogrammetric extension of surveys without ground control. The trouble so far has been that each worker had his own particular problem to solve and hence a completely general and comprehensive approach to the problems is lacking. In this paper these four fundamental problems are considered as essentially one of a system of linear transformations, from one set of coordinates to another, bearing in mind the existence of the significant correspondence between pairs of image points and points in space.     

AERIAL CAMERA CALIBRATION

Abstract

Accidents will happen and the surveyor is therefore sometimes required to do the best he can with photographs taken with an uncalibrated camera which is not available for subsequent calibration. This note outlines a method by which an approximate principal distance can be obtained for high oblique air photographs from points appearing in the photographs.     

总体最小二乘方法在空间后方交会中的应用

在空间后方交会的解算过程中,利用共线条件方程式列出误差方程后,针对地面控制点以及像点坐标均存在误差这一特点,引入总体最小二乘(total least squares,TLS)的方法,对系数矩阵A以及观测向量b同时进行改正,计算像片的6个外方位元素,建立更加合理的计算模型,可获得精度更高、更稳定的解。     

TWO SIMPLIFIED CHECKS

Abstract

The usual method employed is to plot or to compute the traverse from each end; the poin t having the same coordinates in each route is the station where the gross angular error occurred. There is, however, a method of finding the error by plotting the traverse one way only. Let us consider the traverse having the known terminals A B (see Fig.). Suppose that the error occurred at the point P and that the final point obtained (plotting the traverse from A) was B′ in place of the correct point B. We can easily see that the triangle PBB′is isosceles, and that therefore a straight line bisecting BB′at right angles will meet the traverse in the required point P.     

Approximating covariance matrices estimated in multivariate models by estimated auto- and cross-covariances

Quantities like tropospheric zenith delays or station coordinates are repeatedly measured at permanent VLBI or GPS stations so that time series for the quantities at each station are obtained. The covariances of these quantities can be estimated in a multivariate linear model. The covariances are needed for computing uncertainties of results derived from these quantities. The covariance matrix for many permanent stations becomes large, the need for simplifying it may therefore arise under the condition that the uncertainties of derived results still agree. This is accomplished by assuming that the different time series of a quantity like the station height for each permanent station can be combined to obtain one time series. The covariance matrix then follows from the estimates of the auto- and cross-covariance functions of the combined time series. A further approximation is found, if compactly supported covariance functions are fitted to an estimated autocovariance function in order to obtain a covariance matrix which is representative of different kinds of measurements. The simplification of a covariance matrix estimated in a multivariate model is investigated here for the coordinates of points of a grid measured repeatedly by a laserscanner. The approximations are checked by determining the uncertainty of the sum of distances to the points of the grid. To obtain a realistic value for this uncertainty, the covariances of the measured coordinates have to be considered. Three different setups of measurements are analyzed and a covariance matrix is found which is representative for all three setups. Covariance matrices for the measurements of laserscanners can therefore be determined in advance without estimating them for each application.     

A coordinate-invariant model for deforming geodetic networks: understanding rank deficiencies,non-estimability of parameters,and the effect of the choice of minimal constraints

By considering a deformable geodetic network, deforming in a linear-in-time mode, according to a coordinate-invariant model, it becomes possible to get an insight into the rank deficiency of the stacking procedure, which is the standard method for estimating initial station coordinates and constant velocities, from coordinate time series. Comparing any two out of the infinitely many least squares estimates of stacking unknowns (initial station coordinates, velocity components and transformation parameters for the reference system in each data epoch), it is proven that the two solutions differ only by a linear-in-time trend in the transformation parameters. These pass over to the initial coordinates (the constant term) and to the velocity estimates (the time coefficient part). While the difference in initial coordinates is equivalent to a change of the reference system at the initial epoch, the differences in velocity components do not comply with those predicted by the same change of reference system for all epochs. Consequently, the different velocity component estimates, obtained by introducing different sets of minimal constraints, correspond to physically different station velocities, which are therefore non-estimable quantities. The theoretical findings are numerically verified for a global, a regional and a local network, by obtaining solutions based on four different types of minimal constraints, three usual algebraic ones (inner or partial inner) and the lately introduced kinematic constraints. Finally, by resorting to the basic ideas of Felix Tisserand, it is explained why the station velocities are non-estimable quantities in a very natural way. The problem of the optimal choice of minimal constraints and, hence, of the corresponding spatio-temporal reference system is shortly discussed.     

利用空间投影分带方法研究卫星图像的连续制图

试图在遥感图像的连续制图方面做一些理论上的探讨，首次提出利用空间投影方法研究卫星遥感影像的连续制图问题。该方法的宗旨是利用空间投影坐标系来表示遥感图像坐标．利用邻带坐标的相互换算法来实现相邻轨道的图像坐标的统一，从而解决遥感图像的连续制图问题。文中同时研究了空间投影的分带投影方法，讨论了分带规定和邻带坐标换算等问题。     

GCP collection for corona satellite photographs: Issues and methodology

Use of high-resolution and historic CORONA satellite photographs for mapping and other purposes requires Ground Control Points (GCPs), as ephemeris data and image parameters are not available. However, the alterations in landscape in last 34 years (i.e., since the acquisition of these photographs) prevent identification and collection of large number of GCPs in the field. This paper presents a methodology for collection of GCPs for CORONA photographs. The advantages and limitations of the methodology are discussed. For a study site, situated in Siwaliks and Lower Himalayas, the GCPs were identified in CORONA photographs and their WGS84 coordinates were estimated through a process of datum transformation and georeferencing. Estimated GCP coordinates from the topo sheets and 2D and 3D views of photographs, helped in identifying the GCP locations in field, which were observed using DGPS. Investigations were carried out to relate Differential Global Positioning System (DGPS) accuracy with base line length and time of observation. Abase line of 350 km and half an hour observation were found appropriate to yield accuracy in GCP collection by DGPS method, which conforms to CORONA resolution of 3 m.     

The adjustment of intersecting chains of triangulation using a medium sized computer

Summary A method of adjusting intersecting chains of triangulation by direct elimination, using variation of coordinates, is given which is suitable for a computer of modest storage capacity (about 4000–8000 words). The network is considered to be made up of “nodes” (where two or more chains intersect) and “links” (which connect two nodes). The normal equations for the points in each link are computed, the coefficients of the unknown coordinates of the associated nodes being treated as extra right hand sides. These equations are then solved to express the coordinates of any link station in terms of the associated nodes. The process is repeated for all links. The normal equations for the nodes are then set up and substitution made for all “link” terms. The method is particularly powerful for the adjustment of a few, long, interconnected chains since the reduced normal equation coefficients are then banded about the diagonal, the semi band width being a little greater than the largest number of unknowns in the nodes along a single tie chain. For a computer of 7000 words capacity it is possible to solve for a band width of over 100 unknowns i.e. more than 50 stations.     

Conversion of geodetic coordinates from National Geodetic Reference Systems into Standard Earth System

The method of converting geodetic coordinates from a national geodetic reference system into the standard Earth on having known the geodetic coordinates of at least one station in common with the considered systems, is described in detail; the orientation of the Standard Earth at the initial station of the national geodetic reference system, is also determined side by side. For illustration, use has been made of the known coordinates of the Baker-Nunn station at Naini Tal, in India, being in common with the Indian Everest Spheroid and the Smithsonian Institution Standard Earth C₇ system (Veis, 1967). The method advocated is likely to be more precise than the existing ones as it does not assume the parallelism of axes of reference between the Standard Earth and the national geodetic reference systems which may not necessarily hold good in actual practice.     

GPS辅助光束法平差的理论精度

采用一组带ＧＰＳ导航数据的实际航摄资料,通过平差计算出精度矩阵Ｑｘｘ的数值,对ＧＰＳ辅助光束法平差的理论精度变化规律进行了全面讨论。以此为基础,从理论上给出最佳区域网的大小、地面控制点的布设等实用技术要求。此外,还探讨了ＧＰＳ用于单航线航空摄影测量加密的可行性和具体实施方案。     

城市环境下基于C/S架构的影像空间定位

针对城市环境下影像空间定位精度低等问题,提出了一种在C/S架构下基于影像的移动平台空间自定位方法。首先对预采集的城市建筑物序列影像,利用最近邻距离比率(nearest neighbor distance ratio,NNDR)算法和归一化互相关匹配(normalized cross correlation,NCC)算法得到SIFT粗匹配,通过随机抽样一致(random sample consensus,RANSAC)算法对粗匹配点进行优化,通过精确解算基本矩阵 F 和投影矩阵 P ,建立建筑物三维点云模型,进而获得由影像特征点、像点坐标以及物方点坐标组成的物方特征库。其次以用户通过手机拍摄的影像作为定位影像,进行特征提取并与物方特征库影像匹配,获取对应物方点坐标。最后通过精确计算定位影像外方位元素,并在手机客户端中显示所拍照瞬间手机的空间位置,实现移动平台空间自定位。实验结果表明,该方法能够达到厘米级定位精度,可作为其他空间定位方法的有效补充。