Predictor stabilisation of reduction formulae for observations of heavily-damped simple harmonic motions

The paper summarises attempts which have been made to derive general, simple and stable formulae of adequate precision for the reduction of observations to the extremal positions of oscillations which are simple harmonic or near-simple harmonic. A fallacy in the thirty-five year old Schuler Mean is pointed out and general formulae are offered for the reduction of observations for any constant damping, within the range0<f≤1.     

New method for reduction of astrolabe observations using rectangular coordinates on the celestial sphere

A new reduction method usingx, y, z-coordinates is derived for astrolabe observations. By this method, the latitude and the longitude of the station are computed without the need of a priori knowledge of the station position. This method is a significant development in data reduction of astrolabe and other almucantar observations due to its mathematical exactness, simplicity, and the ease of handling the associated statistics.     

特大型精密工程SSC测量投影方式的选择

目前世界上最大的工程超导超级对撞机(SSC)正在建造之中,作者参与这项大型精密工程测量的方案设计和部分咨询工作。根据工程的特点,设计测量投影方式是其中一项工作。本文讨论所设计的双重正形投影(stereographic double conformal projection)以及各种观测量投影归化中的问题。     

Singular value decomposition and cluster analysis as regression diagnostics tools for geodetic applications

It is well known that high-leverage observations significantly affect the estimation of parameters. In geodetic literature, mainly redundancy numbers are used for the detection of single high-leverage observations or of single redundant observations. In this paper a further objective method for the detection of groups of important and less important (and thus redundant) observations is developed. In addition, the parameters which are predominantly affected by these groups of observations are identified. This method thus complements other diagnostics tools, such as, e.g., multiple row diagnostics methods as described in statistical literature (see, e.g., Belsley et al. in Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York, 1980). The method proposed in this paper is based on geometric aspects of adjustment theory and uses the singular value decomposition of the design matrix of an adjustment problem together with cluster analysis methods for regression diagnostics. It can be applied to any geodetic adjustment problem and can be used for the detection of (groups of) observations that significantly affect the estimated parameters or that are of negligible impact. One of the advantages of the proposed method is the improvement of the reliability of observation plans and thus the reduction of the impact of individual observations (and outliers) on the estimated parameters. This is of particular importance for the very long baseline interferometry technique which serves as an application example of the regression diagnostics tool.     

ALMUCANTAR POSITION LINES

Abstract

This article discusses the observation equations which may be solved graphically by plotting position lines using the method of zenith distance intercepts, or solved analytically by the method of least squares.

The general observation equation is modified for the particular case in which zenith distance is made equal to assumed co-latitude, thus simplifying the reduction of the observations.

Adaptation of the theory to use with a theodolite is discussed together with the effects of sources of error and the methods which are proposed for their elimination.

A routine of reduction is proposed and an example is given.     

Error model for geodetic positions derived from Doppler satellite observations

Doppler observations of Navy Navigation Satellites have been used to strengthen and extend many terrestrial geodetic networks. The main sources of errors in positions determined from these observations are random error of observations, random and systematic errors in satellite positions due to uncertainties in the gravity field, and biases in the coordinate system in which the satellite ephemeris is given. Effects of uncertainties in the gravity field on station coordinates computed with respect to a precise satellite ephemeris are reduced to about 70 cm after 20 satellite passes are observed, but systematic effects prevent assurance that additional observations will improve the accuracy further. A one part per million reduction in scale must be applied to positions computed with the ephemeris to obtain agreement with terrestrial and other precise determinations of scale. The origin of the system is coincident with the center of mass of the earth to 1 m accuracy but the polar axis may be tilted three to five meters at the earth's surface with respect to coordinate systems upon which star catalogues are based.     

Algorithm for carrier-adjusted DGPS positioning and some numerical results

This paper derives a DGPS positioning algorithm, referred to as the algorithm for carrier-adjusted DGPS positioning. This algorithm can be applied by a DGPS user when code and carrier observations are available and when the dynamic behaviours of both mobile positions and receiver-clock biases can and cannot be modelled. Since the algorithm directly uses code and carrier observations, the stochastic model of observations has a simple structure and can be easily specified. When the dynamic behaviour of mobile positions can be modelled, the algorithm can provide recursive solutions of the positions, on the other hand, when the behaviour cannot be modelled, it can provide their instantaneous solutions. Furthermore, the algorithm can integrate with a real-time quality-control procedure so that the quality of the position estimates can be guaranteed with a certain probability. Since in the use of the algorithm there always exist redundant observations unless the position parameters are inestimable, the quality control can even be performed when only four satellites are tracked. Using the algorithm and real GPS data collected at a 100-km baseline, this contribution investigates how DGPS positioning accuracies vary with the type of observables used at reference and mobile stations, and how important it is to choose an elevation-dependent standard deviation for code observations in DGPS data reduction. It was found that using carrier observations along with code observations is more important at the reference station than at the mobile station. Choosing an elevation-dependent standard deviation for code observations can result in better positioning accuracy than choosing a constant standard deviation for code observations. For the 100-km baseline, half-metre single-epoch positioning accuracy was achieved when dual-frequency data was used at both reference and mobile stations. The positioning accuracy became better than 0.75m when the types of observable used at the mobile station were replaced by L1 code and carrier. Received: 9 April 1996 / Accepted: 6 February 1997     

On outlier-hiding effects in specific Gauss–Markov models: geodetic examples

 A specific subclass of Gauss–Markov models has been defined as containing the models for which the disturbance/response matrix, determined under the assumption of uncorrelated observations, consists of independent diagonal blocks. A proposed modification of reliability assessment procedure for such models is presented By the appropriate reduction of a given full covariance matrix for the observations, the proposal allows the assessment to be made in the resulting model which, in contrast to the initial model, is free from outlier-hiding effects of the type not occurring in ordinary models. The theoretical findings are demonstrated using simple numerical examples. All the proofs supporting the proposal are gathered in Appendixes. The proposal, which is not without its own weak points, is an attempt to associate the reliability assessment in specific Gauss–Markov models with effective outlier detection. Received: 23 June 1998 / Accepted: 5 July 2000     

论卫星网与地面网在高斯平面坐标系统中的联合平差问题

因为我国一些地区性平面控制网(例如城市平面控制网和矿山控制网等)的点位,一般均在高斯平面直角坐标系统中表示,所以本文研究了卫星精密定位成果在高斯平面坐标系统中应用的理论和方法,推荐了卫星网与地面网的联合平差模型,并在模型中考虑了地面网归算面高程变化而生产的影响。     

Filtering GPS time-series using a Vondrak filter and cross-validation

Multipath disturbance is one of the most important error sources in high-accuracy global positioning system (GPS) positioning and navigation. A new data filtering method, based on the Vondrak filter and the technique of cross-validation, is developed for separating signals from noise in data series, and applied to mitigate GPS multipath effects in applications such as deformation monitoring. Both simulated data series and real GPS observations are used to test the proposed method. It is shown that the method can be used to successfully separate signals from noise at different noise levels, and for varying signal frequencies as long as the noise level is lower than the magnitude of the signals. A multipath model can be derived, based on the current-day GPS observations, with the proposed method and used to remove multipath errors in subsequent days of GPS observations when taking advantage of the sidereal day-to-day repeating characteristics of GPS multipath signals. Tests have shown that the reduction in the root mean square (RMS) values of the GPS errors ranges from 20% to 40% when the method is applied.     

一种快速解算高维模糊度的LLL分块处理算法

由于多频多模GNSS观测数据解算的模糊度具有较高的维数和精度,当采用常规的LLL算法进行模糊度整数估计时,规约耗时显著大于搜索耗时,成为限制高维模糊度解算计算效率的主要因素。针对这一问题,通过分析规约耗时与模糊度维数和精度之间的关系,提出了一种LLL分块处理算法。该算法通过对模糊度方差协方差阵进行分块处理,降低单个规约矩阵的维数,以减少规约耗时,从而提高模糊度解算计算效率。通过两组实测高维模糊度数据对本文提出的分块处理算法进行了效果验证。结果显示,当分块选择合理时,本文提出的算法相对于LLL算法的解算效率分别可提高65.2%和60.2%。     

我国近海平均海面及其变化的研究

建立了计算平均海面及其变化的动态抗差模型，并把它与计算平均海面的平均值法、抗差法和动态模型法作了实测数据的计算和比较，表明动态抗差模型不仅能顾及海面动态变化反应，而且能削弱海面异常变化的影响，其结果更稳定可靠，优于其他方法。最后应用动态抗差模型，计算了我国42个验潮站的平均海面及其变化，结果表明，从50年代到70提供，我国近海的海面平均以0．621mm/a的速率上升。     

弱电离层组合SPP在极区定位效果分析

研究了Klobuchar电离层改正模型和双频消电离层组合在伪距单点定位中的应用。通过实验验证了Klobuchar模型在极区的不适用性,并从理论上分析了消电离层组合在伪码噪声放大方面的缺点。针对消电离层组合中的不足,将噪声放大视为伪距定位中的主要矛盾。在降低伪距噪声和电离层延迟的不完全消除之间寻求平衡,提出了一种兼顾降噪与电离层改正的双频组合,称之为弱电离层组合。利用南极地区多个IGS跟踪站的多天数据,验证了弱电离层组合伪距单点定位相对于消电离层组合具有更好的定位效果,定位精度普遍可以提高15%~30%。不同测站对应的改善程度不尽相同,接收机内部因素造成的观测质量不佳也会使得定位精度改善不显著。     

Calibration of the Wild P32 Camera Using the Camera-On-Theodolite Method

The calibration of phototheodolites such as the Wild P32/T2 combination sometimes involves determining not only the camera interior orientation parameters but also the camera-to-theodolite parameters. The latter become particularly important when the theodolite set orientation parameters are to be used as observations, especially as known quantities for data reduction in subsequent photogrammetric applications. This paper presents experiments to determine these parameters for a Wild P32 camera using a new camera-on-theodolite method, with details of results achieved.     

Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning

The main challenge of dual-frequency precise point positioning (PPP) is that it requires about 30 min to obtain centimeter-level accuracy or to succeed in the first ambiguity-fixing. Currently, PPP is generally conducted with GPS only using the ionosphere-free combination. We adopt a single-differenced (SD) between-satellite PPP model to combine the GPS and GLONASS raw dual-frequency carrier phase measurements, in which the GPS satellite with the highest elevation is selected as the reference satellite to form the SD between-satellite measurements. We use a 7-day data set from 178 IGS stations to investigate the contribution of GLONASS observations to both ambiguity-float and ambiguity-fixed SD PPP solutions, in both kinematic and static modes. In ambiguity-fixed PPP, we only attempt to fix GPS integer ambiguities, leaving GLONASS ambiguities as float values. Numerous experimental results show that PPP with GLONASS and GPS requires much less convergence time than that of PPP with GPS alone. For ambiguity-float PPP, the average convergence time can be reduced by 45.9 % from 22.9 to 12.4 min in static mode and by 57.9 % from 40.6 to 17.7 min in kinematic mode, respectively. For ambiguity-fixed PPP, the average time to the first-fixed solution can be reduced by 27.4 % from 21.6 to 15.7 min in static mode and by 42.0 % from 34.4 to 20.0 min in kinematic mode, respectively. Experimental results also show that the less the GPS satellites are used in float PPP, the more significant is the reduction in convergence time when adding GLONASS observations. In addition, on average, more than 4 GLONASS satellites can be observed for most 2-h observation sessions. Nearly, the same improvement in convergence time reduction is achieved for those observations.     

Strength of long lines in terrestrial geodetic control networks

a knowledge of the à posteriori accuracy of long lines in classical triangulation networks is important not only for establishing the quality of existing primary national control networks, but also for assessing the likely contribution of satellite derived observations. Extensive tests carried out with various networks, ranging from a basic triangulation chain to Block VI of the European Triangulation Network, show definite trends. The à posteriori standard errors of both the scale and the orientation of an adjusted line diminish considerably as the length of the line increases. In the case of medium sized countries, the results compare favourably with those predicted for satellite derived data. The conclusions emphasize the need for great care in the reduction of terrestrial observations and the elimination of all possible systematic errors before proceeding with a least squares adjustment.     

LAPLACE POINTS IN MODERATE AND HIGH LATITUDES

Abstract

A method of applying azimuth control to a survey is given in which the precision with which the astronomical position must be determined is proportional to tan (altitude) instead of tan (latitude) as in the orthodox method. By using the method with stars of low altitude the observational difficulties are greatly reduced, especially in high latitudes. Methods of observation and reduction are discussed which make it possible to avoid altogether special observations to determine the astronomical position.     

On the Reduction of the Systematic Error in Imaging Radiometry by Aperture Synthesis: A New Approach for the SMOS Space Mission

The Soil Moisture and Ocean Salinity (SMOS) mission is a European Space Agency project aimed at global monitoring of surface SMOS from radiometric L-band observations. This letter is concerned with the reduction of the systematic error (or bias) in the reconstruction of radiometric brightness temperature maps from SMOS interferometric measurements. A recent and efficient method has been proposed for reducing this error. However, a residual bias still persists. A new approach for reducing this bias down to residual values less than 0.1 K is presented here and illustrated with numerical simulations.     

Multivariate Monitoring with GPS Observations and Auxillary Multisensor Data

In a multisensor measurement or monitorin environment, p variables are measured simultaneously. The measured data are correlated and can be monitored to identify special causes of variation in order to establish control and to obtain reference samples to use as a basis in determining the control limits for future observations. One common method is to construct a multivariate control chart based on Hotelling's T² statistic. When the monitoring process is at the start-up stage, F and chi-square distributions are used to construct the necessary control limits. An example from a seven-day GPS data sample measured concurrently with the accelerometer response, wind velocity and temperature illustrates that this technique can improve the interpretation of GPS results. Moreover, the computational complexity is reduced through a reduction in the data dimensionality. ? 2002 Wiley Periodicals, Inc.     

Comparison of the Graf sea gravimeter with the Vening Meinesz apparatus on board the submarineU.S.S. Becuna

Measurements of gravity were made on boardU.S.S. Becuna (SS 319) with a Vening Meinesz pendulum apparatus and a Graf sea gravimeter at approximately the same time. Comparison of data uncorrected for depth of submergence, E?tvos correction and second order effects of horizontal acceleration showed that there was a change related to time of observation. These corrections were not made as they would be the same for both sets of observations, and no provision had yet been made to take care of the horizontal accelerations for the Graf sea gravimeter. The variation with otime could be caused by instrumental drift or scale calibration. After removal of this effect by visually fitting the data trend with a straight line, there were three observations with large discrepancies, seventeen with discrepancies of 3–9 mgal and thirty-nine with discrepancies of 0–3 mgal, showing close approach to a statistical distribution. The three large discrepancies may be dismissed because of very bad depth control during the observations. The discrepancies 3–9 mgals are larger than expected and perhaps are attributable to depth control and inadequate observation time for the Graf sea gravimeter. It is concluded that the Graf sea gravimeter shows great promise for use on a submarine. An apparatus to take into account the horizontal acceleration effects must be added, and suitable drift characteristic obtained. Despite its advantages of ruggedness, ease of operation, ease of data reduction, reduced size and weight, many more comparisons of the Graf sea gravimeter with the Vening Meinesz pendulum equipment should be made before the latter are displaced Probably the Graf sea gravimeter will be usable on a stable platform on a surface vessel at least in calm sea states.