The non-linear 2D symmetric helmert transformation : An exact non-linear least-squares solution   总被引：1，自引：1，他引：0  

Peter J. G. Teunissen 《Journal of Geodesy》1988,62(1):1-16

In this paper a particular class of non-linear least-squares problems for which it is possible to take advantage of the special structure of the non-linear model, is discussed. The non-linear models are of the ruled-type (Teunisson, 1985a). The proposed solution strategy is applied to the2D non-linear Symmetric Helmert transformation which is defined in the paper. An exact non-linear least-squares solution, using a rotational invariant covariance structure is given.  相似文献   

Least-squares prediction in linear models with integer unknowns     

P. J. G. Teunissen 《Journal of Geodesy》2007,81(9):565-579

The prediction of spatially and/or temporal varying variates based on observations of these variates at some locations in space and/or instances in time, is an important topic in the various spatial and Earth sciences disciplines. This topic has been extensively studied, albeit under different names. The underlying model used is often of the trend-signal-noise type. This model is quite general and it encompasses many of the conceivable measurements. However, the methods of prediction based on these models have only been developed for the case the trend parameters are real-valued. In the present contribution we generalize the theory of least-squares prediction by permitting some or all of the trend parameters to be integer valued. We derive the solution for least-squares prediction in linear models with integer unknowns and show how it compares to the solution of ordinary least-squares prediction. We also study the probabilistic properties of the associated estimation and prediction errors. The probability density functions of these errors are derived and it is shown how they are driven by the probability mass functions of the integer estimators. Finally, we show how these multimodal distributions can be used for constructing confidence regions and for cross-validation purposes aimed at testing the validity of the underlying model. Dedicated to the memory of Dr. Tech.hc. Torben Krarup (1919–2005).  相似文献   

Analysis of double shearing in frictional materials     

J. A. M. Teunissen  P. A. Vermeer 《国际地质力学数值与分析法杂志》1988,12(3):323-340

The concept that the flow of granular materials is governed by shear on certain critical planes is used to formulate an elastic–plastic model. When the elastic strains are neglected, the Double Shearing model becomes identical to the rigid-plastic model of de Josselin de Jong which he named the Double Sliding model. After a discussion of the model, the small strain formulation is used to describe general boundary-value problems. A comparison is then made between the coaxial Mohr–Coulomb yielding and the Double Shearing model on the basis of several numerical simulations. The non-coaxiality of the axes of principal plastic strain rate and principal stress in the Double Shearing model leads to essentially different behaviour for stress rotations in comparison to the coaxial model. The Double Shearing model predicts in general lower limit loads because, for a given state of stress, it allows for several possible directions of plastic flow rather than a unique direction which derives from a plastic potential.  相似文献   

A canonical theory for short GPS baselines. Part III: the geometry of the ambiguity search space     

P. J. G. Teunissen 《Journal of Geodesy》1997,71(8):486-501

This contribution is the third of four parts. Based on the gain-number concept, canonical forms will be presented of the ambiguity search spaces of the geometry-based model, the time-averaged model, and the geometry-free model. These forms reveal the intrinsic geometry of the search spaces and allow one to study their size, shape, and orientation as function of data precision, sampling rate, satellite redundancy, and change in receiver-satellite geometry. The canonical forms are also used to address the problem of search halting. The phenomenon of search halting is explained and it is shown how decorrelating ambiguity transformations can largely eliminate this computational burden. Received: 16 July 1996 / Accepted: 14 November 1996  相似文献   

On the GPS widelane and its decorrelating property   总被引：2，自引：1，他引：2  

P. J. G. Teunissen 《Journal of Geodesy》1997,71(9):577-587

In this contribution we consider the popular widelaning technique from the viewpoint of ambiguity decorrelation. It enables us to cast the technique into the framework of the least-squares ambiguity decorrelation adjustment (LAMBDA) and to analyse its relative merits. In doing so, we will provide answers to the following three questions. Does the widelane decorrelate? Does it explicitly appear in the automated transformation step of the LAMBDA method? Can one do better than the widelane? It is shown that all three questions can be answered in the affirmative. This holds true for the ionosphere-fixed case, the ionosphere-float case, as well as for the ionosphere-weighted case. Received: 11 November 1996 / Accepted: 23 April 1997  相似文献   

The geometry-free GPS ambiguity search space with a weighted ionosphere   总被引：4，自引：1，他引：4  

P. J. G. Teunissen 《Journal of Geodesy》1997,71(6):370-383

  相似文献   

Anholonomity when using the development method for the reduction of observations to the reference ellipsoid     

P. J. G. Teunissen 《Journal of Geodesy》1982,56(4):356-363

For computing the geodetic coordinates ϕ and γ on the ellipsoid one needs information of the gravity field, thus making it possible to reduce the terrestrial observations to the reference surface. Neglect of gravity field data, such as deflections of the vertical and geoid heights, results in misclosure effects, which can be described using the object of anholonomity.  相似文献   

Least-squares variance component estimation   总被引：19，自引：15，他引：4  

P. J. G. Teunissen  A. R. Amiri-Simkooei 《Journal of Geodesy》2008,82(2):65-82

Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight matrix; and it is attractive because it allows one to directly apply the existing body of knowledge of LS theory. In this contribution, we present the LS-VCE method for different scenarios and explore its various properties. The method is described for three classes of weight matrices: a general weight matrix, a weight matrix from the unit weight matrix class; and a weight matrix derived from the class of elliptically contoured distributions. We also compare the LS-VCE method with some of the existing VCE methods. Some of them are shown to be special cases of LS-VCE. We also show how the existing body of knowledge of LS theory can be used to one’s advantage for studying various aspects of VCE, such as the precision and estimability of VCE, the use of a-priori variance component information, and the problem of nonlinear VCE. Finally, we show how the mean and the variance of the fixed effect estimator of the linear model are affected by the results of LS-VCE. Various examples are given to illustrate the theory.  相似文献   

Penalized GNSS Ambiguity Resolution   总被引：1，自引：1，他引：1  

P. J. G. Teunissen 《Journal of Geodesy》2004,78(4-5):235-244

Global Navigation Satellite System (GNSS) carrier phase ambiguity resolution is the process of resolving the carrier phase ambiguities as integers. It is the key to fast and high precision GNSS positioning and it applies to a great variety of GNSS models which are currently in use in navigation, surveying, geodesy and geophysics. A new principle of carrier phase ambiguity resolution is introduced. The idea is to give the user the possibility to assign penalties to the possible outcomes of the ambiguity resolution process: a high penalty for an incorrect integer outcome, a low penalty for a correct integer outcome and a medium penalty for the real valued float solution. As a result of the penalty assignment, each ambiguity resolution process has its own overall penalty. Using this penalty as the objective function which needs to be minimized, it is shown which ambiguity mapping has the smallest possible penalty. The theory presented is formulated using the class of integer aperture estimators as a framework. This class of estimators was introduced elsewhere as a larger class than the class of integer estimators. Integer aperture estimators, being of a hybrid nature, can have integer outcomes as well as non-integer outcomes. The minimal penalty ambiguity estimator is an example of an integer aperture estimator. The computational steps involved for determining the outcome of the minimal penalty estimator are given. The additional complexity in comparison with current practice is minor, since the optimal integer estimator still plays a major role in the solution of the minimal penalty ambiguity estimator.  相似文献   

Single-frequency L5 attitude determination from IRNSS/NavIC and GPS: a single- and dual-system analysis     

S.?ZaminpardazEmail author  P.?J.?G.?Teunissen  N.?Nadarajah 《Journal of Geodesy》2017,91(12):1415-1433

The Indian Regional Navigation Satellite System (IRNSS) has recently (May 2016) reached its full operational capability. In this contribution, we provide the very first L5 attitude determination analyses of the fully operational IRNSS as a standalone system and also in combination with the fully operational GPS Block IIF along with the corresponding ambiguity resolution results. Our analyses are carried out for both a linear array of two antennas and a planar array of three antennas at Curtin University, Perth, Australia. We study the noise characteristics (carrier-to-noise density, measurement precision, time correlation), the integer ambiguity resolution performance (LAMBDA, MC-LAMBDA) and the attitude determination performance (ambiguity float and ambiguity fixed). A prerequisite for precise and fast IRNSS attitude determination is the successful resolution of the double-differenced integer carrier-phase ambiguities. In this contribution, we will compare the performance of the unconstrained and the multivariate-constrained LAMBDA method. It is therefore also shown what improvements are achieved when the known body geometry of the antenna array is rigorously incorporated into the ambiguity objective function. As our ambiguity-fixed outcomes show consistency between empirical and formal results, we also formally assess the precise attitude determination performance for several locations within the IRNSS service area.  相似文献