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In this contribution it is shown how an extended uncertainty budget of the observations according to the Guide to the Expression of Uncertainty in Measurement (GUM) can be considered in adjustment computations. The extended uncertainty budget results from the combination of Type A standard uncertainties determined with statistical methods and Type B standard uncertainties derived with nonstatistical methods. Two solutions are investigated, namely the adjustment in the classical Gauss-Markov model and the adjustment in the Gauss-Markov model using Monte Carlo simulations for the consideration of the uncertainties of the observations. Numerical examples are given to show that an appropriate interpretation of the dispersion measures for the unknowns is particularly important in order to avoid misinterpretation of the results. Furthermore, the effects of changing the weights of the observations on the adjustment results are shown. Finally, practical advice for the consideration of an extended uncertainty budget of the observations in adjustment computations is given.

Since the orbit repeat cycle of Galileo satellites is about 10 days, existing spatial–temporal repeatability-based station multipath mitigation methods such as the modified sidereal filtering (MSF) and the multipath hemispherical map need more than one week of data in order to model the Galileo phase multipath correction. From this perspective, these methods are improper for most applications. We proposed a random walk multipath method (RWM) to resolve this problem. Since the elevation and azimuth angles between adjacent epochs do not change too much, the low-frequency phase multipath effects at adjacent epochs are similar. Multipath correction value can be estimated by the random walk model. Because the GPS satellite repeat cycle is short, GPS observations easily mitigate the multipath effect and have common coordinate parameters with Galileo. Multipath-reduced GPS signals can be a constant for separating coordinate parameters and multipath parameters. Galileo phase observation residuals of the latest day are used to calculate the variance for the random walk model. Experiment results show that compared to the traditional MSF model, the proposed RWM method can improve the Galileo residual reduction and positioning precision nearly without the need of any historical data. As for the practical real-time GNSS monitoring application in a severe multipath environment, the result shows that the new method can significantly reduce the Galileo multipath effect and subsequently yield a precise positioning solution. Moreover, the RWM method is invulnerable to the sampling rate and observation environment.

To evaluate the benefit of a measurement procedure onto the estimated parameters, the dispersion of the parameters is usually used. To draw objective conclusions, unbiased or at least almost unbias...

In multi-GNSS integration, fixing inter-system double-difference ambiguities to integers is still a challenge due to the existence of inter-system biases (ISB) when mixed types of GNSS receivers are used. It has been shown that when ISB is known, the inter-system ambiguities can be fixed and the reliability of ambiguity fixing can be improved significantly, especially under poor conditions when the number of observed satellites is small. In traditional methods, the intra-system ambiguity is fixed first; then, the ISB is estimated to ultimately fix the inter-system ambiguity. In our work, we use the particle filter-based method to estimate the ISB parameter and fix the inter-system ambiguities to integers at the same time. This method shows higher reliability and higher ambiguity fixing rate. Nevertheless, the existing particle filter approach for ISB parameter estimation is a one-dimensional algorithm. When satellites from three or more systems are observed, there are two or more ISB parameters. We extend the current one-dimensional particle filter approach to multi-dimensional case and estimate multi-ISB parameters in this study. We first present a multi-dimensional particle filter approach that can estimate multi-ISB parameters simultaneously. We also show that the RATIO values can be employed to judge the quality of multi-dimensional ISB values. Afterward, a two-dimensional particle filter approach is taken as an example to validate this approach. For example, in the experiment of GPS L5, Galileo E5a and QZSS L5 integration with 6 satellites using the IGS baseline SIN0-SIN1, only three ambiguities are resolved to integer when the ISBs are unknown. The integer ambiguity fixing rate is 41.0% with 53% of the ambiguity-fixed solutions having positioning errors larger than 3 cm. However, when our approach is adopted, the number of integer ambiguity parameters increases to five. The integer ambiguity fixing rate increases to 99.7% with 100% of ambiguity-fixed solutions having positioning errors smaller than 3 cm.

To examine the capability to detect and localise damage using the Measurement- and Model-based Structural Analysis (MeMoS), a small-scale truss bridge (1520 mm × 720 mm × 720 mm) made of aluminium profiles is built as a test specimen for this purpose. The truss frame of the test bridge is made of aluminium profiles with a sophisticated design of the cross-sectional area. In comparison, with solid profiles, only a fraction of the material is needed to produce the profiles, while their bending resistance decreases slightly. The profiles are built into a truss frame by connecting them by means of fastening sets made of steel. The bridge model is mounted on four steel bearings which each of them consist of a cylinder arranged between two plates. Fixed bearings are made by holding onto one end of the bridge. The bridge is subjected by an external load by placing a heavy object beneath it. At the same time, measurements can be conducted below the bridge. Therefore, the bridge specimen is elevated by attaching it on a pedestal with four columns. Damages can be induced by loosening the fastening pieces.

Suppose a large and dense point cloud of an object with complex geometry is available that can be approximated by a smooth univariate function. In general, for such point clouds the “best” approximation using the method of least squares is usually hard or sometimes even impossible to compute. In most cases, however, a “near-best” approximation is just as good as the “best”, but usually much easier and faster to calculate. Therefore, a fast approach for the approximation of point clouds using Chebyshev polynomials is described, which is based on an interpolation in the Chebyshev points of the second kind. This allows to calculate the unknown coefficients of the polynomial by means of the Fast Fourier transform (FFT), which can be extremely efficient, especially for high-order polynomials. Thus, the focus of the presented approach is not on sparse point clouds or point clouds which can be approximated by functions with few parameters, but rather on large dense point clouds for whose approximation perhaps even millions of unknown coefficients have to be determined.

Global navigation satellite systems (GNSS) are an important tool for positioning, navigation, and timing (PNT) services. The fast and high-precision GNSS data processing relies on reliable integer ambiguity fixing, whose performance depends on phase bias estimation. However, the mathematic model of GNSS phase bias estimation encounters the rank-deficiency problem, making bias estimation a difficult task. Combining the Monte-Carlo-based methods and GNSS data processing procedure can overcome the problem and provide fast-converging bias estimates. The variance reduction of the estimation algorithm has the potential to improve the accuracy of the estimates and is meaningful for precise and efficient PNT services. In this paper, firstly, we present the difficulty in phase bias estimation and introduce the sequential quasi-Monte Carlo (SQMC) method, then develop the SQMC-based GNSS phase bias estimation algorithm, and investigate the effects of the low-discrepancy sequence on variance reduction. Experiments with practical data show that the low-discrepancy sequence in the algorithm can significantly reduce the standard deviation of the estimates and shorten the convergence time of the filtering.

Up until now no appropriate models have been proposed that are capable to describe the stochastic characteristics of reflectorless rangefinders - the key component of terrestrial laser scanners. This state has to be rated as unsatisfactory especially from the perception of Geodesy where comprehensive knowledge about the precision of measurements is of vital importance, for instance to weigh individual observations or to reveal outliers. In order to tackle this problem, a novel intensity-based stochastic model for the reflectorless rangefinder of a Zoller + Frohlich Imager 5006 h is experimentally derived. This model accommodates the influence of the interaction between the emitted signal and object surface as well as the acquisition configuration on distance measurements. Based on two different experiments the stochastic model has been successfully verified for three chosen sampling rates.

With the development of China’s BeiDou Navigation Satellite System (BDS) and the operation of the real-time service (RTS) of the International GNSS service, BDS real-time precise point positioning (RTPPP) has become possible. In this contribution, the RTS product CLK93 is employed for BDS RTPPP, and its quality for BDS orbit and clock corrections is first assessed by availability and accuracy over a period of 24 days. Following this, the convergence time and positioning accuracy of BDS-only RTPPP are evaluated by performing a 24-day processing with ten stations from the multi-GNSS experiment (MGEX) network. Finally, a real-time kinematic test is conducted in an urban environment to further investigate the performance of BDS-only RTPPP. Experimental results show that the average availabilities of the CLK93 corrections are approximately 95% for the inclined geosynchronous satellite orbit (IGSO) satellites, 90% for the medium earth orbit (MEO) satellites and 65% for the geostationary earth orbit satellites. The mean accuracy of the real-time corrections, which is represented by the signal-in-space ranging error (SISRE) value, is 10 cm for the IGSO and MEO satellites. Furthermore, the average positioning accuracies in the north, east and up components of the ten MGEX stations are approximately 1.7, 2.2 and 2.6 cm, respectively, for the static mode and 10.3, 15.6 and 29.2 cm, respectively, for the kinematic mode. In addi-tion, the average time required to converge to a 20-cm accuracy in the three-dimensional component is approximately 100 and 136 min for BDS-only RTPPP in the static and kinematic modes, respectively. In addition, the positioning accuracy of BDS-only RTPPP in the real-time kinematic test is 0.86, 0.92 and 1.68 m in the east, north and up components, respectively, for the whole solutions during the test, which is obviously worse than that obtained by GPS-only RTPPP.

By means of a small-scale truss bridge, the ability of the Measurement- and Model-based Structural Analysis to detect and localise damage was examined in [1]. Although there was no noteworthy difficulty in detecting damage, it turned out that damage localisation responds sensitively to systematic influences, i.e. non-modelled properties of the mechanical model. Therefore, another experiment is being conducted to re-examine the Measurement- and Model-based Structural Analysis. For this purpose, the bending test is carried out as it has been already theoretically respectively numerically discussed in [2]. In this attempt, the systematic influences such as residual stress are kept as low as possible.

Although double-differenced (DD) observations between satellites from different systems can be used in multi-GNSS relative positioning, the inter-system DD ambiguities cannot be fixed to integer because of the existence of the inter-system bias (ISB). Obviously, they can also be fixed as integer along with intra-system DD ambiguities if the associated ISBs are well known. It is critical to fix such inter-system DD ambiguities especially when only a few satellites of each system are observed. In most of the existing approaches, the ISB is derived from the fractional part of the inter-system ambiguities after the intra-system DD ambiguities are successfully fixed. In this case, it usually needs observations over long times depending on the number of observed satellites from each system. We present a new method by means of particle filter to estimate ISBs in real time without any a priori information based on the fact that the accuracy of a given ISB value can be qualified by the related fixing RATIO. In this particle filter-based method, the ISB parameter is represented by a set of samples, i.e., particles, and the weight of each sample is determined by the designed likelihood function related to the corresponding RATIO, so that the true bias value can be estimated successfully. Experimental validations with the IGS multi-GNSS experiment data show that this method can be carried out epoch by epoch to provide precise ISB in real time. Although there are only one, two, or at most three Galileo satellites observed, the successfully fixing rate increases from 75.5% for GPS only to 81.2%. In the experiment with five GPS satellites and one Galileo satellites, the first successfully fixing time is reduced to half of that without fixing the inter-system DD ambiguities.

The case of a singular dispersion matrix within the Gauss–Helmert Model has been considered before, most recently even allowing the rank of BQ to be smaller than the rank of B. In this contribution the emphasis is shifted towards an illuminating example, the 2D Helmert transformation.

A current aim of ongoing research in the field of deformation measurement is to automatically determine geometric changes between several epochs with data captured by terrestrial laser scanners. A critical component within the process chain of deformation measurement is the transformation of captured point clouds into a reference coordinate system. This contribution proposes a surface-based alignment methodology that does not require artificial targets or extracted geometric primitives. A diagnostic method reveals deformations that occurred in between epochs and rejects them from the computation of transformation parameters that would otherwise cause erroneous registrations. The novel approach has been successfully tested on two practical cases where the highest degree of deformation extended to 65% of the total surface area.

Despite the enormous popularity of terrestrial laser scanners in the field of Geodesy, economic aspects in the context of data acquisition are mostly considered intuitively. In contrast to established acquisition techniques, such as tacheometry and photogrammetry, optimisation of the acquisition configuration cannot be conducted based on assumed object coordinates, as these would change in dependence to the chosen viewpoint. Instead, a combinatorial viewpoint planning algorithm is proposed that uses a given 3D-model as an input and simulates laser scans based on predefined viewpoints. The method determines a suitably small subset of viewpoints from which the sampled object surface is preferably large. An extension of the basic algorithm is proposed that only considers subsets of viewpoints that can be registered to a common dataset. After exemplification of the method, the expected acquisition time in the field is estimated based on computed viewpoint plans.

The determination of material parameters from displacement field measurement is being examined for linear elastic solid. A frequently used approach to compute material constants can be found in many studies. Even though they presented the approach in many different variations, but in the end they are essentially based on the same algorithm: Parameters are iteratively tuned until the computed results are in accordance with the measurements. The main drawback of this approach is that mainly commercial software is used that hinders us to investigate its inner evaluation process. This leads to the question, how the results from this commercial software can be trusted. On the contrary to these debatable approaches, we present a method that inverts the procedure of finite element method by using the most general model for a least-squares adjustment – the Gauss - Helmert Model.

Dieser Beitrag fokussiert auf die Uberwachung einer historischen Brucke mittels terrestrischem Laserscanning wahrend eines Belastungsversuchs. Dabei wurde ein Belastungsregime von etwa 1 bis 6 MN durchfahren. Zur Erfassung der statischen Haltephasen wurden 3-D-Laserscanner eingesetzt, welche die Verformung der Brucke infolge des Lasteintrags dokumentieren. Um Verfalschungen der zu berechnenden Verformungen ausschliesen zu konnen, wurde zum einen eine ebenenbasierte Registrierung basierend auf stabilen Objektbereichen und zum anderen eine Referenzierung uber diskrete, signalisierte Stabilpunkte durchgefuhrt. Mit dem Einsatz eines Profillaserscanners konnte zusatzlich zum statischen auch der dynamische Lasteintrag uberwacht werden. Im Rahmen dieses Beitrags wurde dazu das Konzept der Klassenreprasentanten eingesetzt. Das hier gezeigte Rauschniveau lag dabei im Bereich von 0,1 mm und kann somit auch kleinmasstabliche geometrische Veranderungen infolge der Auflast nachweisen.

Relative positioning using multi-GNSS (global navigation satellite systems) can improve accuracy, reliability, and availability compared to the use of a single constellation system. Intra-system double-difference (DD) ambiguities (ISDDAs) refer to the DD ambiguities between satellites of a single constellation system and can be fixed to an integer to derive the precise fixed solution. Inter-system ambiguities, which denote the DD ambiguities between different constellation systems, can also be fixed to integers on overlapping frequencies, once the inter-system bias (ISB) is removed. Compared with fixing ISDDAs, fixing both integer intra- and inter-system DD ambiguities (IIDDAs) means an increase of positioning precision through an integration of multiple GNSS constellations. Previously, researchers have studied IIDDA fixing with systems of the same frequencies, but not with systems of different frequencies. Integer IIDDAs can be determined from single-difference (SD) ambiguities, even if the frequencies of multi-GNSS signals used in the positioning are different. In this study, we investigated IIDDA fixing for multi-GNSS signals of narrowly spaced frequencies. First, the inter-system DD models of multi-GNSS signals of different frequencies are introduced, and the strategy for compensating for ISB is presented. The ISB is decomposed into three parts: 1) a float approximate ISB number that can be considered equal to the ISB of code pseudorange observations and thus can be estimated through single point positioning (SPP); 2) a number that is a multiple of the GNSS signal wavelength; and 3) a fractional ISB part, with a magnitude smaller than a single wavelength. Then, the relationship between intra- and inter-system DD ambiguity RATIO values and ISB was investigated by integrating GPS L1 and GLONASS L1 signals. In our numerical analyses with short baselines, the ISB parameter and IIDDA were successfully fixed, even if the number of observed satellites in each system was small.

Precise Point Positioning (PPP) is a popular technology for precise applications based on the Global Navigation Satellite System (GNSS). Multi-GNSS combined PPP has become a hot topic in recent years with the development of multiple GNSSs. Meanwhile, with the operation of the real-time service (RTS) of the International GNSS Service (IGS) agency that provides satellite orbit and clock corrections to broadcast ephemeris, it is possible to obtain the real-time precise products of satellite orbits and clocks and to conduct real-time PPP. In this contribution, the real-time multi-GNSS orbit and clock corrections of the CLK93 product are applied for real-time multi-GNSS PPP processing, and its orbit and clock qualities are investigated, first with a seven-day experiment by comparing them with the final multi-GNSS precise product ‘GBM’ from GFZ. Then, an experiment involving real-time PPP processing for three stations in the Multi-GNSS Experiment (MGEX) network with a testing period of two weeks is conducted in order to evaluate the convergence performance of real-time PPP in a simulated kinematic mode. The experimental result shows that real-time PPP can achieve a convergence performance of less than 15 min for an accuracy level of 20 cm. Finally, the real-time data streams from 12 globally distributed IGS/MGEX stations for one month are used to assess and validate the positioning accuracy of real-time multi-GNSS PPP. The results show that the simulated kinematic positioning accuracy achieved by real-time PPP on different stations is about 3.0 to 4.0 cm for the horizontal direction and 5.0 to 7.0 cm for the three-dimensional (3D) direction.

The carrier phase inter-frequency bias (IFB) of GLONASS between receivers of different types is usually not zero. This bias must be estimated and removed in data processing so that the integer double difference (DD) ambiguities can be fixed successfully. Recently, the particle filter approach has been proposed to estimate the IFB rate in real time. In this approach, the IFB rate samples are first generated and used to correct the phase IFB in the GLONASS observations. Then, the weights of the rate samples are updated with a function related to RATIO which is for ambiguity acceptance testing in integer ambiguity resolution. Afterwards, the IFB rate is estimated according to the weighted particles. This approach can estimate IFB accurately with short convergence time and without prior information. However, when the system noise is set too low, the estimated results are unstable due to the serious problem of particle diversity-loss, even though the system model is accurate. Additionally, the computational burden is dependent on the number of particles, which has to be optimized for the computation at hand. Therefore, this study proposes two improvements for the IFB estimation in regard to the above two aspects. The first improvement is to solve the noise setting problem by employing a regularized particle filter (RPF). The second improvement optimizes the number of particles in the resampling step according to the standard deviation (STD) of the weighted particles via a controlling function. The two improvements result in significantly better performances. The regularization method allows for the system noise to be set as zero without disturbing the estimates, and consequently, more precise estimates can be achieved. In addition, the approach using the controlling function for adapting the number of particles has comparable performance in precision but the computation load is largely reduced.

Current research questions in the field of geomorphology focus on the impact of climate change on several processes causing subsequently natural hazards. Geodetic deformation measurements are a suitable tool to document such geomorphic mechanisms e.g. under the use of terrestrial laser scanners that capture a region of interest in a quasi-laminar fashion which results in a so-called 3D point cloud. In this context the central problem is linked to the transformation of 3D point clouds captured at different points in time (epochs) into a common reference coordinate system. To date, this step has been carried out by usage of artificial targets and/or control points. Several drawbacks are related to this strategy such as the enormous effort to distribute the targets in object space, the required survey by additional geodetic sensors such as total stations or GNSS-receivers as well as the limited extent within the region of interest. In this contribution a surface-based registration methodology, termed the iterative closest proximity algorithm (ICProx), that solely uses points as input, similar to the iterative closest point-algorithm (ICP), and hence does not require any artificial targets or extracted geometric primitives, such as planes. The aim of this study was to automatically determine deformations that occurred at a rock glacier, an ice glacier as well as in a rock fall area. For every example two epochs were processed while the ICProx-algorithm’s classification accuracy is 70 % on average.

Deformation analysis based on multi-temporal Terrestrial Laser Scanning (TLS) surveys has been applied for many years in commercial and academic problem domains. Downsides of this technique are the sequential data acquisition as well as its limited accuracy compared to terrestrial InSAR or InRAR based technologies that are currently gaining attention of the geodetic community. A drawback of these instruments is its relative operation method while beneficially measurements within the entire field of view can be carried out simultaneously at high frequencies. At first comparative studies between TLS and InRAR scanning are presented which have been carried out at a quarry. Over the course of roughly two hours six epochs have been measured where geometric changes of different degrees have been purposely made. In order to ensure comparability concerning the outcome, both instrument coordinate systems have been transformed into a common coordinate system by applying corner cube reflectors. At last an assisted ground based RADAR approach is presented where advantages of both applied techniques are incorporated.

Terrestrial laser scanning (TLS) can be seen as an established method for geodetic data acquisition. Advantageous is its high achievable accuracy as well as its rapid, active and laminar sampling of the object space. However, problems occur if an object, the scanner itself or both are moving which is referred to as kinematic TLS (k-TLS). The cause of this issue is the sequential scanning principle of TLS which causes temporal offsets between measured points and hence describes a distinctive feature to photometric approaches. Due to this temporal shift movements of the scanner or an object lead to geometric falsification during data acquisition. If, however, one can determine current orientation and position of an object or the scanner at any point of time by applying additional sensor technology, geometrically correct and kinematic data acquisition can be derived. The contribution at hand presents a multi sensor system which applies a terrestrial laser scanner for acquisition of an object’s surface. In addition three tracking total stations are applied that monitor the object’s orientation and position within the coordinate system of the TLS. Influencing factors onto the geometric correction are the accuracy of the applied total stations for determination of six degrees of freedom (6dof) as well as the temporal synchronisation. At first an introduction into the problem domain is exemplified on a simple case. The system is then tested on a 2.5 m long ship model inside a research facility as well as outdoors on a 12 m long vessel. For the sake of assessment the results have been compared to statically acquired scans of the test objects, outside of the water respectively in position of rest, in order to derive reference models.

Geodetic adjustment models are often set up in a way that the model parameters need to fulfil certain constraints. The normalized Lagrange multipliers have been used as a measure of the strength of constraint in such a way that if one of them exceeds in magnitude a certain threshold then the corresponding constraint is likely to be incompatible with the observations and the rest of the constraints. We show that these and similar measures can be deduced as test statistics of a likelihood ratio test of the statistical hypothesis that some constraints are incompatible in the same sense. This has been done before only for special constraints (Teunissen in Optimization and Design of Geodetic Networks, pp. 526–547, 1985). We start from the simplest case, that the full set of constraints is to be tested, and arrive at the advanced case, that each constraint is to be tested individually. Every test is worked out both for a known as well as for an unknown prior variance factor. The corresponding distributions under null and alternative hypotheses are derived. The theory is illustrated by the example of a double levelled line. Geodätische Ausgleichungsmodelle werden oft auf eine Weise formuliert, bei der die Modellparameter bestimmte Bedingungsgleichungen zu erfüllen haben. Die normierten Lagrange-Multiplikatoren wurden bisher als Maß für den ausgeübten Zwang verwendet, und zwar so, dass wenn einer von ihnen betragsmäßig eine bestimmte Schwelle übersteigt, dann ist davon auszugehen, dass die zugehörige Bedingungsgleichung nicht mit den Beobachtungen und den restlichen Bedingungsgleichungen kompatibel ist. Wir zeigen, dass diese und ähnliche Maße als Teststatistiken eines Likelihood-Quotiententests der statistischen Hypothese, dass einige Bedingungsgleichungen in diesem Sinne inkompatibel sind, abgeleitet werden können. Das wurde bisher nur für spezielle Bedingungsgleichungen getan (Teunissen in Optimization and Design of Geodetic Networks, pp. 526–547, 1985). Wir starten vom einfachsten Fall, dass die gesamte Menge der Bedingungsgleichungen getestet werden muss, und gelangen zu dem fortgeschrittenen Problem, dass jede Bedingungsgleichung individuell zu testen ist. Jeder Test wird sowohl für bekannte, wie auch für unbekannte a priori Varianzfaktoren ausgearbeitet. Die zugehörigen Verteilungen werden sowohl unter der Null- wie auch unter der Alternativhypthese abgeleitet. Die Theorie wird am Beispiel einer Doppelnivellementlinie illustriert.

Satellite deficiency degrades the performance of GPS single point positioning (SPP) in city urban areas. If the number of observed satellites is smaller than that of the unknown independent parameters in the data processing, extended Kalman filter (EKF) methods will usually be employed to transit the variable values epoch by epoch. In this case, the prediction model in EKF is very important for the positioning results. This paper focuses on the receiver clock offset models in the prediction equation. The investigation shows that, the clock offset model with clock shift is able to improve the accuracy of the clock offset prediction for internal crystal clocks within a short time span, compared with the clock offset model without clock shift. Besides, in order to further improve the performance of positioning in the case of satellite deficiency, an adaptive EKF is developed to enhance the clock prediction. The experiments show that this approach can improve the positioning accuracy in the scenarios that only fewer satellites are available.

The traditional way of solving non-linear least squares (LS) problems in Geodesy includes a linearization of the functional model and iterative solution of a nonlinear equation system. Direct solutions for a class of nonlinear adjustment problems have been presented by the mathematical community since the 1980s, based on total least squares (TLS) algorithms and involving the use of singular value decomposition (SVD). However, direct LS solutions for this class of problems have been developed in the past also by geodesists. In this contributionwe attempt to establish a systematic approach for direct solutions of non-linear LS problems from a "geodetic" point of view. Therefore, four non-linear adjustment problems are investigated: the fit of a straight line to given points in 2D and in 3D, the fit of a plane in 3D and the 2D symmetric similarity transformation of coordinates. For all these problems a direct LS solution is derived using the same methodology by transforming the problem to the solution of a quadratic or cubic algebraic equation. Furthermore, by applying TLS all these four problems can be transformed to solving the respective characteristic eigenvalue equations. It is demonstrated that the algebraic equations obtained in this way are identical with those resulting from the LS approach. As a by-product of this research two novel approaches are presented for the TLS solutions of fitting a straight line to 3D and the 2D similarity transformation of coordinates. The derived direct solutions of the four considered problems are illustrated on examples from the literature and also numerically compared to published iterative solutions.

In this contribution it is shown how an UAV system can be built at low costs. The components of the system, the equipment as well as the control software are presented. Furthermore an implemented programme for photogrammetric flight planning and its execution are described. The main focus of this contribution is on the generation of 3D point clouds from digital imagery. For this web services and free software solutions are presented which automatically generate 3D point clouds from arbitrary image configurations. Possibilities of georeferencing are described whereas the achieved accuracy has been determined. The presented workflow is finally used for the acquisition of 3D geodata. On the example of a landfill survey it is shown that marketable products can be derived using a low-cost UAV.

Zusammenfassung Die ständige Überwachung von Bauwerken gewinnt zunehmend an Bedeutung. Mit Blick auf die Nachhaltigkeit ist die Verlängerung der Nutzungsdauer bestehender baulicher Konstruktionen von unschätzbarem Wert, sowohl aus finanziellen Gründen als auch unter Denkmalaspekten. Eine neue Methode zur Detektion von Strukturschädigungen basiert auf einer integrierten Auswertung von Messwerten verschiedener Sensoren nach der Methode der kleinsten Quadrate sowie der Interpretation der dabei auftretenden Langrange-Multiplikatoren. Diese Methode der Schädigungsanalyse wird anhand eines numerischen Beispiels aus einem Vier-Punkt-Biegeversuch mit einem Verbundträger näher erläutert.

In this contribution it is shown that the so-called “total least-squares estimate” (TLS) within an errors-in-variables (EIV) model can be identified as a special case of the method of least-squares within the nonlinear Gauss–Helmert model. In contrast to the EIV-model, the nonlinear GH-model does not impose any restrictions on the form of functional relationship between the quantities involved in the model. Even more complex EIV-models, which require specific approaches like “generalized total least-squares” (GTLS) or “structured total least-squares” (STLS), can be treated as nonlinear GH-models without any serious problems. The example of a similarity transformation of planar coordinates shows that the “total least-squares solution” can be obtained easily from a rigorous evaluation of the Gauss–Helmert model. In contrast to weighted TLS, weights can then be introduced without further limitations. Using two numerical examples taken from the literature, these solutions are compared with those obtained from certain specialized TLS approaches.

The first UV-absorption band of the polar molecules trans-4-dimethylamino-4'-nitrostilbene (DMANS), 5-dimethylamino-5'-nitro-2,2'-bithiophene (DMANBT), and 4-nitroanisole (NA), and of the slightly polar pesticide diclofop-methyl in the nonpolar supercritical solvent carbon dioxide (CO2) and in the slightly polar supercritical solvent trifluoromethane (CHF3) was measured in the pressure range from 1.5 to 30 MPa and the temperature range from 298 to 353 K with the purpose of studying the solvent-solute interactions in these molecules. The theory of Liptay for the effect of the solvent on the wave number of the electronic absorption of the solute molecule was applied. In this theory the solvent is represented by an isotropic and homogeneous dielectric continuum characterized by a pressure and temperature dependent dielectric constant ε (P,T), and an optical refraction index n. For the isotherms which approach the critical point in both solvents there is a change in the slope of the plot of the wave number maximum against the solvent parameter g=(ε−1)/(2ε+1) which is reminiscent of complex formation. A possible mechanism for this phenomenon is the arrangement of the solvent molecules around the dilute solute in the intermediate region at the (continuous) transition of the solvent from the dense vapour to the supercritical fluid

GLONASS could hardly reach the positioning performance of GPS, especially for fast and real-time precise positioning. One of the reasons is the phase inter-frequency bias (IFB) at the receiver end prevents its integer ambiguity resolution. A number of studies were carried out to achieve the integer ambiguity resolution for GLONASS. Based on some of the revealed IFB characteristics, for instance IFB is a linear function of the received carrier frequency and L1 and L2 have the same IFB in unit of length, most of recent methods recommend estimating the IFB rate together with ambiguities. However, since the two sets of parameters are highly correlated, as demonstrated in previous studies, observations over several hours up to 1 day are needed even with simultaneous GPS observations to obtain a reasonable solution. Obviously, these approaches cannot be applied for real-time positioning. Actually, it can be demonstrated that GLONASS ambiguity resolution should also be available even for a single epoch if the IFB rate is precisely known. In addition, the closer the IFB rate value is to its true value, the larger the fixing RATIO will be. Based on this fact, in this paper, a new approach is developed to estimate the IFB rate by means of particle filtering with the likelihood function derived from RATIO. This approach is evaluated with several sets of experimental data. For both static and kinematic cases, the results show that IFB rates could be estimated precisely just with GLONASS data of a few epochs depending on the baseline length. The time cost with a normal PC can be controlled around 1 s and can be further reduced. With the estimated IFB rate, integer ambiguity resolution is available immediately and as a consequence, the positioning accuracy is improved significantly to the level of GPS fixed solution. Thus the new approach enables real-time precise applications of GLONASS.

A simple liquid solution model is proposed to describe the effect of solvent-solute interactions on the solubility of nonpolar and slightly polar substances in supercritical solvents. Treating the system as an ideal solution, the effect of pressure on the solubility is zero or nearly zero, as it is governed by the difference in molar volume of the pure supercooled liquid solute and the pure solid solute, and this may be nearly zero. Deviations from ideal behavior are given by activity coefficients of the Margules type with the interaction parameter w interpreted as interchange energy as in the lattice theory. The hypothesis is put forward that the interchange energy is of the same form as a function proposed by Liptay and others to describe the effect of the solvent on the wavelength of the absorption maximum of the solute dissolved in the solvent. The function consists of a radius of interaction a and a function g(ε ) of the dielectric constant ε of the solvent, treated as a continuum. The function g depends on pressure through the pressure dependence of the dielectric constant ε (P). The attractive feature of this formalism, introduced by Baumann et al. and here justified thermodynamically, is that plots of the logarithm of solubility vs. g are linear, except for polar solutes near the solvent’s critical point. Changes in slope then admit interpretation as changes in the radius of interaction a with possible clues about the mechanism of solvation of these molecules.

The use of open GIS standards offers a broad variety of potential, particularly in the field of data exchange, data storage, and interoperability. GML and CityGML are excellent examples for the ontological description of real world objects by means of an open standard whereas SensorML serves to describe measurements, sensors and measuring platforms. The use of such standards offers not only the possibility of using a common standardised language, but also the use of open service standards. The combination of spatial data and sensor standards in services and service-oriented architectures goes far beyond previous existing solutions on the market and provides a novel platform for monitoring structures. That in fact is far more than a simple data storage model. The methods and models presented in this contribution allow a direct integration of sensor data and its provision through an open standard language. In this case, all the intermediate steps at any time through an open service interface are addressed and may be made available and provided to different actors and stakeholders participating in a construction scenario. The great potential and the added value of such an information system is the permanent availability of measurement and object data and an associated integrated analysis of sensor data in combination with a finite element model (FEM). The automatic derivation of a finite element model from the 3D structure model, the visualisation of FEM, the provision of raw (measurement) data and sensor information for each time of measurement transform the platform into a universal tool in the field of structural monitoring. This contribution introduces the individual components, the standards used and the interaction between the components to an overall system.