The determination of potential difference by the joint application of measured and synthetical gravity data: a case study in Hungary

In an elementary approach every geometrical height difference between the staff points of a levelling line should have a corresponding average g value for the determination of potential difference in the Earth’s gravity field. In practice this condition requires as many gravity data as the number of staff points if linear variation of g is assumed between them. Because of the expensive fieldwork, the necessary data should be supplied from different sources. This study proposes an alternative solution, which is proved at a test bed located in the Mecsek Mountains, Southwest Hungary, where a detailed gravity survey, as dense as the staff point density (~1 point/34 m), is available along a 4.3-km-long levelling line. In the first part of the paper the effect of point density of gravity data on the accuracy of potential difference is investigated. The average g value is simply derived from two neighbouring g measurements along the levelling line, which are incrementally decimated in the consecutive turns of processing. The results show that the error of the potential difference between the endpoints of the line exceeds 0.1 mm in terms of length unit if the sampling distance is greater than 2 km. Thereafter, a suitable method for the densification of the decimated g measurements is provided. It is based on forward gravity modelling utilising a high-resolution digital terrain model, the normal gravity and the complete Bouguer anomalies. The test shows that the error is only in the order of 10⁻³mm even if the sampling distance of g measurements is 4 km. As a component of the error sources of levelling, the ambiguity of the levelled height difference which is the Euclidean distance between the inclined equipotential surfaces is also investigated. Although its effect accumulated along the test line is almost zero, it reaches 0.15 mm in a 1-km-long intermediate section of the line.     

Mental maps and travel behaviour: meanings and models

In this paper, the “mental map” concept is positioned with regard to individual travel behaviour to start with. Based on Ogden and Richards’ triangle of meaning (The meaning of meaning: a study of the influence of language upon thought and of the science of symbolism. International library of psychology, philosophy and scientific method. Routledge and Kegan Paul, London, 1966) distinct thoughts, referents and symbols originating from different scientific disciplines are identified and explained in order to clear up the notion’s fuzziness. Next, the use of this concept in two major areas of research relevant to travel demand modelling is indicated and discussed in detail: spatial cognition and decision-making. The relevance of these constructs to understand and model individual travel behaviour is explained and current research efforts to implement these concepts in travel demand models are addressed. Furthermore, these mental map notions are specified in two types of computational models, i.e. a Bayesian Inference Network (BIN) and a Fuzzy Cognitive Map (FCM). Both models are explained, and a numerical and a real-life example are provided. Both approaches yield a detailed quantitative representation of the mental map of decision-making problems in travel behaviour.     

A note on frame transformations with applications to geodetic datums

Rigorous equations in compact symbolic matrix notation are introduced to transform coordinates and velocities between ITRF frames and modern GPS-based geocentric geodetic datums. The theory is general but, after neglecting higher than second-order terms, it is shown that the equations revert to the formulation currently applied in most major continental datums. We discuss several examples: the North American Datum of 1983 (NAD83), the European Terrestrial Reference System of 1989 (ETRS89), the Geodetic Datum of Australia of 1994 (GDA94), and the South American Geocentric Reference System (SIRGAS). Electronic Publication     

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.     

Multifrequency algorithms for precise point positioning: MAP3

We present the new MAP3 algorithms to perform static precise point positioning (PPP) from multifrequency and multisystem GNSS observations. MAP3 represents a two-step strategy in which the least squares theory is applied twice to estimate smoothed pseudo-distances, initial phase ambiguities, and slant ionospheric delay first, and the absolute receiver position and its clock offset in a second adjustment. Unlike the classic PPP technique, in our new approach, the ionospheric-free linear combination is not used. The combination of signals from different satellite systems is accomplished by taking into account the receiver inter-system bias. MAP3 has been implemented in MATLAB and integrated within a complete PPP software developed on site and named PCube. We test the MAP3 performance numerically and contrast it with other external PPP programs. In general, MAP3 positioning accuracy with low-noise GPS dual-frequency observations is about 2.5 cm in 2-h observation periods, 1 cm in 10 h, and 7 mm after 1 day. This means an improvement in the accuracy in short observation periods of at least 7 mm with respect to the other PPP programs. The MAP3 convergence time is also analyzed and some results obtained from real triple-frequency GPS and GIOVE observations are presented.     

From data to decision-making – experiences in Integrated Earth Observation (IEO)

Within the confines of Earth Observation Scientific Knowledge and Technology Transfer in Hungary (EKAT) titled ESA PECS project we gained forum for utilization of our earth observation (EO) knowledge and possibility for further development of experiences. The project aims the horizontal preparation of Hungary for ESA membership – for a dynamically developing sphere in the common part of science, technology and business. For the efficient transfer and dissemination, we preconceived target groups and principles to reach main take-up points and to open new forums of information exchange. Nowadays, user-friendly service, complex supply and real-validation process all have great importance. Joining units of suitable data choice, entire ingestion–processing chains and ergonomic interfaces can only offer a timely and professional solution for the challenges of industry and business sectors. It has to be clearly seen, that information and communication technologies (ICT) and information control becomes a more and more significant part of EO services.     

Spin rate estimation of sounding rockets using GPS wind-up

Carrier phase wind-up is a well-known effect that arises from the relative rotation between a transmitting and receiving antenna. In GPS measurements at L1 frequency, this effect translates into an error of 19.029 cm per full relative rotation of antennas. Since this effect is independent of the satellite elevation for pure rotation about the antenna boresight axis, it is usually absorbed by the clock estimation in navigation algorithms. Therefore, the impact of wind-up is usually neglected for applications that do not require accuracies to the cm level like RTK. However, in receiving platforms with high rotation rate, the accumulated wind-up value can be important and actually be larger than receiver noise or even ionospheric variations. Therefore, in such scenarios, the wind-up contribution can be isolated and used as a source of information to compute the spin rate of such platforms using an appropriate combination of GPS observables. This work shows some results of a coarse, yet simple, approach to monitor the rotation angle and spin-rate of spin stabilized sounding rockets flown by DLR.     

Affine distortion of small GPS networks with large height differences

GPS is a promising tool for real-time monitoring of deformations of slopes or large structures. However, remaining systematic effects in GPS phase observations after double differencing and application of a priori models affect the resulting coordinates. They complicate the proper separation of the actual deformations from pseudo-deformations induced by the systematic effects. This paper shows that for small monitoring networks (baseline lengths <5 km) only affine distortions of the network geometry are generated by the remaining distance dependent systematic effects, e.g. unmodelled tropospheric and ionospheric propagation effects, or satellite orbit errors. Hence, a generic correction model is given by a three-dimensional affine transformation involving a maximum of 12 transformation parameters. For the determination of these parameters, four high quality GPS stations are necessary which are not affected by the actual deformations to be monitored. Based on the analysis of network geometries of synthetic GPS networks with large height differences and considering the physics of the GPS observations it is shown, however, that less than 12 parameters are sufficient for the computation of the corrections. The proposed 8 parameter model was applied to the GPS monitoring network of the Gradenbach landslide. For this small network with large height differences, it was shown that the distortions can be reduced by about 75%.