Frame transformation and geoid undulation transfer to GNSS real time positions through the new RTCM 3.1 transformation messages

Radio Technical Commission for Marine Services (RTCM) standardised messages play an important role in real time Global Navigation Satellite Systems (GNSS) applications such as navigation, positioning, civil engineering, surveying, and cartographic or cadastral production. One of the latest agreements on RTCM definitions contains the data fields for real time geodetic reference frame transformation and orthometric heights computation by received geoid undulations via internet protocol. These parameters can be generated dynamically by a GNSS data centre in a network of reference stations, encapsulated in RTCM messages and broadcasted to the rover location so they are centrally administered and the same frame transformations and geoid model are available to every user in the field, obtaining results in a local reference frame in real time. This paper summarises the functionality of the new RTCM 3?1 transformation messages, describes limitations and provides ideas about the possible use for solving specific problems. Test field campaigns are used to describe the real performance and usefulness of these new RTCM 3?1 messagesCapilla Roma, R.; Martín Furones, ÁE.; Anquela Julián, AB.; Berné Valero, JL. (2012). Frame transformation and geoid undulation transfer to GNSS real time positions through the new RTCM 3.1 transformation messages. Survey Review. 44(324):30-36. doi:10.1179/1752270611Y.0000000010S303644324Benciolini, B., Biagi, L., Crespi, M., Manzino, A. M., & Roggero, M. (2008). Reference frames for GNSS positioning services: Some problems and proposed solutions. Journal of Applied Geodesy, 2(1). doi:10.1515/jag.2008.006González-Matesanz, J., Dalda, A., & Malpica, J. A. (2006). A RANGE OF ED50-ETRS89 DATUM TRANSFORMATION MODELS TESTED ON THE SPANISH GEODETIC NETWORK. Survey Review, 38(302), 654-667. doi:10.1179/sre.2006.38.302.654Soler, T., & Marshall, J. (2003). A note on frame transformations with applications to geodetic datums. GPS Solutions, 7(2), 148-149. doi:10.1007/s10291-003-0063-

Linear Paul trap design for an optical clock with Coulomb crystals

We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10^-18, we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of the ions at a level at which the corresponding second- order Doppler shift contributes less than 10^-18 to the relative uncertainty of the frequency standard

Error sources and data limitations for the prediction ofsurface gravity: a case study using benchmarks

Gravity-based heights require gravity values at levelled benchmarks (BMs), whichsometimes have to be predicted from surrounding observations. We use EGM2008 andthe Australian National Gravity Database (ANGD) as examples of model and terrestrialobserved data respectively to predict gravity at Australian national levelling network(ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BMgravity values and then into gravimetric height corrections (HCs). Our results indicatethat an approximate ±1 arc-minute horizontal position error of the BMs causesmaximum errors in EGM2008 BM gravity of ~ 22 mGal (~55 mm in the HC at ~2200 melevation) and ~18 mGal for ANGD BM gravity because the values are not computed atthe true location of the BM. We use RTM (residual terrain modelling) techniques toshow that ~50% of EGM2008 BM gravity error in a moderately mountainous regioncan be accounted for by signal omission. Non-representative sampling of ANGDgravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmertorthometric correction at ~2200 m elevation). For modelled gravity at BMs to beviable, levelling networks need horizontal BM positions accurate to a few metres, whileRTM techniques can be used to reduce signal omission error. Unrepresentative gravitysampling in mountains can be remedied by denser and more representative re-surveys,and/or gravity can be forward modelled into regions of sparser gravity

The computation of the geoid model in the state of São Paulo using two methodologies and GOCE models

The purpose of this manuscript is to compute and to evaluate the geoid model in the State of São Paulo from two methodologies (Stokes' integral through the Fast Fourier Transform - FFT and Least Squares Collocation - LSC). Another objective of this study is to verify the potentiality of GOCE-based. A special attention is given to GOCE mission. The theory related to Stokes' integral and Least Squares Collocation is also discussed in this work. The spectral decomposition was employed in the geoid models computation and the long wavelength component was represented by EGM2008 up to degree and order 150 and 360 and GOCE-based models up to 150. The models were compared in terms of geoid height residual and absolute and relative comparisons from GPS/leveling and the results show consistency between them. In addition, a comparison in the mountain regions was carried out to verify the methodologies behavior in this area; the results showed that LSC is less consistent than FFT

Geoid Determination: Theory and Methods

Il testo sviluppa con completezza gli argomenti classici e moderni relativi alla determinazione del geoide in geodesia fisica. Il testo è diviso in tre parti, dai titoli "Theory", "Methods and Applications" e "Advanced Analysis Methods". Fernando Sansò è autore della prima (da pag.3 a pag. 256) e della terza parte (da pag. 547 a pag. 704)