Piroska Zaletnyik

Algebraic Geodesy and Geoinformatics

While preparing and teaching Introduction to Geodesy I and II to undergraduate students at Stuttgart University, we noticed a gap which motivated the writing of the present book: Almost every topic that we taught required some skills in algebra, and in particular, computer algebra! From positioning to transformation problems inherent in geodesy and geoinformatics, knowledge of algebra and application of computer algebra software were required. In preparing this book therefore, we have attempted to put together basic concepts of abstract algebra which underpin the techniques for solving algebraic problems. Algebraic computational algorithms useful for solving problems which require exact solutions to nonlinear systems of equations are presented and tested on various problems. Though the present book focuses mainly on the two ?elds, the concepts and techniques presented herein are nonetheless applicable to other ?elds where algebraic computational problems might be encountered. In Engineering for example, network densi?cation and robotics apply resection and intersection techniques which require algebraic solutions. Solution of nonlinear systems of equations is an indispensable task in almost all geosciences such as geodesy, geoinformatics, geophysics (just to mention but a few) as well as robotics. These equations which require exact solutions underpin the operations of ranging, resection, intersection and other techniques that are normally used. Examples of problems that require exact solutions include; three-dimensional resection problem for determining positions and orientation of sensors, e. g. , camera, theodolites, robots, scanners etc.

Crustal Velocity Field Modelling with Neural Network and Polynomials

A comparison of the ability of artificial neural networks and polynomial fitting was carried out in order to model the horizontal deformation field of the Cascadia Subduction Zone, as determined from GPS analyses of the Pacific Northwest Geodetic Array (PANGA).

Sparse representation of full waveform lidar data

Full Waveform Data (FWD) has been increasingly becoming available on modern airborne LiDAR systems. Since the waveform signal is noisy and rather sparse by nature, the compressed FWD representation has several advantages. First, the reduced data volume makes the storage and transmission of waveform data faster and more economic. Second, the sparse representation based on proper feature space selection may potentially support the subsequent waveform interpretation and classification processes. Note that discrete return data represent the most basic compressed waveform representation. This study addresses some aspects of FWD compression. First, the wavelet family selection for FWD compression is analyzed, including compression ratio, average/maximum reconstruction errors. Next wavelet filter optimization with respect to typical FWD is investigated. Finally, the performance potential of compressive sampling is assessed along with a brief insight into wavelet representation based waveform classification.

Combination of GPS/leveling and the gravimetric geoid by using the thin plate spline interpolation technique via finite element method

Abstract The purpose of this paper is to develop an improved local geoid model for Hungary combining GPS and leveling height data with a local gravimetric geoid model, via corrector surface, which accounts for datum inconsistencies, long-wavelength geoid errors and vertical network distortions. The improved model is the so-called GPS-gravimetric geoid, which can be constructed by adding the corrector surface to the original gravimetric geoid. The corrector surface can be represented by means of a Thin Plate Spline Interpolation (TPSI) and finite element solution. In this work 194 GPS/leveling points with a local gravimetric geoid were used to calculate the corrector surface and the combined geoid model. To estimate the realistic error of the solution 110 GPS/ leveling points were used as external control points. Attention is called to the importance of the homogeneous distribution of the GPS/leveling data. The mean accuracy of geoid heights of the used 110 control stations was 1–2 cm after the surface fitting.

Application of Computer Algebra System to Geodesy

This contribution extends the previous work of (2005). Using Groebner basis and Dixon resultant as the engine behind Computer Algebra Systems (CAS). The authors demonstrate how 3D GPS positioning, 3D intersection, as well as datum transformation problems are solved ‘live’ in Mathematica, thanks to modernization in CAS. Mathematica notebooks containing these ‘live’ computational models and examples are available at http://library.wolfram.com/infocenter/ MathSource/6654

Positioning by Intersection Methods

The similarity between resection methods presented in the previous chapter and intersection methods discussed herein is their application of angular observations. The distinction between the two however, is that for resection, the unknown station is occupied while for intersection, the unknown station is observed. Resection uses measuring devices (e.g., theodolite, total station, camera etc.) which occupy the unknown station. Angular (direction) observations are then measured to three or more known stations as we saw in the preceding chapter. Intersection approach on the contrary measures angular (direction) observations to the unknown station; with the measuring device occupying each of the three or more known stations. It has the advantage of being able to position an unknown station which can not be physically occupied. Such cases are encountered for instance during engineering constructions or cadastral surveying. During civil engineering construction for example, it may occur that a station can not be occupied because of swampiness or risk of sinking ground. In such a case, intersection approach can be used. The method is also widely applicable in photogrammetry. In aero-triangulation process, simultaneous resection and intersection are carried out where common rays from two or more overlapping photographs intersect at a common ground point (see e.g., Fig. 12.1).

Positioning by ranging

Throughout history, position determination has been one of the fundamental task undertaken by man on daily basis. Each day, one has to know where one is, and where one is going. To mountaineers, pilots, sailors etc., the knowledge of position is of great importance. The traditional way of locating one’s position has been the use of maps or campus to determine directions. In modern times, the entry into the game by Global Navigation Satellite Systems GNSS that comprise the Global Positioning System (GPS) , Russian based GLONASS and the proposed European’s GALILEO have revolutionized the art of positioning.