Piroska Zaletnyik

Budapest University of Technology and Economics · Department of Geodesy and Surveying

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...

Today's advanced LiDAR systems are able to record the entire laser echo pulse, provided that sufficient data storage is available on the airborne platform. The recorded echo pulses, frequently called waveform data or full-waveform, can then be used to analyze the properties of the reflecting surface, such as classifying objects based on their mater...

We demonstrate a symbolic elimination technique to solve a nine-parameter 3D affine transformation when only three known points in both systems are given. The system of nine equations is reduced to six by subtracting the equations and eliminating the translation parameters. From these six equations, five variables are eliminated using a Gröbner bas...

Full waveform recording is becoming increasingly affordable and, consequently, available in today's state-of-the-art LiDAR systems. Therefore, there is no practical limitation to the complexity of pulse detection and other methods that can be applied in post-processing mode. Analyzing the entire return signal, the full waveform can provide addition...

The Procrustes method is a very effective method for determining the Helmert's datum transformation parameters since it requires neither initial starting values nor iteration. Due to these attractive attributes, the ABC-Procrustes algorithm is extended to solve the 3D affine transformation problem where scale factors are different in the 3 principa...

A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods...

In Chap. 7, we have seen that overdetermined nonlinear systems are common in geodetic and geoinformatic applications, that is there are frequently more measurements than it is necessary to determine unknown variables, consequently the number of the variables n is less then the number of the equations m. Mathematically, a solution for such systems c...

In establishing a proper reference frame of geodetic point positioning, namely by the Global Positioning System (GPS) - the Global Problem Solver - we are in need to establish a proper model for the Topography of the Earth, the Moon, the Sun or planets.By the theory of equilibrium figures, we are informed that an ellipsoid, two-axes or three-axes i...

The 7-parameter datum transformation \({\mathbb C}_{7}(3)\) problem involves the determination of seven parameters required to transform coordinates from one system to another. The transformation of coordinates is a computational procedure that maps one set of coordinates in a given system onto another. This is achieved by translating the given sys...

Since the advent of the Global Navigation Satellite System (GNSS) , in particular the Global Positioning System (GPS), many fields within geosciences, such as geodesy, geoinformatics, geophysics, hydrology etc., have undergone tremendous changes. GPS satellites have in fact revolutionized operations in these fields and the entire world in ways th...

In Chap. 7, we introduced parameter estimation from observational data sample and defined the models applicable to linear and nonlinear cases.

In Chap. 12, ranging method for positioning was presented where distances were measured to known targets. In this chapter, an alternative positioning technique which uses direction measurements as opposed to distances is presented. This positioning approach is known as the resection. Unlike in ranging where measured distances are affected by atmosp...

This chapter presents you the reader with one of the most powerful computer algebra tools, besides the polynomial resultants (discussed in the next chapter), for solving nonlinear systems of equations which you may encounter. The basic tools that you will require to develop your own algorithms for solving problems requiring closed form (exact) solu...

In 1997, the Kyoto protocol to the United Nation’s framework convention on climate change spelt out measures that were to be taken to reduce the greenhouse gas emission that has contributed to global warming . Global warming is just but one of the many challenges facing our environment today. The rapid increase in desertification on one hand and fl...

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 t...

This chapter presents the concepts of ring theory from a geodetic and geoinformatics perspective. The presentation is such that the mathematical formulations are augmented with examples from the two fields. Ring theory forms the basis upon which polynomial rings operate. As we shall see later, exact solution of nonlinear systems of equations are pi...

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 (...

In geodesy and geoinformatics, field observations are normally collected with the aim of estimating parameters. Very frequently, one has to handle overdetermined systems of nonlinear equations. In such cases, there exist more equations than unknowns, therefore “the solution” of the system can be interpreted only in least squares sense. In geodynami...

A fundamental task in geodesy is the solving of systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to the convergence to solutions with no physical meaning, or convergence that requires global...

In geodesy and geoinformatics, most observations are related to unknowns parameters through equations of algebraic (polynomial) type. In cases where the observations are not of polynomial type, as exemplified by the GPS meteorology problem of Chap. 15, they are converted via Theorem3.1 on p. 19 into polynomials. The unknown parameters are then be o...

Besides Groebner basis approach discussed in Chap. 4, the other powerful algebraic tools for solving nonlinear systems of equations are the polynomial resultants approaches. While Groebner basis may require large storage capacity during its computations, polynomial resultants approaches presented herein offers remedy to users who may not be lucky t...

This chapter presents the minimization approach known as “Procrustes” which falls within the multidimensional scaling techniques discussed in Sect. 9-22. Procrustes analysis is the technique of matching one configuration into another in-order to produce a measure of match. In adjustment terms, the partial Procrustes problem is formulated as the lea...

The book presents modern and efficient methods for solving Geodetic and Geoinformatics algebraic problems. Numerous examples are illustrated with Mathematica using the computer algebra techniques of Ring, Polynomials, Groebner basis, Resultants (including Dixon resultants), Gauss-Jacobi combinatorial and Procrustes algorithms, as well as homotopy m...

Given sufficient data storage capacity, today's full-waveform LiDAR systems are able to record and store the entire laser pulse echo signal. This provides the possibility of further analyzing the physical characteristics of the reflecting objects. However the size of the captured data is enormous and currently not practical. Thus arises the need fo...

The Dixon resultant is proposed as an alternative to Gröbner basis or multipolynomial resultant approaches for solving systems of polynomial equations inherent in geodesy. Its smallness in size, high density (ratio on the number of nonzero elements to the number of all elements), speed, and robustness (insensitive to combinatorial sequence and mono...

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 contain...

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). One set of data was used to calculate the unknown parameters of the model (training set...

Support vector machines (SVM) with wavelet kernel has been applied to the correcting gravimetric geoid using GPS/levelling data. These data were divided into a training and a validation set in order to ensure the extendability of the approximation of the corrector surface. The optimal parameters of the SVM were considered as a trade-off between acc...

Linear homotopy solution is given for GPS N-point navigation problem. The overdetermined polynomial system has been solved without initial guessed value using natural start system resulting real solutions. In geometric terms, the homotopy H provides us a continuous deformation from p(x) - which is obtained for λ = 0 by H(x, 0) - to q(x) - which is...

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, whic...

The efficiency of the application of soft computing methods like Artificial Neural Networks (ANN) or Support Vector Machines (SVM) depends considerably on the representativeness of the learning sample set employed for training the model. In this study a simple method based on the Coefficient of Representativity (CR) is proposed for extracting repre...

For global data representation, like the approximation of a surface, algebraic or trigonometric polynomials may be used. However, polynomial approaches are limited concerning their accuracy. In the last decade neural networks were applied very successfully in many fields of data mining and representation. In this research sequence of neural network...

In case of considerable nonlinearity e.g. in geodesy, photogrammetry, robotics, it is difficult to find proper initial values to solve the parameter estimation problem of 3D affine transformation with 9 parameters via linearization and/or iteration. In this paper we develop a symbolic - numeric method to achieve the solution without initial guess....

Peak detection from full-waveform LiDAR data – Most airborne LiDAR systems extract the return pulses and intensity signal during data acquisition in real-time, which information is then logged. As full waveform recording is becoming increasingly affordable and consequently available on today's state-of-the-art LiDAR systems, there is no practical l...

A vizsgálatainkat a magyarországi geoidmeghatározás, a geoidfelület interpoláció, továbbá a GOCE gradiométeres műhold jövőbeni méréseinek felhasználása főbb területein végeztük. Elvégeztük a kombinált geoidmegoldáshoz felhasználható adatok gyűjtését és rendszerezését, adatbázisba vitelét és az adatok vizsgálatát. Megfelelő számítási eljárásokat dol...