Lecture

Orientation Calculation in Geomatics

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In course

ENV-140: Fundamentals of geomatics

Bases de la géomatique pour les ingénieur·e·s civil et en environnement. Présentation des méthodes d'acquisition, de gestion et de représentation des géodonnées. Apprentissage pratique avec des méthodes topométriques et d'imagerie du territoire. ...

Description

This lecture covers the process of determining the orientation of a station using a theodolite in geomatics. It explains how to calculate the bearing between the station and a known point, set up the theodolite, and use geomatics elements. Numerical examples are provided to illustrate the orientation calculation, emphasizing the importance of having at least two fixed points for accurate results. The lecture also discusses the significance of making multiple determinations and direction measures to detect faults and ensure precision in the orientation process.

Instructors (2)

Pierre-Yves Gilliéron

He graduated in Surveying Engineering at the Swiss Federal Institute of Technology Lausanne in 1988. He started his professional career in photogrammetry and digital mapping. He joined the Geodetic Eng. Laboratory in 1997 where he worked as research scientist on various navigation and satellite positioning projects. Since 2018 he is deputy head of the section in environmental sciences and engineering at EPFL. -- He was member of the board of the swiss institute of navigation (ION-CH), member of the swiss geodetic committee (SGK) and expert in different committees of the swiss road association (VSS).

Devis Tuia

I come from Ticino and studied in Lausanne, between UNIL and EPFL. After my PhD at UNIL in remote sensing, I was postdoc in Valencia (Spain), Boulder (CO) and EPFL, working on model adaptation and prior knowledge integration in machine learning. In 2014 I became Research Assistant Professor at University of Zurich, where I started the 'multimodal remote sensing' group. In 2017, I joined Wageningen University (NL), where I was professor of the GeoInformation Science and Remote Sensing Laboratory. Since 2020, I joined EPFL Valais, to start the ECEO lab, working at the interface between Earth observation, machine learning and environmental sciences.

Official source

Related concepts (10)

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Fixed point (mathematics)

hatnote|1=Fixed points in mathematics are not to be confused with other uses of "fixed point", or stationary points where math|1=f(x) = 0. In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically for functions, a fixed point is an element that is mapped to itself by the function. Formally, c is a fixed point of a function f if c belongs to both the domain and the codomain of f, and f(c) = c.

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

Fixed-point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

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