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Helmert Transformation
The Helmert transformation (named after Friedrich Robert Helmert, 1843–1917) is a geometric transformation method within a three-dimensional space. It is frequently used in geodesy to produce datum transformations between datums. The Helmert transformation is also called a seven-parameter transformation and is a similarity transformation. Definition It can be expressed as: : X_T = C + \mu R X \, where * is the transformed vector * is the initial vector The parameters are: * – translation vector. Contains the three translations along the coordinate axes * – scale factor, which is unitless; if it is given in ppm, it must be divided by 1,000,000 and added to 1. * – rotation matrix. Consists of three axes (small rotations around each of the three coordinate axes) , , . The rotation matrix is an orthogonal matrix. The angles are given in either degrees or radians. Variations A special case is the two-dimensional Helmert transformation. Here, only f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmert (seven-parameter) Transformation
Friedrich Robert Helmert (31 July 1843 – 15 June 1917) was a German geodesist and statistician with important contributions to the theory of errors. Career Helmert was born in Freiberg, Kingdom of Saxony. After schooling in Freiberg and Dresden, he entered the Polytechnische Schule, now Technische Universität, in Dresden to study engineering science in 1859. Finding him especially enthusiastic about geodesy, one of his teachers, , hired him while still a student to work on the of the Ore Mountains and the drafting of the trigonometric network for Saxony. In 1863 Helmert became Nagel's assistant on the . After a year's study of mathematics and astronomy Helmert obtained his doctor's degree from the University of Leipzig in 1867 for a thesis based on his work for Nagel. In 1870 Helmert became instructor and in 1872 professor at RWTH Aachen, the new Technical University in Aachen. At Aachen he wrote ''Die mathematischen und physikalischen Theorieen der höheren Geodäsie' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photography
Photography is the visual arts, art, application, and practice of creating images by recording light, either electronically by means of an image sensor, or chemically by means of a light-sensitive material such as photographic film. It is employed in many fields of science, manufacturing (e.g., photolithography), and business, as well as its more direct uses for art, film and video production, recreational purposes, hobby, and mass communication. A person who operates a camera to capture or take Photograph, photographs is called a photographer, while the captured image, also known as a photograph, is the result produced by the camera. Typically, a lens is used to focus (optics), focus the light reflected or emitted from objects into a real image on the light-sensitive surface inside a camera during a timed Exposure (photography), exposure. With an electronic image sensor, this produces an Charge-coupled device, electrical charge at each pixel, which is Image processing, electro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arcsecond
A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of a degree. Since one degree is of a turn, or complete rotation, one arcminute is of a turn. The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth's circumference is very near . A minute of arc is of a radian. A second of arc, arcsecond (abbreviated as arcsec), or arc second, denoted by the symbol , is a unit of angular measurement equal to of a minute of arc, of a degree, of a turn, and (about ) of a radian. These units originated in Babylonian astronomy as sexagesimal (base 60) subdivisions of the degree; they are used in fields that involve very small angles, such as astronomy, optometry, ophthalmology, optics, navigation, land surveying, and marksmanship. To express even smaller angles, standard SI prefixes can be employed; the milliarcse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Squares
The method of least squares is a mathematical optimization technique that aims to determine the best fit function by minimizing the sum of the squares of the differences between the observed values and the predicted values of the model. The method is widely used in areas such as regression analysis, curve fitting and data modeling. The least squares method can be categorized into linear and nonlinear forms, depending on the relationship between the model parameters and the observed data. The method was first proposed by Adrien-Marie Legendre in 1805 and further developed by Carl Friedrich Gauss. History Founding The method of least squares grew out of the fields of astronomy and geodesy, as scientists and mathematicians sought to provide solutions to the challenges of navigating the Earth's oceans during the Age of Discovery. The accurate description of the behavior of celestial bodies was the key to enabling ships to sail in open seas, where sailors could no longer rely on la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Squares Adjustment
Least-squares adjustment is a model for the solution of an overdetermined system of equations based on the principle of least squares of observation residuals. It is used extensively in the disciplines of surveying, geodesy, and photogrammetry—the field of geomatics, collectively. Formulation There are three forms of least squares adjustment: ''parametric'', ''conditional'', and ''combined'': * In parametric adjustment, one can find an observation equation relating observations explicitly in terms of parameters (leading to the A-model below). * In conditional adjustment, there exists a condition equation which is involving only observations (leading to the B-model below) — with no parameters at all. * Finally, in a combined adjustment, both parameters and observations are involved implicitly in a mixed-model equation . Clearly, parametric and conditional adjustments correspond to the more general combined case when and , respectively. Yet the special cases warrant simp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reference Ellipsoid
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is a spheroid (an ellipsoid of revolution) whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation. The ellipsoid is defined by the ''equatorial axis'' () and the ''polar axis'' (); their radial difference is slightly more than 21 km, or 0.335% of (which is not quite 6,400 km). Many methods exist for determination of the axes of an Earth ellipsoid, ranging from meridian arcs up to modern satellite geodesy or the analysis and interconnection of continental geodetic networks. Amongst the different set of data used in national surveys are several of special importance: the Bessel ellipsoid of 1841, the international Hayfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geocentric Coordinates
The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as ''X'', ''Y'', and ''Z'' measurements from its center of mass. Its most common use is in tracking the orbits of satellites and in satellite navigation systems for measuring locations on the surface of the Earth, but it is also used in applications such as tracking crustal motion. The distance from a given point of interest to the center of Earth is called the geocentric distance, , which is a generalization of the ''geocentric radius'', , not restricted to points on the reference ellipsoid surface. The geocentric altitude is a type of altitude defined as the difference between the two aforementioned quantities: ; it is not to be confused for the '' geodetic altitude''. Conversions between ECEF ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodetic Coordinates
Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a '' reference ellipsoid''. They include geodetic latitude (north/south) , ''longitude'' (east/west) , and ellipsoidal height (also known as geodetic height). The triad is also known as Earth ellipsoidal coordinates (not to be confused with '' ellipsoidal-harmonic coordinates''). Definitions Longitude measures the rotational angle between the zero meridian and the measured point. By convention for the Earth, Moon and Sun, it is expressed in degrees ranging from −180° to +180°. For other bodies a range of 0° to 360° is used. For this purpose, it is necessary to identify a ''zero meridian'', which for Earth is usually the Prime Meridian. For other bodies a fixed surface feature is usually referenced, which for Mars is the meridian passing through the crater Airy-0. It is possible for many different coordinate systems to be defined upon the same reference ellipsoid. Geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map Projection
In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections. More generally, proje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauss–Krüger Coordinate System
The transverse Mercator map projection (TM, TMP) is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the Universal Transverse Mercator coordinate system, Universal Transverse Mercator. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent. Standard and transverse aspects The transverse Mercator projection is the map projection#Aspect of the projection, transverse aspect of the standard (or ''Normal'') Mercator projection. They share the same underlying mathematical construction and consequently the transverse Mercator inherits many traits from the normal Mercator: * Both map projection, projections are map projection#Cylindrical, cylindrical: for the normal Mercator, the axis of the cylinder coincides with the polar axis and the line of tangency with the equator. For the transver ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Positioning System
The Global Positioning System (GPS) is a satellite-based hyperbolic navigation system owned by the United States Space Force and operated by Mission Delta 31. It is one of the global navigation satellite systems (GNSS) that provide geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites. It does not require the user to transmit any data, and operates independently of any telephone or Internet reception, though these technologies can enhance the usefulness of the GPS positioning information. It provides critical positioning capabilities to military, civil, and commercial users around the world. Although the United States government created, controls, and maintains the GPS system, it is freely accessible to anyone with a GPS receiver. Overview The GPS project was started by the U.S. Department of Defense in 1973. The first prototype spacecraft was launched in 1978 an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
WGS84
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM). The standard is published and maintained by the United States National Geospatial-Intelligence Agency. History Efforts to supplement the various national surveying systems began in the 19th century with F.R. Helmert's book (''Mathematical and Physical Theories of Physical Geodesy''). Austria and Germany founded the (Central Bureau of International Geodesy), and a series of global ellipsoids of the Earth were derived (e.g., Helmert 1906, Hayford 1910 and 1924). A unified geodetic system for the whole world became essential in the 1950s for several reasons: * International space science and the beginning of astronautics. * The lack of inter-continental ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
