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class="mw-redirect" title="Reference ellipsoid">Reference ellipsoid</a></li> <li><a href="/wiki/Satellite_geodesy" title="Satellite geodesy">Satellite geodesy</a></li> <li><a href="/wiki/Spatial_reference_system" title="Spatial reference system">Spatial reference system</a></li> <li><a href="/wiki/Spatial_relation" title="Spatial relation">Spatial relations</a></li> <li><a href="/wiki/Vertical_position" title="Vertical position">Vertical positions</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)">Technologies</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Satellite_navigation" title="Satellite navigation">Global Nav. Sat. Systems (GNSSs)</a></li> <li><a href="/wiki/Global_Positioning_System" title="Global Positioning System">Global Pos. System (GPS)</a></li> <li><a href="/wiki/GLONASS" title="GLONASS">GLONASS <span style="font-size:85%;">(Russia)</span></a></li> <li><a href="/wiki/BeiDou" title="BeiDou">BeiDou (BDS) <span style="font-size:85%;">(China)</span></a></li> <li><a href="/wiki/Galileo_(satellite_navigation)" title="Galileo (satellite navigation)">Galileo <span style="font-size:85%;">(Europe)</span></a></li> <li><a href="/wiki/Indian_Regional_Navigation_Satellite_System" title="Indian Regional Navigation Satellite System">NAVIC <span style="font-size:85%;">(India)</span></a></li> <li><a href="/wiki/Quasi-Zenith_Satellite_System" title="Quasi-Zenith Satellite System">Quasi-Zenith Sat. Sys. (QZSS) <span style="font-size:85%;">(Japan)</span></a></li> <li><a href="/wiki/Discrete_Global_Grid" class="mw-redirect" title="Discrete Global Grid">Discrete Global Grid and Geocoding</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed plainlist"><div class="sidebar-list-title" style="color: var(--color-base)">Standards (history)</div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="nowrap" style="width:100%;border-collapse:collapse;border-spacing:0px 0px;border:none;line-height:1.2em;"><tbody><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/Sea_Level_Datum_of_1929" class="mw-redirect" title="Sea Level Datum of 1929">NGVD 29</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Sea Level Datum 1929</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/OSGB36" class="mw-redirect" title="OSGB36">OSGB36</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Ordnance Survey Great Britain 1936</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/SK-42_reference_system" title="SK-42 reference system">SK-42</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Systema Koordinat 1942 goda</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/ED50" title="ED50">ED50</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> European Datum 1950</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/South_American_Datum#SAD69" title="South American Datum">SAD69</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> South American Datum 1969</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/GRS_80" class="mw-redirect" title="GRS 80">GRS 80</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Geodetic Reference System 1980</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/ISO_6709" title="ISO 6709">ISO 6709</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Geographic point coord. 1983</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/North_American_Datum#North_American_Datum_of_1983" title="North American Datum">NAD 83</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> North American Datum 1983</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/World_Geodetic_System" title="World Geodetic System">WGS 84</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> World Geodetic System 1984</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/North_American_Vertical_Datum_of_1988" title="North American Vertical Datum of 1988">NAVD 88</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> N. American Vertical Datum 1988</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/European_Terrestrial_Reference_System_1989" title="European Terrestrial Reference System 1989">ETRS89</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> European Terrestrial Ref. Sys. 1989</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/Restrictions_on_geographic_data_in_China" title="Restrictions on geographic data in China">GCJ-02</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Chinese obfuscated datum 2002</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/wiki/Geo_URI_scheme" title="Geo URI scheme">Geo URI</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Internet link to a point 2010</td></tr></tbody></table> <ul><li><a href="/wiki/International_Terrestrial_Reference_System" class="mw-redirect" title="International Terrestrial Reference System">International Terrestrial Reference System</a></li> <li><a href="/wiki/SRID" class="mw-redirect" title="SRID">Spatial Reference System Identifier (SRID)</a></li> <li><a href="/wiki/Universal_Transverse_Mercator_coordinate_system" title="Universal Transverse Mercator coordinate system">Universal Transverse Mercator (UTM)</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Geodesy" title="Template:Geodesy"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Geodesy" title="Template talk:Geodesy"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Geodesy" title="Special:EditPage/Template:Geodesy"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>A <i><a href="/wiki/Position_representation" class="mw-redirect" title="Position representation">position representation</a></i> is a set of parameters used to express a position relative to a <a href="/wiki/Reference_frame" class="mw-redirect" title="Reference frame">reference frame</a>. When representing positions relative to the <a href="/wiki/Earth" title="Earth">Earth</a>, it is often most convenient to represent <i><a href="/wiki/Vertical_position" title="Vertical position">vertical position</a></i> (height or depth) separately, and to use some other parameters to represent <b>horizontal position</b>. There are also several applications where only the horizontal position is of interest, this might e.g. be the case for ships and ground vehicles/cars. It is a type of <a href="/wiki/Geographic_coordinate_system" title="Geographic coordinate system">geographic coordinate system</a>. </p><p>There are several options for horizontal position representations, each with different properties which makes them appropriate for different applications. <a href="/wiki/Latitude" title="Latitude">Latitude</a>/<a href="/wiki/Longitude" title="Longitude">longitude</a> and <a href="/wiki/Universal_Transverse_Mercator_coordinate_system" title="Universal Transverse Mercator coordinate system">UTM</a> are common horizontal position representations. </p><p>The horizontal position has two <a href="/wiki/Degrees_of_freedom_(mechanics)" title="Degrees of freedom (mechanics)">degrees of freedom</a>, and thus two parameters are sufficient to uniquely describe such a position. However, similarly to the use of <a href="/wiki/Euler_angles" title="Euler angles">Euler angles</a> as a <a href="/wiki/Rotation_formalisms_in_three_dimensions" title="Rotation formalisms in three dimensions">formalism for representing rotations</a>, using only the minimum number of parameters gives <a href="/wiki/Mathematical_singularity" class="mw-redirect" title="Mathematical singularity">singularities</a>, and thus three parameters are required for the horizontal position to avoid this. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Latitude_and_longitude">Latitude and longitude</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horizontal_position_representation&action=edit&section=1" title="Edit section: Latitude and longitude"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Geodetic_coordinates" title="Geodetic coordinates">Geodetic coordinates</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Latitude" title="Latitude">Latitude</a> and <a href="/wiki/Longitude" title="Longitude">Longitude</a></div> <p>The most common horizontal position representation is <a href="/wiki/Latitude" title="Latitude">latitude</a> and <a href="/wiki/Longitude" title="Longitude">longitude</a>. The parameters are intuitive and well known, and are thus suited for communicating a position to humans, e.g. using a position plot. </p><p>However, latitude and longitude should be used with care in mathematical expressions (including calculations in computer programs). The main reason is the <a href="/wiki/Mathematical_singularity" class="mw-redirect" title="Mathematical singularity">singularities</a> at the <a href="/wiki/Geographical_pole" title="Geographical pole">Poles</a>, which makes longitude undefined at these points. Also near the poles the latitude/longitude grid is highly non-linear, and several errors may occur in calculations that are sufficiently accurate on other locations. <sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Another problematic area is the <a href="/wiki/Meridian_(geography)" title="Meridian (geography)">meridian</a> at ±<a href="/wiki/180th_meridian" title="180th meridian">180°</a> longitude, where the longitude has a <a href="/wiki/Discontinuity_(mathematics)" class="mw-redirect" title="Discontinuity (mathematics)">discontinuity</a>, and hence specific program code must often be written to handle this. An example of the consequences of omitting such code is the crash of the navigation systems of twelve <a href="/wiki/F-22_Raptor" class="mw-redirect" title="F-22 Raptor">F-22 Raptor</a> fighter aircraft while crossing this meridian.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="n-vector"><i>n</i>-vector</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horizontal_position_representation&action=edit&section=2" title="Edit section: n-vector"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/N-vector" title="N-vector">n-vector</a></div> <p><a href="/wiki/N-vector" title="N-vector"><i>n</i>-vector</a> is a three parameter <a href="/wiki/Mathematical_singularity" class="mw-redirect" title="Mathematical singularity">non-singular</a> horizontal position representation that can replace latitude and longitude. Geometrically, it is a <a href="/wiki/Unit_vector" title="Unit vector">unit vector</a> which is normal to the <a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">reference ellipsoid</a>. The vector is <a href="/wiki/Vector_decomposition" class="mw-redirect" title="Vector decomposition">decomposed</a> in an <a href="/wiki/ECEF" class="mw-redirect" title="ECEF">Earth centered earth fixed</a> <a href="/wiki/Coordinate_system" title="Coordinate system">coordinate system</a>. It behaves the same at all Earth positions, and it holds the mathematical <a href="/wiki/Injective_function" title="Injective function">one-to-one</a> property. The vector formulation makes it possible to use standard 3D <a href="/wiki/Vector_calculus" title="Vector calculus">vector algebra</a>, and thus <i>n</i>-vector is well-suited for mathematical calculations, e.g. adding, subtracting, interpolating and averaging positions. </p><p>Using three parameters, <i>n</i>-vector is inconvenient for communicating a position directly to humans and before showing a position plot, a <a href="/wiki/N-vector#Converting_n-vector_to_latitude/longitude" title="N-vector">conversion to latitude/longitude</a> might be needed. </p> <div class="mw-heading mw-heading2"><h2 id="Local_flat_Earth_approximation">Local flat Earth approximation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horizontal_position_representation&action=edit&section=3" title="Edit section: Local flat Earth approximation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Local_tangent_plane" class="mw-redirect" title="Local tangent plane">Local tangent plane</a></div> <p>When carrying out several calculations within a limited area, a <a href="/wiki/Cartesian_coordinate_system" title="Cartesian coordinate system">Cartesian coordinate system</a> might be defined with the <a href="/wiki/Origin_(mathematics)" title="Origin (mathematics)">origin</a> at a specified Earth-fixed position. The origin is often selected at the surface of the reference ellipsoid, with the <i>z</i>-axis in the vertical direction. Hence (three dimensional) position vectors relative to this coordinate frame will have two horizontal and one vertical parameter. The axes are typically selected as <a href="/wiki/North_East_Down" class="mw-redirect" title="North East Down">North-East-Down</a> or <a href="/wiki/East_North_Up" class="mw-redirect" title="East North Up">East-North-Up</a>, and thus this system can be viewed as a <a href="/wiki/Linearization" title="Linearization">linearization</a> of the <a href="/wiki/Meridian_(geography)" title="Meridian (geography)">meridians</a> and <a href="/wiki/Circle_of_latitude" title="Circle of latitude">parallels</a>. </p><p>For small areas a local coordinate system can be convenient for relative positioning, but with increasing (horizontal) distances, errors will increase and repositioning of the <a href="/wiki/Tangent_point" class="mw-redirect" title="Tangent point">tangent point</a> may be required. The alignment along the north and east directions is not possible at the <a href="/wiki/Geographical_pole" title="Geographical pole">Poles</a>, and near the Poles these directions might have significant errors (here the linearization is valid only in a very small area). </p> <div class="mw-heading mw-heading2"><h2 id="Grid_reference_system">Grid reference system</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horizontal_position_representation&action=edit&section=4" title="Edit section: Grid reference system"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Grid_reference_system" class="mw-redirect" title="Grid reference system">Grid reference system</a></div> <p>Instead of one local Cartesian grid, that needs to be repositioned as the position of interest moves, a fixed set of <a href="/wiki/Map_projections" class="mw-redirect" title="Map projections">map projections</a> covering the Earth can be defined. </p> <div class="mw-heading mw-heading3"><h3 id="UTM">UTM</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horizontal_position_representation&action=edit&section=5" title="Edit section: UTM"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Universal_Transverse_Mercator_coordinate_system" title="Universal Transverse Mercator coordinate system">Universal Transverse Mercator coordinate system</a></div> <p><a href="/wiki/Universal_Transverse_Mercator_coordinate_system" title="Universal Transverse Mercator coordinate system">UTM</a> is one such system, dividing the Earth into 60 longitude zones (and with <a href="/wiki/Universal_Polar_Stereographic_coordinate_system" class="mw-redirect" title="Universal Polar Stereographic coordinate system">UPS</a> covering the <a href="/wiki/Polar_regions" class="mw-redirect" title="Polar regions">Polar regions</a>). </p><p>UTM is widely used, and the coordinates approximately corresponds to meters north and east. However, as a set of map-projections it has inherent <a href="/wiki/Distortions" class="mw-redirect" title="Distortions">distortions</a>, and thus most calculations based on UTM will not be exact. The crossing of zones gives additional complexity. </p> <div class="mw-heading mw-heading2"><h2 id="Comparison">Comparison</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horizontal_position_representation&action=edit&section=6" title="Edit section: Comparison"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When deciding which parameters to use for representing position in a specific application, there are several properties that should be considered. The following table gives a summary of what to consider. </p> <table class="wikitable"> <caption>Comparison of horizontal position representations </caption> <tbody><tr> <th>Representation</th> <th>Pros</th> <th>Cons </th></tr> <tr> <td><a href="/wiki/Latitude" title="Latitude">Latitude</a> and <a href="/wiki/Longitude" title="Longitude">longitude</a> </td> <td> <ul><li>Widely used</li> <li>Parameters are easy to recognize by humans (well-suited for plotting)</li></ul> </td> <td> <ul><li><a href="/wiki/Mathematical_singularity" class="mw-redirect" title="Mathematical singularity">Singularities</a> at the <a href="/wiki/Geographical_pole" title="Geographical pole">Poles</a></li> <li>Complex behavior near the Poles</li> <li>Discontinuity at the ±<a href="/wiki/180th_meridian" title="180th meridian">180° meridian</a></li></ul> </td></tr> <tr> <td><a href="/wiki/N-vector" title="N-vector"><i>n</i>-vector</a> </td> <td> <ul><li><a href="/wiki/Mathematical_singularity" class="mw-redirect" title="Mathematical singularity">Nonsingular</a></li> <li>Efficient in equations/calculations since standard 3D <a href="/wiki/Vector_calculus" title="Vector calculus">vector algebra</a> can be used</li> <li>All Earth positions are treated equally</li></ul> </td> <td> <ul><li>Inconvenient for communicating a position to humans</li> <li>Uses three parameters</li></ul> </td></tr> <tr> <td>Local <a href="/wiki/Cartesian_coordinate_system" title="Cartesian coordinate system">Cartesian coordinate system</a> </td> <td> <ul><li>Cartesian vectors in meters along the directions of north, east and down are obtained</li></ul> </td> <td> <ul><li>Can only be used for relative positioning (the tangent point must be represented by some other quantity)</li> <li>Errors increase with increasing horizontal distance from the tangent point (which may require repositioning of the tangent point)</li> <li>North and east directions are undefined at the Poles, and near the Poles these directions may change significantly within the area of interest</li></ul> </td></tr> <tr> <td><a href="/wiki/Universal_Transverse_Mercator_coordinate_system" title="Universal Transverse Mercator coordinate system">UTM</a> </td> <td> <ul><li>Widely used</li> <li>Approximate north and east directions</li> <li>One unit corresponds approximately to one meter</li></ul> </td> <td> <ul><li>Inherent <a href="/wiki/Distortion" title="Distortion">distortion</a> (due to the <a href="/wiki/Map_projection" title="Map projection">map projection</a>) gives only approximate answers for most calculations</li> <li>Calculations get complex when crossing the zones</li> <li>The <a href="/wiki/Polar_Regions" class="mw-redirect" title="Polar Regions">Polar Regions</a> are not covered</li></ul> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horizontal_position_representation&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Rotation_formalisms_in_three_dimensions" title="Rotation formalisms in three dimensions">Rotation formalisms in three dimensions</a></li> <li><a href="/wiki/Geodetic_coordinates" title="Geodetic coordinates">Geodetic coordinates</a></li> <li><a href="/wiki/Geodetic_system" class="mw-redirect" title="Geodetic system">Geodetic system</a></li> <li><a href="/wiki/Plane_coordinates" class="mw-redirect" title="Plane coordinates">Plane coordinates</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Horizontal_position_representation&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFGade2010" class="citation journal cs1">Gade, Kenneth (2010). <a rel="nofollow" class="external text" href="http://www.navlab.net/Publications/A_Nonsingular_Horizontal_Position_Representation.pdf">"A non-singular horizontal position representation"</a> <span class="cs1-format">(PDF)</span>. <i>The Journal of Navigation</i>. <b>63</b> (3). Cambridge University Press: 395–417. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010JNav...63..395G">2010JNav...63..395G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FS0373463309990415">10.1017/S0373463309990415</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Journal+of+Navigation&rft.atitle=A+non-singular+horizontal+position+representation&rft.volume=63&rft.issue=3&rft.pages=395-417&rft.date=2010&rft_id=info%3Adoi%2F10.1017%2FS0373463309990415&rft_id=info%3Abibcode%2F2010JNav...63..395G&rft.aulast=Gade&rft.aufirst=Kenneth&rft_id=http%3A%2F%2Fwww.navlab.net%2FPublications%2FA_Nonsingular_Horizontal_Position_Representation.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHorizontal+position+representation" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.itnews.com.au/News/74081,stealth-fighters-hit-by-software-crash.aspx">"Stealth fighters hit by software crash"</a>. 27 February 2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Stealth+fighters+hit+by+software+crash&rft.date=2007-02-27&rft_id=http%3A%2F%2Fwww.itnews.com.au%2FNews%2F74081%2Cstealth-fighters-hit-by-software-crash.aspx&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHorizontal+position+representation" class="Z3988"></span></span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Horizontal_position_representation&oldid=1239733208">https://en.wikipedia.org/w/index.php?title=Horizontal_position_representation&oldid=1239733208</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Navigation" title="Category:Navigation">Navigation</a></li><li><a href="/wiki/Category:Geodesy" title="Category:Geodesy">Geodesy</a></li><li><a href="/wiki/Category:Geographic_coordinate_systems" title="Category:Geographic coordinate systems">Geographic coordinate systems</a></li><li><a href="/wiki/Category:Geographic_position" title="Category:Geographic position">Geographic position</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden category: <ul><li><a href="/wiki/Category:Use_dmy_dates_from_February_2023" title="Category:Use dmy dates from February 2023">Use dmy dates from February 2023</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 11 August 2024, at 05:26<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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