Editing Navigation

{{short description|Process of monitoring and controlling the movement of a craft or vehicle from one place to another}}
{{other uses}}
[[File:Navigation system on a merchant ship.jpg|thumb|A navigation system on an [[oil tanker]]]]
'''Navigation''' is a field of study that focuses on the process of monitoring and controlling the [[motion|movement]] of a craft or [[vehicle]] from one place to another.<ref name="hofman" /><ref name="bow799">Bowditch, 2003:799.</ref> The field of navigation includes four general categories: land navigation,<ref>The Handbook Of The SAS And Elite Forces. How The Professionals Fight And Win. Edited by Jon E. Lewis. p.363-Tactics And Techniques, Personal Skills And Techniques. Robinson Publishing Ltd 1997. ISBN 1-85487-675-9</ref> [[marine navigation]], [[air navigation|aeronautic navigation]], and space navigation.<ref name="hofman">{{cite book|last=Rell Pros-Wellenhof|first=Bernhard|title=Navigation: Principles of Positioning and Guidances|year=2007|publisher=Springer|isbn=978-3-211-00828-7|pages=5–6}}</ref> It is also the term of art used for the specialized knowledge used by [[navigator]]s to perform navigation tasks.<ref name="SafeNaviii"/> All navigational techniques involve locating the navigator's [[Position (geometry)|position]] compared to known locations or patterns. Navigation, in a broader sense, can refer to any skill or study that involves the determination of position and [[Relative direction|direction]].<ref name="hofman"/> In this sense, navigation includes [[orienteering]] and [[pedestrian]] navigation.<ref name="hofman"/>

For marine navigation, this involves the safe movement of ships, boats and other nautical craft either on or underneath the water using positions from navigation equipment with appropriate nautical charts (electronic and paper).<ref name="SafeNaviii">{{cite book | title=Safe Nav Watch | publisher=[[Witherby Publishing Group]] | publication-place=Livingston, Scotland | date=2023 | isbn=978-1-914993-46-6 | page=iii}}</ref> Navigation equipment for ships is mandated under the requirements of the [[SOLAS Convention]], depending on ship size.<ref name="SafeNav4">{{cite book | title=Safe Nav Watch | publisher=[[Witherby Publishing Group]] | publication-place=Livingston, Scotland | date=2023 | isbn=978-1-914993-46-6 | page=4}}</ref> For land navigation, this involves the movement of persons, animals and vehicles from one place to another by means of navigation equipment (such as a compass or GNSS receivers), maps and visual navigation marks across urban or rural environments.<ref name="d440">{{cite journal | title=Land-vehicle navigation using GPS | journal=Proceedings of the IEEE | date=1999-01-31 | doi=10.1109/5.736347 | url=https://ieeexplore.ieee.org/document/736347 | access-date=2025-02-24 | last1=Abbott | first1=E. | last2=Powell | first2=D. | volume=87 | pages=145–162 | url-access=subscription }}</ref><ref name="r925">{{cite book | last=Hawkins | first=Pete | title=Navigation | publisher=Cicerone Press Limited | date=2024-05-13 | isbn=978-1-78362-788-2}}</ref> Aeronautic (air) navigation involves piloting an aircraft from one geographic position to another position while monitoring the position as the flight progresses.<ref name="n027">{{cite web | title=Navigation | url=https://www.faa.gov/sites/faa.gov/files/18_phak_ch16.pdf | publisher=Federal Aviation Administration | access-date=2025-02-24}}</ref> 

==Etymology==
The term stems from the 1530s, from [[Latin]] ''navigationem'' (nom. ''navigatio''), from ''navigatus'', pp. of ''navigare'' "to sail, sail over, go by sea, steer a ship," from ''navis'' "ship" and the root of ''agere'' "to drive".<ref>{{Cite web |title=Etymonline - Online Etymology Dictionary |url=https://www.etymonline.com/search?q=navigation&ref=searchbar_searchhint |website=www.etymonline.com}}</ref>

==History==
[[File:Licht der Zeevaert, Frontispiz.jpg|thumb|"The light of navigation", Dutch sailing handbook, 1608, showing  compass, hourglass, sea astrolabe, terrestrial and celestial globes, divider, [[Jacob's staff]] and astrolabe.]]
{{Further|History of navigation}}
{{see also|History of geodesy}} 
[[Polynesian navigation]] is probably the earliest form of open-ocean navigation; it was based on memory and observation recorded on scientific instruments like the [[Marshall Islands stick chart|Marshall Islands Stick Charts of Ocean Swells]]. Early Pacific Polynesians used the motion of stars, weather, the position of certain wildlife species, or the size of waves to find the path from one island to another.<ref name="x565">{{cite web | last=Vermillion | first=Stephanie | title=Polynesia's master voyagers who navigate by nature | website=BBC Home | date=2021-07-27 | url=https://www.bbc.com/travel/article/20210726-polynesias-master-voyagers-who-navigate-by-nature | access-date=2025-04-18}}</ref><ref name="n388">{{cite web | title=The history and mystery of Polynesian navigation | website=Phys.org | date=2019-03-25 | url=https://phys.org/news/2019-03-history-mystery-polynesian.html | access-date=2025-04-18}}</ref><ref name="s290">{{cite web | last=Martins | first=Kim | title=Polynesian Navigation & Settlement of the Pacific | website=World History Encyclopedia | date=2020-08-07 | url=https://www.worldhistory.org/article/1586/polynesian-navigation--settlement-of-the-pacific/ | access-date=2025-04-18}}</ref> Among the first proper navigational instruments was the [[compass]], with one of the oldest [[China|Chinese]] in origin from the [[Han dynasty]] (since c. 206 BC).<ref name="Li Shu-hua, p. 176">[[#Li|Li Shu-hua]], p. 176</ref> The compass was later adopted for sea navigation by the [[Song dynasty]] Chinese during the 11th century.<ref name="Barbara M. Kreutz 367">[[#Kreutz|Kreutz]], p. 367</ref><ref name="needham volume 4 part 1 252">Needham, Joseph (1986) ''Science and civilisation in China'', Vol. 4: "Physics and physical technology", Pt. 1: "Physics", Taipei. p. 252 Caves Books, originally publ. by Cambridge University Press (1962), {{ISBN|0-521-05802-3}}</ref><ref name="Li Shu-hua, p. 182f">[[#Li|Li Shu-hua]], p. 182f.</ref> The first usage of a compass recorded in [[Western Europe]] and the [[Islamic world]] occurred around 1190.<ref name=OEPST>{{Cite encyclopedia | publisher = Oxford University Press| isbn = 978-0-19-981257-8| editor= Ibrahim Kalin | last = Schmidl | first = Petra G. | title = Compass | encyclopedia = The Oxford Encyclopedia of Philosophy, Science, and Technology in Islam| date = 2014| pages=144–146}}</ref>

Maritime navigation using scientific instruments such as the [[mariner's astrolabe]] first occurred in the Mediterranean during the Middle Ages. Although [[astrolabe|land astrolabes]] were invented in the [[Hellenistic period]] and existed in [[classical antiquity]] and the [[Islamic Golden Age]], the oldest record of a sea astrolabe is that of [[Spanish people|Spanish]] astronomer [[Ramon Llull]] dating from 1295.<ref name="oxfordShipsAndSea">''The Ty Pros Companion to Ships and the Sea'', Peter Kemp ed., 1976 {{ISBN|0-586-08308-1}}</ref> The perfecting of this navigation instrument is attributed to [[Portuguese Empire|Portuguese]] navigators during early [[Portuguese discoveries]] in the [[Age of Discovery]].<ref>{{cite book |author=Comandante Estácio dos Reis |title=Astrolábios Náuticos |year=2002  |publisher=INAPA |isbn=978-972-797-037-7}}</ref><ref name="ancruzeiros.pt">{{cite web |url=http://www.ancruzeiros.pt/anci-astrolabio.html |title=Archived copy |access-date=2013-04-02 |url-status=dead |archive-url=https://web.archive.org/web/20121122134304/http://www.ancruzeiros.pt/anci-astrolabio.html |archive-date=2012-11-22 }}</ref> The earliest known description of how to make and use a sea astrolabe comes from Spanish cosmographer [[Martín Cortés de Albacar]]'s ''Arte de Navegar'' (''The Art of Navigation'') published in 1551,<ref name="swanick">Swanick, Lois Ann. ''An Analysis Of Navigational Instruments In The Age Of Exploration: 15th Century To Mid-17th century'', MA Thesis, Texas A&M University, December 2005</ref> based on the principle of the [[archipendulum]] used in constructing the [[Egyptian pyramids]]. However, the first altitude measuring instrument to navigate extensively used at sea was the [[Quadrant (instrument)|quadrant]].<ref name="Williams1992">Williams, 1992:35</ref> This was reintroduced by Leonardo of Pisa in the 13th century.<ref name="Williams1992"/> Its first recorded use was in 1461 by [[Diogo Gomes]].<ref name="Williams1992"/> As well as astrolabes and quadrants, the first [[Jacob's staff|cross-staff]] used in navigation was known from the 14th century onwards, believed to have come from early Arab navigators.<ref name="Williams37">Williams, 1992:37</ref> However, it had many errors and was also difficult to use as it required squinting at the sun.<ref name="Williams37"/> These disadvantages were overcome with the invention of the [[backstaff]] in 1595 by [[John Davis (explorer)|John Davis]].<ref name="Williams37"/>

[[File:Yale's Hartmann astrolabe.jpg|thumb|right|German 16th century astrolabe]]
Widespread open-seas navigation using the astrolabe, quadrant, backstaff and the [[compass]] started during the Age of Discovery in the 15th century. The Portuguese began systematically exploring the [[Atlantic]] coast of [[Africa]] from 1418, under the sponsorship of [[Henry the Navigator|Prince Henry]]. In 1488 [[Bartolomeu Dias]] reached the [[Indian Ocean]] by this route. In 1492 the [[Ferdinand and Isabella|Spanish monarchs]] funded [[Christopher Columbus]]'s expedition to sail west to reach the [[Indies]] by crossing the Atlantic, which resulted in the [[Discovery of the Americas]]. In 1498, a Portuguese expedition commanded by [[Vasco da Gama]] reached [[India]] by sailing around Africa, opening up direct trade with [[Asia]]. Soon, the Portuguese sailed further eastward, to the [[Maluku Islands|Spice Islands]] in 1512, landing in [[China]] one year later. The first circumnavigation of the earth was completed in 1522 with the [[Timeline of Magellan's circumnavigation|Magellan-Elcano expedition]], a Spanish voyage of discovery led by Portuguese explorer [[Ferdinand Magellan]] and completed by Spanish navigator [[Juan Sebastián Elcano]] after the former's death in the [[Philippines]] in 1521. 

For sailing ships, other developments took place with [[nautical chart|charting]] and methods to record courses.<ref name="Williams30">Williams, 1992:30</ref> One of the oldest surviving marine charts is the Carta Pisana, drawn on a sheepskin, dating to 1275.<ref name="Williams28">Williams, 1992:28</ref> On land, improvements in the production of [[maps]] led to improved navigation by armies, traders and other travellers.<ref name="l842">{{cite book | last=Andrews | first=John Harwood | title=Maps in Those Days | publisher=Four Courts press | publication-place=Dublin | date=2009 | isbn=978-1-84682-188-2}}</ref> For sailing ships, navigation by [[dead reckoning]] requires frequent recording of course changes and the ship tacks with the wind.<ref name="Williams30"/> To prevent paper charts, which were expensive and in the early days, rare, from being worn out, other methods were used, including the [[Traverse board]] and traverse tables (the oldest traverse tables, dates back to 1428).<ref name="Williams30"/> Quadrants were further developed by inventors such as [[Robert Hooke]], [[Isaac Newton]] and [[John Hadley]] leading to the invention of the [[Octant (instrument)|octant]].<ref name="Williams96">Williams, 1992:96-97</ref> 
[[file:Harrison's Chronometer H5.JPG|thumb|right|Harrison's Chronometer H5 of 1772, now on display at the [[Science Museum, London]]]]
Developments in mathematics were also important in the history of navigation.<ref name="Williams41">Williams, 1992:41</ref> These include initially [[meridional parts]], then developments in [[spherical trigonometry]] and [[logarithms]] enabled navigators from the 1700s onwards to navigate more accurately.<ref name="Williams41"/> On land, mathematical and new instruments led to developments in [[Surveying]] and [[triangulation]] which further improved maps, as well as the construction of better roads, paths, canals and eventually railways.<ref name="z725">{{cite web | title=Evolution of surveying and surveying technology | website=Intergovernmental Committee on Surveying and Mapping | url=https://www.icsm.gov.au/education/fundamentals-land-ownership-land-boundaries-and-surveying/surveyors-and-surveying-0 | access-date=2025-04-18}}</ref><ref name="x749">{{cite web | last=Tyrrell | first=Rachel | title=Surveying the past – the origins of surveying | website=The Survey Association | date=2023-08-16 | url=https://www.tsa-uk.org.uk/surveying-the-past-the-origins-of-surveying/ | access-date=2025-04-18}}</ref> Development of an accurate [[marine chronometer]] under [[John Harrison]] and others ensured accurate timekeeping for calculating [[longitude]].<ref name="Williams81">Williams, 1992:81</ref> Further improvements in ocean navigation led to the first proper [[sextant]] in 1757, the parts and usage developed by various inventors including [[Pierre Vernier]] and [[John Campbell (Royal Navy officer)|John Campbell]].<ref name="Williams98">Williams, 1992:98</ref> Various methods for calculation with sextant and chronometer evolved over time, beginning with the Duller method (1728) but reached their most accessible with the Douwes method (1821), the Sumner method (1837), modified by Henry Raper (1844) and the Marc St Hilaire or [[intercept method]] (1877).<ref name="Williams110">Williams, 1992:110-114</ref> Modifications to the magnetic compass and better methods of determining course were also important, include developments in the compass by [[Matthew Flinders]], [[Lord Kelvin]] and others.<ref name="Williams132">Williams, 1992:132-135</ref> 

The sextant, together with the chronometer, compass and astronomical calculations became the most widely used methods of maritime navigation until developments in the 20th century with [[radio-navigation]] and [[gyrocompasses]].<ref name="Williams98"/> These in turn were superseded with the advent of computers, [[electronic calculator]]s and later [[satellite navigation]] in the 20th century.<ref name="Williams198">Williams, 1992:198</ref> On land, the development of handheld [[GPS]] occurred in the 1980s and with the advent of smartphones, with in-build compassess and satellite receivers, navigation is now widely achieved through technology globally.<ref name="n283">{{cite web | title=Release date history | website=GPS Training | date=2024-07-19 | url=https://gpstraining.co.uk/blogs/news/outdoor-gps-units-release-date-history?srsltid=AfmBOoprplgSwqjwguO3zPnJjOKaACMATgJGNsUQKXW2ZVi2j29_ensk | access-date=2025-04-18}}</ref><ref name="c139">{{cite web | last=Yohannes | first=Samraweet | title=Smartphones may be our greatest tool for outdoor and indoor navigation | website=CBC | date=2023-02-24 | url=https://www.cbc.ca/radio/spark/smartphones-may-be-our-greatest-tool-for-outdoor-and-indoor-navigation-1.6751354 | access-date=2025-04-18}}</ref>

==Basic concepts==
{{longlat}}
In terrestrial navigation, the location of a person, ship, plane, etc is defined as a position using a reference point/coordinates (see [[Cartesian coordinate system]]). Positions can either be referenced as latitude/longitude or a distance and [[Cardinal direction|direction]] from a fixed reference point ([[Bearing (navigation)|bearing]]).<ref name="Smith1">{{cite book | last=Smith | first=Philip M. | title=Terrestrial Navigation | publisher=Routledge | publication-place=London ; New York | date=2017-10-16 | isbn=978-1-317-20046-8 | page=1}}</ref> Lines of position can be derived from a variety of methods and equipment. By determining and monitoring positions it is possible to find and direct a person, ship, plane, etc in a scientific way from one place to another.<ref name="r313">{{cite web | title=navigation | website=Cambridge Dictionary | date=2025-02-19 | url=https://dictionary.cambridge.org/dictionary/english/navigation | access-date=2025-02-24}}</ref> This often involves the use of [[maps]] or [[charts]] from which if desired, courses can be calculated or followed depending on the projection or methods used ([[Rhumb line]], [[Great circle]], etc).<ref name="Smith24">{{cite book | last=Smith | first=Philip M. | title=Terrestrial Navigation | publisher=Routledge | publication-place=London ; New York | date=2017-10-16 | isbn=978-1-317-20046-8 | page=24}}</ref>

===Latitude===
{{Further|Latitude}}
Roughly, the latitude of a place on Earth is its angular distance north or south of the [[equator]].<ref name="bow4">Bowditch, 2003:4.</ref> Latitude is usually expressed in [[degree (angle)|degrees]] (marked with °) ranging from 0° at the [[Equator]] to 90° at the North and South poles.<ref name="bow4"/> The latitude of the [[North Pole]] is 90° N, and the latitude of the [[South Pole]] is 90° S.<ref name="bow4" /> Mariners calculated latitude in the Northern Hemisphere by sighting the [[pole star]] ([[Polaris]]) with a [[sextant]] and using sight reduction tables to correct for height of eye and atmospheric refraction. The height of Polaris in degrees above the horizon is the latitude of the observer, within a degree or so.

===Longitude===
{{Further|Longitude}}
Similar to latitude, the longitude of a place on Earth is the angular distance east or west of the [[prime meridian]] or [[Greenwich meridian]].<ref name="bow4"/> Longitude is usually expressed in [[degree (angle)|degrees]] (marked with °) ranging from [[prime meridian|0°]] at the Greenwich meridian to [[180th meridian|180°]] east and west. [[Sydney]], for example, has a longitude of about [[151st meridian east|151° east]]. [[New York City]] has a longitude of [[74th meridian west|74° west]]. For most of history, mariners struggled to determine longitude. Longitude can be calculated if the precise time of a sighting is known. Lacking that, one can use a [[sextant]] to take a [[Lunar distance (navigation)|lunar distance]] (also called ''the lunar observation'', or "lunar" for short) that, with a [[nautical almanac]], can be used to calculate the time at zero longitude (see [[Greenwich Mean Time]]).<ref name="Norie 1828 pg 222">
 {{cite book
  | last =Norie
  | first =J.W.
  | title =New and Complete Epitome of Practical Navigation
  | year =1828
  | location =London
  | url =http://www.mysticseaport.org/library/initiative/ImPage.cfm?PageNum=3&BibId=13617&ChapterId=30
  | access-date =2007-08-02
  | page =222
  | url-status=dead
  | archive-url =https://web.archive.org/web/20070927203111/http://www.mysticseaport.org/library/initiative/ImPage.cfm?PageNum=3&BibId=13617&ChapterId=30
  | archive-date =2007-09-27
  }}</ref> Reliable [[marine chronometer]]s were unavailable until the late 18th century and not affordable until the 19th century.<ref name="Norie 1828 pg 221">
{{cite book
  | last =Norie
  | first =J.W.
  | title =New and Complete Epitome of Practical Navigation
  | year =1828
  | location =London
  | url =http://www.mysticseaport.org/library/initiative/ImPage.cfm?PageNum=2&BibId=13617&ChapterId=30
  | access-date =2007-08-02
  | page =221
  | url-status=dead
  | archive-url =https://web.archive.org/web/20070927202912/http://www.mysticseaport.org/library/initiative/ImPage.cfm?PageNum=2&BibId=13617&ChapterId=30
  | archive-date =2007-09-27
  }}</ref><ref name="Taylor 1851 pg 195">{{Cite book
| last = Taylor
| first = Janet
| title=An Epitome of Navigation and Nautical Astronomy
| publisher = Taylor
| edition = Ninth
| year = 1851
| url=https://archive.org/details/anepitomenaviga00taylgoog
| quote = Nautical Almanac 1849-1851.
| access-date=2007-08-02
| page = 295f
}}
</ref><ref name="Watchmakers and their Work, pg 230">
{{cite book
| first=Frederick James
| last=Britten
| title = Former Clock & Watchmakers and Their Work
| year = 1894
| publisher=Spon & Chamberlain
| location = New York
|url=https://archive.org/details/formerclockwatc00britgoog
| quote=Chronometers were not regularly supplied to the Royal Navy until about 1825
|access-date=2007-08-08
| page=[https://archive.org/details/formerclockwatc00britgoog/page/n242 230]
}}</ref> For about a hundred years, from about 1767 until about 1850,<ref>Lecky, Squire, ''Wrinkles in Practical Navigation''</ref> mariners lacking a chronometer used the method of lunar distances to determine Greenwich time to find their longitude. A mariner with a chronometer could check its reading using a lunar determination of Greenwich time.<ref name="Norie 1828 pg 221"/><ref name = "Roberts">{{cite book
|last= Roberts |first= Edmund |author-link= Edmund Roberts (diplomat)
|title=1837, Embassy to the Eastern courts of Cochin-China, Siam, and Muscat: in the U.S. sloop-of-war Peacock ... during the years 1832–3–4
|url=  https://books.google.com/books?id=aSgPAAAAYAAJ |publisher=   Harper & brothers  
|page=   373 |no-pp= <!-- 0 hides automatic 'p' or 'pp'.--> 
|chapter=   Chapter XXIV―departure from Mozambique
|isbn=9780608404066 |chapter-url= https://books.google.com/books?id=aSgPAAAAYAAJ&pg=PA365
|access-date=  April 25, 2012
|edition=   Digital
|quote= ...what I have stated, will serve to show the absolute necessity of having first rate chronometers, or the lunar observations carefully attended to; and never omitted to be taken when practicable.
}}</ref>

===Loxodrome===
{{Further|Rhumb line}}
In navigation, a rhumb line (or loxodrome) is a line crossing all meridians of longitude at the same angle, i.e. a path derived from a defined initial bearing. That is, upon taking an initial bearing, one proceeds along the same bearing, without changing the direction as measured relative to true or magnetic north.

==Methods of navigation==
Most [[Navigation system|modern navigation]] relies primarily on positions determined electronically by receivers collecting information from satellites. Most other modern techniques rely on finding intersecting [[line of position|lines of position]] or LOP.<ref name="mal615">Maloney, 2003:615.</ref>

A line of position can refer to two different things, either a line on a chart or a line between the observer and an object in real life.<ref name="mal614">Maloney, 2003:614</ref> A bearing is a measure of the direction to an object.<ref name="mal614"/> If the navigator measures the direction in real life, the angle can then be drawn on a [[nautical chart]] and the navigator will be somewhere on that bearing line on the chart.<ref name="mal614"/>

In addition to bearings, navigators also often measure distances to objects.<ref name="mal615"/> On the chart, a distance produces a circle or arc of position.<ref name="mal615"/> Circles, arcs, and hyperbolae of positions are often referred to as lines of position.

If the navigator draws two lines of position, and they intersect he must be at that position.<ref name="mal615"/> A [[fix (position)|fix]] is the intersection of two or more LOPs.<ref name="mal615"/>

If only one line of position is available, this may be evaluated against the [[dead reckoning]] position to establish an estimated position.<ref name="mal618">Maloney, 2003:618.</ref>

Lines (or circles) of position can be derived from a variety of sources:
* celestial observation (a short segment of the [[circle of equal altitude]], but generally represented as a line),
* terrestrial range (natural or man made) when two charted points are observed to be in line with each other,<ref name="mal622">Maloney, 2003:622.</ref>
* compass bearing to a charted object,
* radar range to a charted object,
* on certain coastlines, a depth sounding from [[Fathometer|echo sounder]] or hand [[Sounding line|lead line]].

There are some methods seldom used today such as the maritime method of "dipping a light" to calculate the geographic range from observer to lighthouse, where the height of the lighthouse is known (from a list of lights or from a chart).<ref name="q471">{{cite book | last=Rousmaniere | first=John | title=The Annapolis Book of Seamanship: Third Edition | publisher=Simon and Schuster | publication-place=New York | date=1999 | isbn=978-0-684-85420-5 | page=214-215}}</ref>

Methods of navigation have changed through history.<ref name="bow1">Bowditch, 2002:1.</ref> Each new method has enhanced the mariner's ability to complete his voyage.<ref name="bow1"/> One of the most important judgments the navigator must make is the best method to use.<ref name="bow1"/> Some types of navigation are depicted in the table.

{| class="wikitable" style="font-size:95%"
|-
! Illustration !! Description !! Application
|- valign="top"
! colspan="3" | Traditional navigation methods include:
|- valign="top"
|[[File:Cruising sailor navigating.jpg|100px]]
|In marine navigation, [[dead reckoning]] or DR, in which one advances a prior position using the ship's course and speed. The new position is called a DR position. It is generally accepted that only course and speed determine the DR position. Correcting the DR position for [[leeway]], current effects, and steering error result in an estimated position or EP. An [[Inertial guidance system|inertial navigator]] develops an extremely accurate EP.<ref name="bow1"/>
|Used at all times.
|-valign="top"
|[[File:SplitPointLighthouse.jpg|100px]]
|In marine navigation, [[pilotage]] involves navigating in restricted/coastal waters with frequent determination of position relative to geographic and hydrographic features.<ref name="bow1"/>
|When within sight of land.
|-valign="top"
|[[File:Orienteering map.jpg|100px]]
|[[Land navigation]] is the discipline of following a route through terrain on foot or by vehicle, using maps with reference to terrain, a compass, and other basic navigational tools and/or using landmarks and signs. [[Wayfinding]] is the more basic form.
|Used at all times.
|-valign="top"
|[[File:Moon-Mdf-2005.jpg|100px]]
|[[Celestial navigation]] involves reducing celestial measurements to lines of position using tables, [[spherical trigonometry]], and [[Nautical almanac|almanacs]]. It is primarily used at sea but can also be used on land.
|Used primarily as a backup to [[satellite navigation|satellite]] and other [[Radio navigation|electronic systems]] in the open ocean.<ref name="bow1"/>
|-valign="top"
! colspan="3" | [[Electronic navigation]] covers any method of [[position fixing]] using electronic means, including:
|-valign="top"
|[[File:Decca Navigator Mk 12.jpg|100px]]
|[[Radio navigation]] uses radio waves to determine position by either [[radio direction finder|radio direction finding systems]] or hyperbolic systems, such as [[Decca Navigator System|Decca]], [[OMEGA Navigation System|Omega]] and [[LORAN-C]].
| Availability has declined due to the development of accurate GNSS.
|-valign="top"
|[[File:Radar screen.JPG|100px]]
|[[Radar navigation]] uses radar to determine the distance from or bearing of objects whose position is known. This process is separate from radar's use as a collision avoidance system.<ref name="bow1"/>
| Primarily when within radar range of land.
|-valign="top"
|[[File:GPS Satellite NASA art-iif.jpg|100px]]
|[[Satellite navigation]] uses a Global Navigation Satellite System (GNSS) to determine position.<ref name="bow1"/>
|Used in all situations.
|}

The practice of navigation usually involves a combination of these different methods.<ref name="bow1"/>

===Mental navigation checks===
By mental navigation checks, a pilot or a navigator estimates tracks, distances, and altitudes which will then help the pilot avoid gross navigation errors.<ref>''The Handbook of the SAS and Elite Forces. How the Professionals Fight and Win''. Edited by Jon E. Lewis. p. 370 "Tactics And Techniques, Personal Skills And Techniques". Robinson Publishing Ltd 1997. {{ISBN|1854876759}}</ref>

===Piloting===
{{Further|Pilotage}}
[[File:Navigatie.jpg|thumb|Manual navigation through Dutch airspace]]
Piloting (also called pilotage) involves navigating an aircraft by visual reference to landmarks,<ref name="14cfr1">Federal Aviation Regulations Part 1 §1.1</ref> or a water vessel in restricted waters and fixing its position as precisely as possible at frequent intervals.<ref name="bow105">Bowditch, 2002:105.</ref> More so than in other phases of navigation, proper preparation and attention to detail are important.<ref name="bow105"/> Procedures vary from vessel to vessel, and between military, commercial, and private vessels.<ref name="bow105"/> As pilotage takes place in [[Waves and shallow water|shallow waters]], it typically involves following courses to ensure sufficient [[under keel clearance]], ensuring a sufficient depth of water below the [[Draft (hull)|hull]] as well as a consideration for [[Squat effect|squat]].<ref name="Gilardoni Presedo 2017">{{cite book | last1=Gilardoni | first1=Eduardo O. | last2=Presedo | first2=Juan P. | title=Navigation in Shallow Waters | publisher=[[Witherby Publishing Group]] | publication-place=Livingston, Scotland | date=2017 | isbn=978-1-85609-667-6}}</ref> It may also involve navigating a ship within a river, [[canal]] or [[Channel (geography)|channel]] in close proximity to land.<ref name="Gilardoni Presedo 2017"/>

A military navigation team will nearly always consist of several people.<ref name="bow105"/> A military navigator might have bearing takers stationed at the gyro repeaters on the bridge wings for taking simultaneous bearings, while the civilian navigator on a merchant ship or leisure craft must often take and plot their position themselves, typically with the aid of electronic position fixing.<ref name="bow105"/> While the military navigator will have a bearing book and someone to record entries for each fix, the civilian navigator will simply pilot the bearings on the chart as they are taken and not record them at all.<ref name="bow105"/> If the ship is equipped with an [[ECDIS]], it is reasonable for the navigator to simply monitor the progress of the ship along the chosen track, visually ensuring that the ship is proceeding as desired, checking the compass, sounder and other indicators only occasionally.<ref name="bow105"/> If a [[harbour pilot|pilot]] is aboard, as is often the case in the most restricted of waters, his judgement can generally be relied upon, further easing the workload.<ref name="bow105"/> But should the ECDIS fail, the navigator will have to rely on his skill in the manual and time-tested procedures.<ref name="bow105"/>

===Celestial navigation===
{{Main|Celestial navigation}}
[[File:Sun-Moon path.PNG|thumb|upright=1.2|A celestial fix will be at the intersection of two or more circles.]]

Celestial navigation systems are based on observation of the positions of the [[Sun]], [[Moon]], [[planet]]s and [[list of selected stars for navigation|navigational stars]] using a [[sextant]] or similar navigation instrument.<ref name="s102">{{cite web | title=Celestial Navigation | website=Time and Navigation | url=https://timeandnavigation.si.edu/navigating-at-sea/navigating-without-a-clock/celestial-navigation | access-date=2025-02-24}}</ref> By knowing which point on the rotating Earth a celestial object is above and measuring its height above the observer's horizon, the navigator can determine his distance from that subpoint using mathematical calculation.<ref name="q565">{{cite book | last=Cunliffe | first=Tom | title=Celestial Navigation | publisher=*Wiley Nautical | publication-place=London | date=2010-09-28 | isbn=978-0-470-66633-3}}</ref> A [[nautical almanac]] and a source of time, typically a [[marine chronometer]] are used to compute the subpoint on Earth a celestial body is over, and a [[sextant]] is used to measure the body's angular height above the horizon.<ref name="q565"/> That height can then be used to compute distance from the subpoint to create a circular line of position. Alternatively sight reduction tables can be used.<ref name="j728">{{cite book | last=Prinet | first=Dominique F. | title=Celestial Navigation | publisher=FriesenPress | date=2014-07-18 | isbn=978-1-4602-4212-4}}</ref> A navigator shoots a number of stars in succession to give a series of overlapping lines of position. Where they intersect is the celestial fix. The Moon and Sun may also be used. The Sun can also be used by itself to shoot a succession of lines of position (best done around local noon) to determine a position.<ref name="bow269"/> Since the advent of GNSS, celestial navigation is less used for marine and air navigation, though it remains useful as a backup or as another method to cross-check the accuracy of electronic systems, particularly in the open ocean.<ref name="t697">{{cite book | last=Karl | first=John | title=Celestial navigation in the GPS age | publisher=Paradiese Cay Publ | publication-place=Arcata,CA | date=2007 | isbn=978-0-939837-75-5}}</ref><ref name="u717">{{cite web | last=Escobar | first=Lieutenant Juan J. | last2=Navy | first2=Chilean | title=Bring Celestial Navigation into the 21st Century | website=U.S. Naval Institute | date=2021-12-01 | url=https://www.usni.org/magazines/proceedings/2021/december/bring-celestial-navigation-21st-century | access-date=2025-02-24}}</ref>

====Marine chronometer====
{{main|Marine chronometer}}
[[File:Breguet marine clock-CnAM 16767-1-IMG 1525-white.jpg|thumb|right|Breguet marine chronometer]]
In order to accurately measure longitude, the precise time is required of a sextant sighting (down to the second, if possible) which is then recorded for subsequent calculation. Each second of error is equivalent to 15 seconds of longitude error, which at the equator is a position error of .25 of a nautical mile, about the accuracy limit of manual celestial navigation. The spring-driven marine chronometer is a precision timepiece used aboard ship to provide accurate time for celestial observations.<ref name="bow269">Bowditch, 2002:269.</ref> A chronometer differs from a spring-driven watch principally in that it contains a variable lever device to maintain even pressure on the mainspring, and a special balance designed to compensate for temperature variations.<ref name="bow269"/> A spring-driven chronometer is set approximately to Greenwich mean time (GMT) and is not reset until the instrument is overhauled and cleaned, usually at three-year intervals.<ref name="bow269"/> The difference between GMT and chronometer time is carefully determined and applied as a correction to all chronometer readings.<ref name="bow269"/> Spring-driven chronometers must be wound at about the same time each day.<ref name="bow269"/>

[[Quartz clock#Accuracy enhancement|Quartz crystal marine chronometers]] have replaced spring-driven chronometers onboard modern ships because of their greater accuracy.<ref name="bow269"/> They are maintained on GMT directly from radio time signals.<ref name="bow269"/> This eliminates chronometer error and watch error corrections.<ref name="bow269"/> Should the second hand be in error by a readable amount, it can be reset electrically.<ref name="bow269"/> The basic element for time generation is a quartz crystal oscillator.<ref name="bow269"/> The quartz crystal is temperature compensated and is hermetically sealed in an evacuated envelope.<ref name="bow269"/> A calibrated adjustment capability is provided to adjust for the aging of the crystal.<ref name="bow269"/>

The chronometer is typically designed to operate for a minimum of one year on a single set of batteries.<ref name="bow269"/> Observations may be timed and ship's clocks set with a comparing watch, which is set to chronometer time and taken to the bridge wing for recording sight times.<ref name="bow269"/> In practice, a wrist watch coordinated to the nearest second with the chronometer will be adequate.<ref name="bow269"/> A stop watch, either spring wound or digital, may also be used for celestial observations.<ref name="bow269"/> In this case, the watch is started at a known GMT by chronometer, and the elapsed time of each sight added to this to obtain GMT of the sight.<ref name="bow269"/> All chronometers and watches should be checked regularly with a radio time signal.<ref name="bow269"/> Times and frequencies of radio time signals are listed in publications such as [[Radio Navigational Aids]].<ref name="bow269"/>

====The marine sextant====
[[File:Marine sextant.svg|thumb|upright=1.2|The marine [[sextant]] is used to measure the elevation of celestial bodies above the horizon.]]
{{Further|Sextant}}
The second critical component of celestial navigation is to measure the angle formed at the observer's eye between the celestial body and the sensible horizon. The sextant, an optical instrument, is used to perform this function. The sextant consists of two primary assemblies. The frame is a rigid triangular structure with a pivot at the top and a graduated segment of a circle, referred to as the "arc", at the bottom. The second component is the index arm, which is attached to the pivot at the top of the frame. At the bottom is an endless vernier which clamps into teeth on the bottom of the "arc". The optical system consists of two mirrors and, generally, a low power telescope. One mirror, referred to as the "index mirror" is fixed to the top of the index arm, over the pivot. As the index arm is moved, this mirror rotates, and the graduated scale on the arc indicates the measured angle ("altitude").<ref name="q939">{{cite book | last=House | first=D.J. | title=Seamanship Techniques | publisher=Routledge | publication-place=London | date=2013-11-12 | isbn=978-1-135-08015-0 | page=350-252}}</ref> The second mirror, referred to as the "horizon glass", is fixed to the front of the frame. One half of the horizon glass is silvered and the other half is clear. Light from the celestial body strikes the index mirror and is reflected to the silvered portion of the horizon glass, then back to the observer's eye through the telescope. The observer manipulates the index arm so the reflected image of the body in the horizon glass is just resting on the visual horizon, seen through the clear side of the horizon glass.<ref name="q939"/>

There are three main errors that must be corrected in order to each usage for navigation.<ref name="q939"/> The main errors are perpendicular error, side error and index error.<ref name="q939"/> Adjustment of the sextant consists of checking and aligning all the optical elements to eliminate the overall "index error" (or index correction). Index correction should be checked, using the horizon or more preferably a star, each time the sextant is used.<ref name="q939"/> The practice of taking celestial observations from the deck of a rolling ship, often through cloud cover and with a hazy horizon, is by far the most challenging part of celestial navigation.<ref>{{Cite web |title=How Did Aviators "Shoot" the Sun and Stars? {{!}} Time and Navigation |url=http://timeandnavigation.si.edu/navigating-air/challenges/overcoming-challenges/celestial-navigation |access-date=2023-06-12 |website=timeandnavigation.si.edu |language=en}}</ref>

====Bubble octant====
Until the widespread usage of technologies such as inertial navigation systems, [[VHF omnidirectional range]] and GNSS, air navigators used the [[Bubble octant]] or bubble sextant.<ref name="t804">{{cite book | author=United States. Navy Department | title=Air Navigation: Flying Training | publisher=Air Training Command in accordance with AFR 5-6 | series=Air Force AFM | year=1983 | url=https://books.google.com/books?id=Te-mFCmtDOwC | access-date=2025-02-25 | page=16-1}}</ref> Using this instrument to take sights, mathematical calculations could then be carried out to determine the past position of the aircraft.<ref name="m792">{{cite book | last=Wolper | first=James S. | title=Understanding Mathematics for Aircraft Navigation | publisher=McGraw Hill Professional | date=2001-06-13 | isbn=978-0-07-163879-1 | page=109-150}}</ref>

===Inertial navigation===
{{Further|Inertial navigation system}}

[[Inertial navigation system]] (INS) is a [[dead reckoning]] type of navigation system that computes its position based on motion sensors.<ref name="k075">{{cite book | last=Jekeli | first=Christopher | title=Inertial Navigation Systems with Geodetic Applications | publisher=Walter de Gruyter | publication-place=Berlin | date=2012-10-25 | isbn=978-3-11-080023-4 | page=113}}</ref> Before actually navigating, the initial latitude and longitude and the INS's physical orientation relative to the Earth (e.g., north and level) are established. After alignment, an INS receives impulses from motion detectors that measure (a) the acceleration along three axes (accelerometers), and (b) rate of rotation about three orthogonal axes (gyroscopes). These enable an INS to continually and accurately calculate its current latitude and longitude (and often velocity).

Advantages over other navigation systems are that, once aligned, an INS does not require outside information. An INS is not affected by adverse weather conditions and it cannot be detected or jammed. Its disadvantage is that since the current position is calculated solely from previous positions and motion sensors, its errors are cumulative, increasing at a rate roughly proportional to the time since the initial position was input. Inertial navigation systems must therefore be frequently corrected with a location 'fix' from some other type of navigation system.

The first inertial system is considered to be the V-2 guidance system deployed by the Germans in 1942. However, inertial sensors are traced to the early 19th century.<ref name="Tazartes">"An historical perspective on inertial navigation systems", Daniel Tazartes, ''2014 International Symposium on Inertial Sensors and Systems (ISISS)'',  Laguna Beach, CA</ref> The advantages INSs led their use in aircraft, missiles, surface ships and submarines. For example, the U.S. Navy developed the Ships Inertial Navigation System (SINS) during the [[Polaris missile]] program to ensure a reliable and accurate navigation system to initial its missile guidance systems. Inertial navigation systems were in wide use until [[satellite navigation]] systems (GPS) became available. INSs are still in common use on submarines (since GPS reception or other fix sources are not possible while submerged) and long-range missiles but are not now widely found elsewhere.<ref name="Jek296">{{cite book | last=Jekeli | first=Christopher | title=Inertial Navigation Systems with Geodetic Applications | publisher=Walter de Gruyter | publication-place=Berlin | date=2012-10-25 | isbn=978-3-11-080023-4 | page=296}}</ref>

==== Space navigation ====
Not to be confused with satellite navigation, which depends upon satellites to function, space navigation refers to the navigation of spacecraft themselves. This has historically been achieved (during the [[Apollo program]]) via a [[Apollo Guidance Computer|navigational computer]], an Inertial navigation system, and via celestial inputs entered by astronauts which were recorded by sextant and telescope. Space rated navigational computers, like those found on Apollo and later missions, are designed to be hardened against possible data corruption from radiation. Navigation in space has three main components: the use of a suitable reference trajectory which describes the planned flight path of the spacecraft, monitoring the actual spacecraft position while the mission is in flight (orbit determination) and creating maneuvers to bring the spacecraft back to the reference trajectory as required (flight path control).<ref name="r120">{{cite web | title=Chapter 13: Navigation | website=NASA Science | date=2023-07-20 | url=https://science.nasa.gov/learn/basics-of-space-flight/chapter13-1/ | access-date=2025-02-24}}</ref>

Another possibility that has been explored for deep space navigation is [[Pulsar-based navigation|Pulsar navigation]], which compares the X-ray bursts from a collection of known pulsars in order to determine the position of a spacecraft. This method has been tested by multiple space agencies, such as [[NASA]] and [[European Space Agency|ESA]].<ref>{{Cite web |title=GSP Executive Summary |url=https://gsp.esa.int/documents/10192/43064675/C4000106174ExS.pdf/8a26a304-9d5f-447d-aa75-bc0c955a4b78 |url-status=dead |website=gsp.esa.int |access-date=2022-12-07 |archive-date=2017-03-16 |archive-url=https://web.archive.org/web/20170316044511/http://gsp.esa.int/documents/10192/43064675/C4000106174ExS.pdf/8a26a304-9d5f-447d-aa75-bc0c955a4b78 }}</ref><ref>{{Cite web |author1=Rafi Letzter |date=2018-04-16 |title=NASA's Got a Plan for a 'Galactic Positioning System' to Save Astronauts Lost in Space |url=https://www.livescience.com/62309-galactic-positioning-system-nasa.html |access-date=2022-12-07 |website=livescience.com |language=en}}</ref>

===Electronic navigation===
[[File:Navigation_system_on_a_merchant_ship_2.jpg|thumb|right|Radar ranges and bearings can be used to determine a position.]]
====Radar navigation====
{{Further|Radar navigation|Doppler radar#navigation}}

Radars can be used for navigation and [[Marine radar|marine radars]] are commonly fitted to ships for navigation at sea.<ref name="e303">{{cite book | title=Safe Nav Watch | publisher=[[Witherby Publishing Group]] | publication-place=Livingston, Scotland | date=2023 | isbn=978-1-914993-46-6 | page=37}}</ref> Radar is an effective aid to navigation because it provides ranges and bearings to objects within range of the radar scanner.<ref name="Anwar133">{{cite book | last = Anwar | first = Nadeem | title = Navigation Advanced for Mates and Masters | edition = 2nd | date = 2015 | publisher = [[Witherby Publishing Group]] | location = Edinburgh | pages=133–139 |isbn = 978-1-85609-627-0}}</ref> When a vessel (ship or boat) is within radar range of land or fixed objects (such as special radar aids to navigation and navigation marks) the navigator can take distances and angular bearings to charted objects and use these to establish arcs of position and lines of position on a chart.<ref name="chap744">Maloney, 2003:744.</ref> A fix consisting of only radar information is called a radar fix.<ref name="bow816">Bowditch, 2002:816.</ref> Types of radar fixes include "range and bearing to a single object,"<ref name="nima163">National Imagery and Mapping Agency, 2001:163.</ref> "two or more bearings,"<ref name="nima163"/> "tangent bearings,"<ref name="nima163"/> and "two or more ranges."<ref name="nima163"/> Radar can also be used with [[ECDIS]] as a means of position fixing with the radar image or distance/bearing overlaid onto an [[Electronic navigational chart|Electronic nautical chart]].<ref name="Anwar133"/>

Parallel indexing is a technique defined by William Burger in the 1957 book ''The Radar Observer's Handbook''.<ref name="nima169">National Imagery and Mapping Agency, 2001:169.</ref> This technique involves creating a line on the screen that is parallel to the ship's course, but offset to the left or right by some distance.<ref name="nima169"/> This parallel line allows the navigator to maintain a given distance away from [[navigational hazard|hazards]].<ref name="nima169"/> The line on the radar screen is set to a specific distance and angle, then the ship's position relative to the parallel line is observed. This can provide an immediate reference to the navigator as to whether the ship is on or off its intended course for navigation.<ref name="Victor">{{cite book | last = Victor| first = Alain| title = Parallel Index Techniques in Restricted Waters -| edition = 2nd | date = 2020 | publisher = [[Witherby Publishing Group]] | location = Edinburgh |isbn = 9781856099165}}</ref>

Other techniques that are less used in general navigation have been developed for special situations. One, known as the "contour method," involves marking a transparent plastic template on the radar screen and moving it to the chart to fix a position.<ref name="nima164">National Imagery and Mapping Agency, 2001:164.</ref> Another special technique, known as the Franklin Continuous Radar Plot Technique, involves drawing the path a radar object should follow on the radar display if the ship stays on its planned course.<ref name="nima182">National Imagery and Mapping Agency, 2001:182.</ref> During the transit, the navigator can check that the ship is on track by checking that the pip lies on the drawn line.<ref name="nima182"/>

====Radio navigation====
{{main|Radio navigation|Radio direction finder}}
[[File:Accuracy of Navigation Systems.svg|thumb|upright=1.2]]
A radio direction finder or RDF is a device for finding the direction to a [[radio]] source. Due to radio's ability to travel very long distances "over the horizon", it makes a particularly good navigation system for ships and aircraft that might be flying at a distance from land. RDFs works by rotating a directional [[Antenna (electronics)|antenna]] and listening for the direction in which the signal from a known station comes through most strongly. This sort of system was widely used in the 1930s and 1940s. RDF antennas are easy to spot on [[Germany|German]] [[World War II]] aircraft, as loops under the rear section of the fuselage, whereas most [[United States|US]] aircraft enclosed the antenna in a small teardrop-shaped fairing.

In navigational applications, RDF signals are provided in the form of ''radio beacons'', the radio version of a [[lighthouse]]. The signal is typically a simple [[Amplitude modulation|AM]] broadcast of a [[morse code]] series of letters, which the RDF can tune in to see if the beacon is "on the air". Most modern detectors can also tune in any commercial radio stations, which is particularly useful due to their high power and location near major cities.

[[Decca Navigator System|Decca]], [[OMEGA Navigation System|OMEGA]], and [[LORAN-C]] are three similar hyperbolic navigation systems. Decca was a [[hyperbola|hyperbolic]] [[low frequency]] [[radio navigation]] system (also known as [[multilateration]]) that was first deployed during [[World War II]] when the Allied forces needed a system which could be used to achieve accurate landings. As was the case with [[Loran C]], its primary use was for ship navigation in coastal waters. Fishing vessels were major post-war users, but it was also used on aircraft, including a very early (1949) application of moving-map displays. The system was deployed in the North Sea and was used by helicopters operating to [[oil platform]]s.

The OMEGA Navigation System was the first truly global [[radio navigation]] system for aircraft, operated by the [[United States]] in cooperation with six partner nations. OMEGA was developed by the United States Navy for military aviation users. It was approved for development in 1968 and promised a true worldwide oceanic coverage capability with only eight transmitters and the ability to achieve a four-mile (6&nbsp;km) accuracy when fixing a position. Initially, the system was to be used for navigating nuclear bombers across the North Pole to Russia. Later, it was found useful for submarines.<ref>{{Cite web |last=Proc |first=Jerry |title=Omega |url=http://www.jproc.ca/hyperbolic/omega.html |access-date=2024-11-22 |website=www.jproc.ca}}</ref> Due to the success of the [[Global Positioning System]] the use of Omega declined during the 1990s, to a point where the cost of operating Omega could no longer be justified. Omega was terminated on September 30, 1997, and all stations ceased operation.

LORAN is a terrestrial [[radio-navigation|navigation]] system using [[low frequency]] radio transmitters that use the time interval between radio signals received from three or more stations to determine the position of a ship or aircraft. The current version of LORAN in common use is LORAN-C, which operates in the [[low frequency]] portion of the EM spectrum from 90 to 110 [[Hertz|kHz]]. Many nations are users of the system, including the [[United States]], [[Japan]], and several European countries. Russia uses a nearly exact system in the same frequency range, called [[CHAYKA]]. LORAN use is in steep decline, with [[Global Positioning System|GPS]] being the primary replacement. However, there are attempts to enhance and re-popularize LORAN. LORAN signals are less susceptible to interference and can penetrate better into foliage and buildings than GPS signals.

====Satellite navigation====
{{Further|Satellite navigation}}
[[File:Furuno Electric GPS Navigator GP-80 at Greenpeace's Rainbow Warrior II 20110108.jpg|thumb|right|A ship's Furuno GNSS receiver showing a GPS position]]
A GNSS allow small [[electronics|electronic]] receivers to determine their location ([[longitude]], [[latitude]], and [[altitude]]) within a few meters using [[time signal]]s transmitted along a [[Line-of-sight propagation|line of sight]] by [[radio]] from [[satellite]]s.<ref name="SafeNavWatchGNSS"/> Positions derived can then be used with maps and charts for [[satellite navigation]]. Since the first experimental satellite was launched in 1978, GNSS have become an indispensable aid to navigation around the world, and an important tool for [[cartography|map-making]] and [[surveying|land surveying]]. GNSS also provides a precise [[time transfer|time reference]] used in many applications including scientific study of [[earthquake]]s, and [[synchronization]] of telecommunications networks. Global Navigation Satellite System or GNSS is the term for satellite navigation systems that provide positioning with global coverage.<ref name="SafeNavWatchGNSS">{{cite book | title=Safe Nav Watch | publisher=[[Witherby Publishing Group]] | publication-place=Livingston, Scotland | date=2023 | isbn=978-1-914993-46-6 | page=34-36}}</ref>  The first system, GPS was developed by the [[United States Department of Defense]] and officially named NAVSTAR GPS (NAVigation Satellite Timing And Ranging Global Positioning System). The [[satellite constellation]] is managed by the [[United States Air Force]] [[50th Space Wing]]. The cost of maintaining the system is approximately [[United States dollar|US$]]750 million per year,<ref name="GPS overview from JPO">[http://gps.losangeles.af.mil/jpo/gpsoverview.htm GPS Overview from the NAVSTAR Joint Program Office] {{webarchive|url=https://web.archive.org/web/20060928042828/http://gps.losangeles.af.mil/jpo/gpsoverview.htm |date=2006-09-28 }}. Accessed December 15, 2006.</ref> including the replacement of aging satellites, and research and development. Despite this fact, GPS is free for civilian use as a [[Public good (economics)|public good]].

With improvements in technology and developments globally, as of 2024, there are several different operational GNSS now available for navigation by the public. These include the [[United States]] NAVSTAR [[Global Positioning System]] (GPS), the [[Russia]]n [[GLONASS]], the [[European Union]]'s [[Galileo positioning system]] and the [[Beidou navigation system]] of [[China]].<ref name="SafeNavWatchGNSS"/> The different global systems have varying differences in accuracy but stated positions are normally in the range of between 1 and 10 metres accuracy depending on system and on that system's satellite coverage.<ref name="SafeNavWatchGNSS"/> As a result over 100 satellites are in [[medium Earth orbit]], transmitting signals allowing GNSS receivers to determine the receiver's [[geographic location|location]], speed and direction.<ref name="SafeNavWatchGNSS"/> There are also several regional GNSS systems available for navigation, including the [[Indian Regional Navigation Satellite System]] and the [[Quasi-Zenith Satellite System]]. However, not all GNSS receivers are capable of operating with these systems and older GNSS receivers, such as on old ships may not be capable of receiving all of the GNSS now available to users.<ref name="SafeNavWatchGNSS"/>

Modern [[smartphones]] act as personal [[GNSS]] navigators for civilians who own them. Overuse of these devices, whether in the vehicle or on foot, can lead to a relative inability to learn about navigated environments, resulting in sub-optimal navigation abilities when and if these devices become unavailable.<ref>{{Cite journal|last=Gardony|first=Aaron L|date=April 2013|title=How Navigational Aids Impair Spatial Memory: Evidence for Divided Attention|journal=Spatial Cognition & Computation|volume=13|issue=4|pages=319–350|doi=10.1080/13875868.2013.792821|bibcode=2013SpCC...13..319G |s2cid=7905481}}</ref><ref>{{Cite journal|last=Gardony|first=Aaron L.|date=June 2015|title=Navigational Aids and Spatial Memory Impairment: The Role of Divided Attention|journal=Spatial Cognition & Computation|volume=15|issue=4|pages=246–284|doi=10.1080/13875868.2015.1059432|bibcode=2015SpCC...15..246G |s2cid=42070277}}</ref><ref>{{Cite book|title=Spatial Information Theory|last=Winter|first=Stephen|publisher=Springer Berlin|year=2007|isbn=978-3540747888|location=Heidelberg, Germany|pages=238–254}}</ref> Typically a [[compass]] is also provided to determine direction when not moving.

==== Acoustic navigation ====
{{main|Sonar|Acoustic location}}

[[Acoustic location]] is a method of navigation by the use of acoustic positioning systems which determine the position of an object by using [[sound waves]]. It is primarily used by [[submarines]] and ships fitted with [[sonar]] and similar transducer based technologies.<ref name="l124">{{cite book | last1=Christ | first1=Robert D. | last2=Wernli | first2=Robert L. | title=The ROV Manual | chapter=Practical Applications | publisher=Elsevier | year=2014 | isbn=978-0-08-098288-5 | doi=10.1016/b978-0-08-098288-5.00021-x | pages=561–599}}</ref><ref name="k448">{{cite web | title=Long Range Acoustic Communications and Navigation in the Arctic | url=https://acomms.whoi.edu/wp-content/uploads/sites/20/2016/11/FreitagBallPartanKoskiSingh_Arctic_2015.pdf | publisher=Woods Hole Oceanographic Institution |access-date=2025-02-24}}</ref> [[Underwater acoustic positioning system]]s are also commonly used by divers and [[Remotely operated underwater vehicle]]s, specifically the [[Long baseline acoustic positioning system]], the [[Short baseline acoustic positioning system]] and the [[Ultra-short baseline acoustic positioning system]].<ref name="l124"/><ref name="c798">{{cite web | title=Precision acoustic navigation for remotely operated vehicles (ROV) | url=https://bibliotekanauki.pl/articles/985799.pdf | publisher=Hydroacoustics, 2005 - bibliotekanauki.pl| access-date=2025-02-24}}</ref>

==Navigation processes==
=== Passage planning ===
{{Main|Passage planning}}
[[File:Exval.jpeg|thumb|right|Poor passage planning and deviation from the plan can lead to groundings, ship damage and cargo loss.]]Passage planning or voyage planning is a procedure to develop a complete description of vessel's voyage from start to finish. The plan includes leaving the dock and harbor area, the en route portion of a voyage, approaching the destination, and [[Mooring (watercraft)|mooring]]. According to international law, a vessel's [[captain (nautical)|captain]] is legally responsible for passage planning,<ref name="reg34">{{cite web
 | title = Regulation 34 – Safe Navigation
 | url = https://mcanet.mcga.gov.uk/public/c4/solas/solas_v/Regulations/regulation34.htm
 | work = IMO RESOLUTION A.893(21) adopted on 25 November 1999
 | access-date = March 26, 2007
 | archive-date = 27 September 2007
 | archive-url = https://web.archive.org/web/20070927002958/https://mcanet.mcga.gov.uk/public/c4/solas/solas_v/Regulations/regulation34.htm
 | url-status = dead
 }}</ref> however on larger vessels, the task will be delegated to the ship's [[navigator]].<ref name="annex24">{{cite web
 | title = ANNEX 24 – MCA Guidance Notes for Voyage Planning
 | url = https://mcanet.mcga.gov.uk/public/c4/solas/solas_v/Annexes/Annex24.htm
 | work = IMO RESOLUTION A.893(21) adopted on 25 November 1999
 | access-date = March 26, 2007
 | archive-date = 27 September 2007
 | archive-url = https://web.archive.org/web/20070927002748/https://mcanet.mcga.gov.uk/public/c4/solas/solas_v/Annexes/Annex24.htm
 | url-status = dead
 }}</ref>

Studies show that [[human error]] is a factor in 80 percent of navigational accidents and that in many cases the human making the error had access to information that could have prevented the accident.<ref name="annex24"/> The practice of voyage planning has evolved from penciling lines on [[nautical chart]]s to a process of [[risk management]].<ref name="annex24"/>

Passage planning consists of four stages: appraisal, planning, execution, and monitoring,<ref name="annex24"/> which are specified in ''[[International Maritime Organization]] Resolution A.893(21), Guidelines For Voyage Planning,''<ref name="annex25">{{cite web
 | title = ANNEX 25 – MCA Guidance Notes for Voyage Planning
 | url = https://mcanet.mcga.gov.uk/public/c4/solas/solas_v/Annexes/Annex25.htm
 | work = IMO RESOLUTION A.893(21) adopted on 25 November 1999
 | access-date = January 28, 2011
 | archive-date = 24 July 2011
 | archive-url = https://web.archive.org/web/20110724014258/https://mcanet.mcga.gov.uk/public/c4/solas/solas_v/Annexes/Annex25.htm
 | url-status = dead
 }}</ref> and these guidelines are reflected in the local laws of IMO signatory countries (for example, Title 33 of the U.S. [[Code of Federal Regulations]]), and a number of professional books or publications. There are some fifty elements of a comprehensive passage plan depending on the size and type of vessel.

The appraisal stage deals with the collection of information relevant to the proposed voyage as well as ascertaining risks and assessing the key features of the voyage. This will involve considering the type of navigation required e.g. [[Ice navigation]], the region the ship will be passing through and the [[hydrography|hydrographic]] information on the route. In the next stage, the written plan is created. The third stage is the execution of the finalised voyage plan, taking into account any special circumstances which may arise such as changes in the weather, which may require the plan to be reviewed or altered. The final stage of passage planning consists of monitoring the vessel's progress in relation to the plan and responding to deviations and unforeseen circumstances.

=== Integrated bridge systems ===
[[File:Integriertes Brückensystem.jpg|thumb|Integrated Bridge System, integrated on an Offshore Service Ship]]
Electronic integrated bridge concepts are driving future navigation system planning.<ref name="bow1"/> Integrated systems take inputs from various ship sensors, electronically display positioning information, and provide control signals required to maintain a vessel on a preset course.<ref name="bow1"/> The navigator becomes a system manager, choosing system presets, interpreting system output, and monitoring vessel response.<ref name="bow1"/>

[[File:Two ship's officers 'shoot' in one morning with the sextant, the sun altitude.jpg|thumb|Two ship's officers practicing traditional celestial navigation taking a sunsight by sextant]]
===Ships and similar vessels===
====One day's work in traditional navigation====
In traditional marine navigation, one day's work in navigation is a minimal set of tasks consistent with prudent celestial navigation. The definition and processes vary on military and civilian vessels, and from ship to ship, but the traditional method takes a form resembling:<ref name="mmoh6-18">Turpin and McEwen, 1980:6–18.</ref>
# Maintain a continuous dead reckoning plot.
# Take two or more star observations at morning twilight for a celestial fix (prudent to observe six stars).
# Morning Sun observation. Can be taken on or near [[prime vertical]] for longitude, or at any time for a line of position.
# Determine compass error by azimuth observation of the Sun.
# Computation of the interval to noon, watch time of local apparent noon, and constants for meridian or ex-meridian sights.
# Noontime meridian or ex-meridian observation of the Sun for noon latitude line. Running fix or cross with Venus line for noon fix.
# Noontime determination the day's run and day's set and drift.
# At least one afternoon Sun line, in case the stars are not visible at twilight.
# Determine compass error by azimuth observation of the Sun.
# Take two or more star observations at evening twilight for a celestial fix (prudent to observe six stars).

Navigation on ships is usually always conducted on the [[Bridge (nautical)#Navigation station|bridge]]. It may also take place in adjacent space, where chart tables and publications are available. However, increasingly traditional navigation processes have been replaced with technological processes for marine navigation using GNSS and marine radar.

===Land navigation===
Navigation for cars and other land-based travel typically uses [[map]]s, [[landmark]]s, and in recent times [[Navigation system|computer navigation]] ("[[satnav]]", short for satellite navigation), as well as any means available on water.

Computerized navigation commonly relies on [[GPS]] for current location information, a [[electronic map|navigational map database]] of roads and navigable routes, and uses [[algorithm]]s related to the [[shortest path problem]] to identify optimal routes.

Pedestrian navigation is involved in [[orienteering]], [[Land navigation|land navigation (military)]], and [[wayfinding]].

===Underwater navigation===
{{main|Diver navigation|Submarine navigation}}
Submariners, divers, [[Remotely operated underwater vehicle|remotely operated underwater vehicles]] (ROVs) and other underwater craft carry out underwater navigation by a variety of methods and processes including GNSS, radar navigation and sonar/acoustic position fixing.<ref name="l373">{{cite web | last1=Homeier | first1=Lieutenant Matthew G. | last2=Navy | first2=U.S. | title=Navigate by the Stars—From Beneath the Waves | website=U.S. Naval Institute | date=2021-10-01 | url=https://www.usni.org/magazines/proceedings/2021/october/navigate-stars-beneath-waves | access-date=2025-02-24}}</ref><ref name="f657">{{cite book | last1=Christ | first1=Robert D. | last2=Sr. | first2=Robert L. Wernli | title=The ROV Manual | publisher=Butterworth-Heinemann | publication-place=Amsterdam | date=2013-10-30 | isbn=978-0-08-098288-5}}</ref>

===Artificial intelligence===
[[Artificial intelligence]] can be utilised to assist with planning, problem-serving and decision-making processes in navigation.<ref name="e302">{{cite conference | last=Duffany | first=Jeffrey L. | title=2010 2nd International Conference on Software Technology and Engineering | chapter=Artificial intelligence in GPS navigation systems | publisher=IEEE | year=2010 | doi=10.1109/icste.2010.5608862 | page=| isbn=978-1-4244-8667-0 }}</ref><ref name="a073">{{cite book | last1=Jindal | first1=R. | last2=Mittal | first2=S.K. | title=Artificial Intelligence: Application and Real-Time Use | publisher=Codex International Publishers | year=2023 | isbn=978-93-94799-24-0 | url=https://books.google.com/books?id=hKzEEAAAQBAJ&pg=PA45 | access-date=2025-02-24 | page=45}}</ref> This includes using AI in navigation systems such as GNSS as well as in general computing to assist with position fixing and monitoring from one position to another such as in vehicles, planes and cars.<ref name="t787">{{cite journal | last1=Viveiros | first1=Inês | last2=Silva | first2=Hélder | last3=Andrade | first3=Yuri | last4=Pendão | first4=Cristiano | title=Smart GNSS Integrity Monitoring for Road Vehicles: An Overview of AI Methods | journal=IEEE Access | volume=13 | date=2025 | issn=2169-3536 | doi=10.1109/ACCESS.2025.3534659 | doi-access=free | pages=20278–20296| bibcode=2025IEEEA..1320278V }}</ref><ref name="f467">{{cite book | last=Yu | first=K. | title=Positioning and Navigation Using Machine Learning Methods | publisher=Springer Nature Singapore | series=Navigation: Science and Technology | year=2024 | isbn=978-981--976199-9 | url=https://books.google.com/books?id=ovYhEQAAQBAJ&pg=PA32 | access-date=2025-02-24 | page=32}}</ref>

==Standards, training and organisations==

Professional standards for navigation depend on the type of navigation and vary by country. For marine navigation, [[Merchant Navy]] [[Deck department|deck officers]] are trained and internationally certified according to the [[STCW Convention]].<ref name="STCW">{{cite book |title=Standards of Training and Certification of Watchkeeping' (STCW) Convention |publisher= [[International Maritime Organization]]|date= 2010 }}</ref> Leisure and amateur mariners may undertake lessons in navigation at local/regional training schools. [[Navy|Naval]] officers receive navigation training as part of their naval training.

In land navigation, courses and training is often provided to young persons as part of general or extra-curricular education. Land navigation is also an essential part of army training. Additionally, organisations such as the [[Scouting|Scouts]] and [[The Duke of Edinburgh's Award|DoE programme]] teach navigation to their students. [[Orienteering]] organisations are a type of sports that require navigational skills using a map and compass to navigate from point to point in diverse and usually unfamiliar terrain whilst moving at speed.<ref>{{cite web
 |url         = http://www.orienteering.ca/about_orienteering.htm
 |title       = About Orienteering
 |publisher   = The Canadian Orienteering Federation
 |access-date  = 2008-08-11
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20081002091244/http://www.orienteering.ca/about_orienteering.htm
 |archive-date = 2008-10-02
}}</ref>

In aviation, pilots undertake [[air navigation]] training as part of learning to fly.

Professional organisations also assist to encourage improvements in navigation or bring together navigators in learned environments. The [[Royal Institute of Navigation]] (RIN) is a [[learned society]] with charitable status, aimed at furthering the development of navigation on land and sea, in the air and in space. It was founded in 1947 as a forum for mariners, pilots, engineers and academics to compare their experiences and exchange information.<ref>{{Cite journal|year=2016|title=The Royal Institute of Navigation - Aims and Objects|journal=Journal of Navigation|volume=69|issue=66|pages= b1–b2 }}</ref> In the US, the [[Institute of Navigation]] (ION) is a non-profit professional organisation advancing the art and science of positioning, navigation and timing.<ref name="ION">{{cite web
 | title =  The Institute of Navigation
 | url = https://www.ion.org/about/index.cfm
 | access-date=February 6, 2020}}</ref>

===Publications===
[[File:Bowditch 1910 Figure 2 Compass Rose navigatorpracti00bowdrich 0021.jpg|thumb|right|An illustration showing a compass used for navigation from Bowditch's American Practical Navigator]]
Numerous [[nautical publications]] are available on navigation, which are published by professional sources all over the world. In the UK, the [[United Kingdom Hydrographic Office]], the [[Witherby Publishing Group]] and the [[Nautical Institute]] provide numerous navigational publications, including the comprehensive Admiralty Manual of Navigation.<ref name="Manual of Navigation">{{cite web
 | title =  The Admiralty Manual of Navigation
 | publisher = The Nautical Institute
 | url = https://www.nautinst.org/shop/the-admiralty-manual-of-navigation-vol-1-principles-of-navigation.html
 | access-date=February 6, 2020}}</ref><ref name="Navigation, Witherbys">{{cite web
 | title =  Navigation Publications
 | publisher = Witherby Publishing Group
 | url = https://www.witherbyseamanship.com/categories/navigation.html
 | access-date=February 6, 2020}}</ref>

In the US, [[Bowditch's American Practical Navigator]] is a free available encyclopedia of navigation issued by the US Government.<ref name="Bowditch1">{{cite web
 | title =  The American Practical Navigator
 | url = https://en.wikisource.org/wiki/The_American_Practical_Navigator
 | access-date=February 6, 2020}}</ref>

==Navigation in spatial cognition==
Navigation is an essential everyday activity that involves a series of abilities that help humans and animals to locate, track, and follow paths in order to arrive at different destinations.<ref>{{Cite journal |date=November 2017 |title=Focus on spatial cognition |url=https://www.nature.com/articles/nn.4666 |journal=Nature Neuroscience |language=en |volume=20 |issue=11 |pages=1431 |doi=10.1038/nn.4666 |pmid=29073640 |s2cid=205441391 |issn=1546-1726}}</ref><ref>{{Cite journal |last1=Wolbers |first1=Thomas |last2=Hegarty |first2=Mary |date=March 2010 |title=What determines our navigational abilities? |url=https://linkinghub.elsevier.com/retrieve/pii/S1364661310000021 |journal=Trends in Cognitive Sciences |language=en |volume=14 |issue=3 |pages=138–146 |doi=10.1016/j.tics.2010.01.001|pmid=20138795 |s2cid=15142890 |url-access=subscription }}</ref> Navigation, in [[spatial cognition]], allows for acquiring information about the environment by using the body and [[Landmark|landmarks]] of the environment as [[Frame of reference|frames of references]] to create [[Mental representation|mental representations]] of our environment, also known as a [[cognitive map]]. Humans navigate by transitioning between different spaces and coordinating both [[Frame of reference|egocentric and allocentric frames of reference]].

Navigation can be distinguished into two sptial components: locomotion and wayfinding.<ref name=":0">{{Citation |last=Montello |first=Daniel R. |title=Navigation |date=2005-07-18 |url=https://www.cambridge.org/core/product/identifier/9780511610448%23c80710-dcz-s9i-re2-gh5/type/book_part |work=The Cambridge Handbook of Visuospatial Thinking |pages=257–294 |editor-last=Shah |editor-first=Priti |edition=1 |publisher=Cambridge University Press |doi=10.1017/cbo9780511610448.008 |isbn=978-0-511-61044-8 |access-date=2022-05-06 |editor2-last=Miyake |editor2-first=Akira|url-access=subscription }}</ref> Locomotion is the process of movement from one place to another, both in humans and in animals. Locomotion helps you understand an environment by moving through a space in order to create a mental representation of it.<ref>{{Cite web |title=APA Dictionary of Psychology/Locomotion |url=https://dictionary.apa.org/locomotion |access-date=2022-05-06 |website=dictionary.apa.org |language=en}}</ref> [[Wayfinding]] is defined as an active process of following or deciding upon a path between one place to another through mental representations.<ref>{{Cite journal |last=GOLLEDGE |first=Reginald G. |date=December 2000 |title=Cognitive Maps, Spatial Abilities, and Human Wayfinding |url=https://mural.maynoothuniversity.ie/7262/1/RK-Cognitive.pdf |journal=Geographical Review of Japan |volume=73 |pages=93–104}}</ref> It involves processes such as representation, planning and decision which help to avoid obstacles, to stay on course or to regulate pace when approaching particular objects.<ref name=":0" /><ref>{{Cite journal |last=Tolman |first=Edward C. |date=1948 |title=Cognitive maps in rats and men. |url=http://doi.apa.org/getdoi.cfm?doi=10.1037/h0061626 |journal=Psychological Review |language=en |volume=55 |issue=4 |pages=189–208 |doi=10.1037/h0061626 |pmid=18870876 |issn=1939-1471|url-access=subscription }}</ref>

Navigation and wayfinding can be approached in the [[Spatial cognition|environmental space]]. According to [[Daniel R. Montello|Dan Montello]]’s [[Spatial cognition|space classification]], there are four levels of space with the third being the environmental space. The environmental space represents a very large space, like a city, and can only be fully explored through movement since all objects and space are not directly visible.<ref name=":1">{{Cite book |last=Denis |first=Michel |url=https://www.taylorfrancis.com/books/9781351596183 |title=Space and Spatial Cognition: A Multidisciplinary Perspective |date=2017-11-13 |publisher=Routledge |isbn=978-1-315-10380-8 |edition=1 |language=en |doi=10.4324/9781315103808}}</ref> Also [[Barbara Tversky]] systematized the space, but this time taking into consideration the three dimensions that correspond to the [[Axis (anatomy)|axes]] of the human body and its extensions: above/below, front/back and left/right. Tversky ultimately proposed a fourfold classification of navigable space: space of the body, space around the body, space of navigation and space of graphics.<ref>{{Cite journal |last=Tversky |first=Barbara |date=January 2003 |title=Structures Of Mental Spaces: How People Think About Space |url=http://journals.sagepub.com/doi/10.1177/0013916502238865 |journal=Environment and Behavior |language=en |volume=35 |issue=1 |pages=66–80 |doi=10.1177/0013916502238865 |s2cid=16647328 |issn=0013-9165|url-access=subscription }}</ref>

===Wayfinding===
There are two types of wayfinding in navigation: aided and unaided.<ref name=":1" /> Aided wayfinding requires a person to use various types of [[Media (communication)|media]], such as [[Map|maps]], [[Global Positioning System|GPS]], [[Direction, position, or indication sign|directional signage]], etc., in their navigation process which generally involves low spatial reasoning and is less cognitively demanding. Unaided wayfinding involves no such devices for the person who is navigating.<ref name=":1" /> Unaided wayfinding can be subdivided into a [[taxonomy]] of tasks depending on whether it is undirected or directed, which basically makes the distinction of whether there is a precise destination or not: undirected wayfinding means that a person is simply [[Exploration|exploring]] an environment for pleasure without any set destination.<ref name=":2">{{Cite journal |last1=Wiener |first1=Jan M. |last2=Büchner |first2=Simon J. |last3=Hölscher |first3=Christoph |date=2009-05-20 |title=Taxonomy of Human Wayfinding Tasks: A Knowledge-Based Approach |url=http://www.tandfonline.com/doi/abs/10.1080/13875860902906496 |journal=Spatial Cognition & Computation |language=en |volume=9 |issue=2 |pages=152–165 |doi=10.1080/13875860902906496 |bibcode=2009SpCC....9..152W |s2cid=16529538 |issn=1387-5868|url-access=subscription }}</ref>

Directed wayfinding, instead, can be further subdivided into search vs. target approximation.<ref name=":2" /> Search means that a person does not know where the destination is located and must find it either in an unfamiliar environment, which is labeled as an uninformed search, or in a familiar environment, labeled as an informed search. In target approximation, on the other hand, the location of the destination is known to the navigator but a further distinction is made based on whether the navigator knows how to arrive or not to the destination. Path following means that the environment, the path, and the destination are all known which means that the navigator simply follows the path they already know and arrive at the destination without much thought. For example, when you are in your city and walking on the same path as you normally take from your house to your job or university.<ref name=":2" /> However, path finding means that the navigator knows where the destination is but does not know the route they have to take to arrive at the destination: you know where a specific store is but you do not know how to arrive there or what path to take. If the navigator does not know the environment, it is called path search which means that only the destination is known while neither the path nor the environment is: you are in a new city and need to arrive at the train station but do not know how to get there.<ref name=":2" /> Path planning, on the other hand, means that the navigator knows both where the destination is and is familiar with the environment so they only need to plan the route or path that they should take to arrive at their target. For example, if you are in your city and need to get to a specific store that you know the destination of but do not know the specific path you need to take to get there.<ref name=":2" />

== See also ==
{{Portal|Geography}}
* [[Robot navigation]]
* [[TVMDC]]
* [[Collision avoidance in transportation]]
* [[Spatial cognition#Navigation]]

==References==
{{Reflist}}

==Bibliography==
{{refbegin}}
* [https://en.wikisource.org/wiki/ Nathaniel Bowditch, ''The American Practical Navigator,'' (2002) by the United States government]
* {{cite book | last = Anwar | first = Nadeem | title = Navigation Advanced for Mates and Masters | edition = 2nd | date = 2015 | publisher = [[Witherby Publishing Group]] | location = Edinburgh | isbn = 978-1-85609-627-0}}
* {{cite book
 | last = Cutler
 | first = Thomas J.
 | title = Dutton's Nautical Navigation
 | edition = 15th
 | date = December 2003
 | publisher = Naval Institute Press
 | location = Annapolis, MD
 | isbn = 978-1-55750-248-3
}}
* {{cite book| author =Department of the Air Force| author-link =United States Air Force| title =Air Navigation| url =http://www.e-publishing.af.mil/pubfiles/af/11/afpam11-216/afpam11-216.pdf| access-date =2007-04-17| date =March 2001| publisher =Department of the Air Force| url-status=dead| archive-url =https://web.archive.org/web/20070325022639/http://www.e-publishing.af.mil/pubfiles/af/11/afpam11-216/afpam11-216.pdf| archive-date =2007-03-25}}
* {{cite book
 | last = Great Britain Ministry of Defence (Navy)
 | title = Admiralty Manual of Seamanship
 | publisher = [[The Stationery Office]]
 | year = 1995
 | isbn = 978-0-11-772696-3
}}
* {{cite book | last1=Gilardoni | first1=Eduardo O. | last2=Presedo | first2=Juan P. | title=Navigation in Shallow Waters | publisher=Witherbys | publication-place=Livingston, Scotland | date=2017 | isbn=978-1-85609-667-6}}
* {{cite book|author1=Bernhard Hofmann-Wellenhof|author2=K. Legat|author3=M. Wieser|title=Navigation: principles of positioning and guidance|url=https://books.google.com/books?id=losWr9UDRasC|access-date=7 February 2012|year=2003|publisher=Springer|isbn=978-3-211-00828-7}}
* {{cite book
 | last = Maloney
 | first = Elbert S.
 | title = Chapman Piloting and Seamanship
 | url = https://archive.org/details/chapmanpilotings00elbe_1
 | edition = 64th
 | date = December 2003
 | publisher = Hearst Communications Inc.
 | location = New York
 | isbn = 978-1-58816-089-8
 | url-access = registration
 }}
* {{cite book
 |author=National Imagery and Mapping Agency
 |author-link=National Imagery and Mapping Agency
 |title=Publication 1310: Radar Navigation and Maneuvering Board Manual
 |url=http://www.nga.mil/portal/site/maritime/
 |format=PDF
 |edition=7th
 |year=2001
 |publisher=U.S. Government Printing Office
 |location=Bethesda, MD
 |url-status=dead
 |archive-url=https://web.archive.org/web/20070307132409/http://www.nga.mil/portal/site/maritime/
 |archive-date=2007-03-07
}}
* {{cite book
 | last = Turpin
 | first = Edward A.
 | author2 = McEwen, William A.
 | title = Merchant Marine Officers' Handbook
 | edition = 4th
 | year = 1980
 | publisher = Cornell Maritime Press
 | location = Centreville, MD
 | isbn = 978-0-87033-056-8
}}
* {{Cite EB1911|wstitle=Navigation|volume=19|pages=284–298|first=William Robert|last=Martin}}
* {{Cite EB1911|wstitle=Pytheas|volume=22|pages=703–704|first1=Edward Herbert|last1=Bunbury|author-link=Edward Bunbury|first2=Charles Raymond|last2=Beazley|author-link2=Raymond Beazley}}
* {{Citation | last1 =Raol| first1 =Jitendra | last2 =Gopal | first2 =Ajith | year =2013 | title =Mobile Intelligent Autonomous Systems | url = https://books.google.com/books?id=HaS91phGuRQC&q=sanskrit+navgati&pg=PA141 | publisher = CRC Press Taylor and Francis Group |location=Boca Raton, FL | isbn =978-1-4398-6300-8 }}
* {{cite book | last=Williams | first=J. E. D. | title=From Sails to Satellites | publisher=Oxford University Press, USA | publication-place=Oxford | date=1992 | isbn=0-19-856387-6}}
{{refend}}

==External links==
{{wikiquote}}
{{Commons}}
{{Wikisource|Portal:Navigation}}
{{Wikivoyage}}
* [https://www.gutenberg.org/ebooks/27642 ''Lectures in Navigation''] by Ernest Gallaudet Draper
* [https://archive.today/20121208170816/http://alsworld.topcities.com/bwgg/index.html How to navigate with less than a compass or GPS] (archived 8 December 2012)

{{Geodesy navbox|state=uncollapsed}}
{{Orienteering|type=collapsed}}
{{Seamanship}}
{{Satellite navigation systems}}

{{Authority control}}

[[Category:Navigation| ]]
[[Category:Geodesy]]