Longitude and latitude and its transformation with coordinate system

reference ： The word of the day 20190306—— Longitude and latitude （longitude and latitude）_gis0911178 The blog of -CSDN Blog _longitude and latitude

One 、 The concept of longitude and latitude （longitude and latitude）

Longitude and latitude yes longitude And latitude The joint name of , Form a Coordinate system , be called Geographic coordinate system , It's a use of Three dimensional space Of sphere Come on Define space on earth Of Spherical coordinate system , Can mark any position on the earth .

1.1 longitude

  longitude It refers to passing through a place Longitude plane And prime meridian plane As a result Dihedral . stay East of the prime meridian The longitude of is called East longitude , West of the prime meridian Call The west longitude . Dongjingyong “E” Express , Western Classics “W” Express .

stay 1884 year Of International primary meridian Conference On Greenwich Of Meridian By Officially set as the starting point of longitude . East longitude 180° That is, the Western Scripture 180°, About equal to International Day exchange line , On both sides of the international day exchange line , The date differs by one day .

Positive east longitude , The west longitude is negative .

1.2 latitude

latitude It refers to making normal , This point normal And Equatorial plane Of Line surface angle , Its value is in 0 to 90 Between degrees . The latitude of the point north of the equator is called north latitude , Write it down as N; The latitude of the point south of the equator is called south latitude , Write it down as S.

North latitude by Positive numbers , South latitude by negative .

1.3 Basic order of magnitude

Every difference in longitude and latitude 1 degree , The distance is about 111km;

Every difference in longitude and latitude 1 branch , The distance is about 1.85km;

Every difference in longitude and latitude 1 second , The distance is about 0.031km;

1.4  How to generate longitude and latitude from satellite triangulation ？

reference ：

[1] Zhang Cuifang . GPS Design and verification of satellite positioning algorithm [D]. University of electronic technology , 2011.

[2]Bancroft, S. An Algebraic Solution of the GPS Equations[J]. IEEE Transactions on Aerospace & Electronic Systems, 1985, AES-21(1):56-59.

GPS The position of the satellite is measured by the ground monitoring station and then compiled into a message and injected into the satellite , Then the satellite releases the broadcast ephemeris . For users , The position of the satellite is calculated according to the navigation message of the satellite broadcast .

step 1： adopt GPS Satellite ephemeris solution satellite in the geocentric earth fixed coordinate system （WGS-84 Coordinate system ） Position in ;

step 2： adopt GPS The satellite ephemeris calculates the satellite speed ;

step 3： The least square method calculates the position of the receiver in the geocentric earth fixed coordinate system （WGS-84 Coordinate system ） Middle position ;

step 4： Calculate the speed of the receiver ;

step 5： Convert to latitude and longitude .

Two 、 Common geographic coordinate systems

reference ：CGJ02、BD09、 Xi'an 80、 Beijing 54、CGCS2000 Detailed explanation of common coordinate system _mrib The blog of -CSDN Blog _cgcs2000 Coordinate system

2.1 WGS-84 Coordinate system

WGS-84 Coordinate system _EagleLY5894 The blog of -CSDN Blog _wgs84 Coordinate system

WGS-84 Coordinate system （World Geodetic System One 1984 Coordinate System） It is a kind of established by the U.S. Department of defense Geocentric geostationary coordinate system , Global positioning system GPS Is based on WGS-84 In coordinate system .
WGS-84 Coordinate system The origin is the center of mass of the earth , Of space rectangular coordinate system Z Axis pointing BIH（1984.0） Defined Earth pole （CTP） Direction , The origin of international agreements CIO, It consists of IAU and IUGG Joint recommendation .X Axis pointing BIH Defined Zero meridian and CTP The intersection of the equator ,Y Axis and Z、X Shaft composition Right hand coordinate system .

                                        
WGS-84 The earth model established is a Standard ellipsoid .

                                                      

  among ： The semi major axis of the earth ：a ≡ 6378137.0 m ; The earth's short half axis ：b = 6356752 m .

3、 ... and 、 Code ： Latitude and longitude WGS-84 Coordinate system conversion （c++ Language version ）

Online longitude and latitude conversion tool _ Longitude, latitude, rotation, minutes and seconds _ Degrees, minutes and seconds to longitude and latitude format - Look at the map together

GPS Latitude and longitude 84 Coordinate system _telnetipc The blog of -CSDN Blog _ Longitude and latitude are converted to wgs84 Coordinate system

/**
* WGS84 Rotating geocentric coordinate system 
*  Longitude and latitude units ： degree ; Height unit ： rice 
**/
public static double[] WGS84toECEF(double latitude, double longitude, double height) {
		double X;
		double Y;
		double Z;
		double a = 6378137.0;% Company m
		double b = 6356752.31424518;% Company m
		double E = (a * a - b * b) / (a * a);
		double COSLAT = Math.cos(latitude * Math.PI / 180);
		double SINLAT = Math.sin(latitude * Math.PI / 180);
		double COSLONG = Math.cos(longitude * Math.PI / 180);
		double SINLONG = Math.sin(longitude * Math.PI / 180);
		double N = a / (Math.sqrt(1 - E * SINLAT * SINLAT));
		double NH = N + height;
		X = NH * COSLAT * COSLONG;
		Y = NH * COSLAT * SINLONG;
		Z = (b * b * N / (a * a) + height) * SINLAT;
		return new double[] { X, Y, Z };
	}

   /**
   *  The geocentric coordinate system turns WGS84
   */
	public static String ECEFtoWGS84(double x, double y, double z){
		double a, b, c, d;
		double Longitude;//  longitude 
		double Latitude;//  latitude 
		double Altitude;//  Altitude 
		double p, q;
		double N;
		a = 6378137.0;
		b = 6356752.31424518;
		c = Math.sqrt(((a * a) - (b * b)) / (a * a));
		d = Math.sqrt(((a * a) - (b * b)) / (b * b));
		p = Math.sqrt((x * x) + (y * y));
		q = Math.atan2((z * a), (p * b));
		Longitude = Math.atan2(y, x);
		Latitude = Math.atan2((z + (d * d) * b * Math.pow(Math.sin(q), 3)),
				(p - (c * c) * a * Math.pow(Math.cos(q), 3)));
		N = a / Math.sqrt(1 - ((c * c) * Math.pow(Math.sin(Latitude), 2)));
		Altitude = (p / Math.cos(Latitude)) - N;
		Longitude = Longitude * 180.0 / Math.PI;
		Latitude = Latitude * 180.0 / Math.PI;
		return Longitude + "," + Latitude + "," + Altitude;
	}

Four 、 Code ： Latitude and longitude WGS-84 Coordinate system conversion （Matlab Language version ）

%%  Latitude and longitude WGS84 Rectangular coordinate system 
%  Positive east longitude , The west longitude is negative 
%  North latitude is positive , The south latitude is negative 
%  Input parameters 1： latitude ; Input parameters 2： longitude ; Input parameters 3： Height 
%  Longitude and latitude units ： degree ; Height unit ： rice 
function [x,y,z]=LL2WGS84(latitude,longitude,height)
a = 6378137.0;% Company m
b = 6356752.31424518;% Company m
E = (a * a - b * b) / (a * a);
COSLAT = cos(latitude * pi / 180);
SINLAT = sin(latitude * pi / 180);
COSLONG = cos(longitude * pi / 180);
SINLONG = sin(longitude * pi / 180);
N = a / (sqrt(1 - E * SINLAT * SINLAT));
NH = N + height;
x = NH * COSLAT * COSLONG;
y = NH * COSLAT * SINLONG;
z = (b * b * N / (a * a) + height) * SINLAT;
end

%% WGS84 Rectangular coordinate system turns longitude and latitude 
%  Positive east longitude , The west longitude is negative 
%  North latitude is positive , The south latitude is negative 
%  Input parameters 1： latitude ; Input parameters 2： longitude ; Input parameters 3： Height 
%  Longitude and latitude units ： degree ; Height unit ： rice 
function [latitude,longitude,height]=WGS842LL(x,y,z)

a = 6378137.0;
b = 6356752.31424518;
c = sqrt(((a * a) - (b * b)) / (a * a));
d = sqrt(((a * a) - (b * b)) / (b * b));
p = sqrt((x * x) + (y * y));
q = atan((z * a)/ (p * b));
longitude = atan(y/x);
latitude = atan((z + (d * d) * b * sin(q)^3)/(p - (c * c) * a * cos(q)^3));
N = a / sqrt(1 - ((c * c) * sin(latitude)^2));
height = (p / cos(latitude)) - N;
longitude = longitude * 180.0 / pi;
latitude = latitude * 180.0 / pi;
end