Conversion relationship between coordinate systems (ECEF, LLA, ENU)

One Introduction to coordinate system

1 ECEF Coordinate system
Also called geocentric geostationary rectangular coordinate system . Its origin is the center of mass of the earth ,x The axis extends through the prime meridian （0 Longitude ） And the equator （0deglatitude） The intersection of . z The axis extends through the North Pole （ namely , Coincide with the earth's rotation axis ）. y The axis completes the right-hand coordinate system , Across the equator and 90 Longitude .

2 WGS-84 Coordinate system （LLA)
It is also called the longitude and latitude coordinate system ( longitude (longitude), latitude (latitude) And height (altitude)LLA Coordinate system )., Global geographic coordinate system 、 Geodetic coordinate system . It is the most widely used earth coordinate system , It gives the geodetic latitude of a point 、 The earth longitude and earth elevation tell us the position of the point in the earth more intuitively , Therefore, it is also called longitude latitude high coordinate system .WGS-84 In coordinate system X Axis pointing BIH( International time service )1984.0 Defined zero meridian plane (Greenwich) And agreement earth pole (CTP) The intersection of the equator .Z Axis pointing CTP Direction .Y Shaft with X、Z The axis forms the right-hand coordinate system .

In a word, the explanation is ： Put the previously mentioned ECEF The coordinate system is used in GPS in , Namely WGS-84 Coordinate system .
among ：
（1）： The geodetic latitude is the crossing point P The angle between the normal of the reference ellipsoid and the equatorial plane . Latitude value at -90° To +90° Between . The northern hemisphere is positive , Negative in the southern hemisphere .

（2）： The earth longitude is the point of transit P The angle between the meridian of and the prime meridian . Longitude value at -180° To +180° Between .

（3）： Earth height h It is the user point P The normal distance to the datum ellipsoid , Negative within the reference ellipsoid , The outside is positive .

3 Northeast sky coordinate system （ENU）
It is also called the station center coordinate system, which is based on the user's location P It's the origin of the coordinates .

The coordinate system is defined as ： X Axis ： Point East Y Axis ： Point north Z Axis ： Point to the zenith

ENU The local coordinate system uses a three-dimensional rectangular coordinate system to describe the earth's surface , Practical application is difficult , Therefore, the simplified two-dimensional projection coordinate system is generally used to describe . In many two-dimensional projection coordinate systems , Unified horizontal Mercator （The Universal Transverse Mercator ,UTM） Coordinate system is a kind of widely used .UTM The coordinate system uses a grid based method to represent coordinates , It divides the earth into 60 Longitude zones , Each zone contains 6 The longitude range of degrees , The coordinates in each zone are based on the transverse Mercator projection , As shown in the figure below ：
 

Two Transformation between coordinate systems

LLA The coordinate system turns ECEF Coordinate system

** ECEF The coordinate system turns LLA Coordinate system **

ECEF Points in the coordinate system (X,Y,Z) Convert to LLA In a coordinate system (lon,lat,alt)

In limine lon It is unknown. , We can assume that 0, It can converge after several iterations

update:alt=(p/cos(lat))-N

ECEF The coordinate system turns ENU Coordinate system

User's coordinate origin 𝑃0=(𝑥0,𝑦0,𝑧0), Calculation point 𝑃=(𝑥,𝑦,𝑧) In order to point 𝑃0 Is the origin of the coordinates ENU Coordinate system position (e,n,u) I need to use LLA Data in coordinate system ,𝑃0 Of LLA The coordinate point is 𝐿𝐿𝐴0=(𝑙𝑜𝑛0,𝑙𝑎𝑡0,𝑎𝑙𝑡0)

ENU The coordinate system turns ECEF Coordinate system

LLA The coordinate system is directly rotated ENU Coordinate system

As can be seen above , from LLA Coordinate system conversion to enu The coordinate system has a lot of calculation , Considering the eccentricity of the earth 𝑒 Very small premise , Can do some approximate formula calculation