A discussion on the relevant knowledge of coordinate system and projection

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Recall that the professional contact with remote sensing for several years, and now more and more deviated from remote sensing, suddenly thinking of their own brain in the remote sensing knowledge to sort out. The first thought is the coordinate system and projection, I think this thing bothers more than 80% of surveying, remote sensing and GIS practitioners in the field, the group often asked, I was also very confused, what Earth coordinate system ah, geocentric coordinate system ah, Gauss projection Ah, utm projection Ah, make head is big, But this thing can not play, after all, spatial information is the soul of remote sensing data, if the location is not allowed to image only when landscape view. Well, then chew it, the basic things still want, after some exploration, plus last year specifically done coordinate conversion some work, is clear, this will be some of my ideas to share to everyone, welcome you rookie and experts come to spit groove. OK, let's get down to the beginning of the coordinate system expedition.

1. What is a coordinate system?

Perhaps many people understand this concept, but they do not understand it. What is a coordinate system? People describe a point or a position in a space, usually using the concept of coordinates. But how do we calculate this coordinate? Who does it refer to? If China defines the Zhongnanhai coordinates (1921,1949,2012), the Yankees also define their coordinates for the White House (1921,1949,2012), which day the dark Horse says we hit it with a cannon, it might bake him. So it is necessary to establish a reasonable coordinate system (⊙﹏⊙ B Sweat ~ ~, this reason is very far-fetched AH).

The coordinate system consists of the origin and the axis. There are many kinds of coordinate system, we all have learned the Cartesian coordinate system, the polar coordinate system, the spherical coordinate system and the cylindrical coordinate system in mathematics, in the Geoscience field, the most used is the plane coordinate system, the space Right angle coordinate system (the former two belong to Cartesian coordinate system) and the spherical coordinate system. For example, a point coordinate is ( -2850017.472,4690744.523,3237959.973) a space coordinate, and we often see the coordinates of points on Google Earth (37°20′17″n,112°33′20″ E) refers to the spherical coordinates.

How is the coordinate system defined in geodesy? The earth is an irregular class ellipsoid, how to express it in a strict mathematical way, it should be the peak of the pursuit of surveying and mapping scientists. In order to represent the position of every point on the earth, is it necessary to establish a unified world coordinate system? is establishing a coordinate system to determine the coordinates origin and axis? How to build it? The survey of the Earth as a rule of the ellipsoid to deal with, this is better to do more, the ellipsoid Center on the original point, long axis short axis as an axis, so a coordinate system out AH. But some people will ask, what does this ellipsoid say? Well, I would also like to ask, originally this is the use of astronomical observations by scientists, and different scientists to get the ellipsoid is not the same, for example, a person called Krasovsky made a Krasovsky ellipsoid, and someone engaged in what IUGG-1975, WGS-84, GRS80 ellipsoid, Their main feature is the difference in the length of the shaft and the flattening ratio. But some people will ask (Y, the problem is a lot of AH), make so many ellipsoid why, there is one not on the line. Hehe, we know that the earth is a bumpy, with a strict ellipsoid to show that there must be errors, some countries in order to make their own country and the ellipsoid match (preferably everyone standing on the ellipsoid), so that according to their respective circumstances define a different reference ellipsoid, For example, the Beijing 54 coordinate system uses the Soviet Union Big Brother's Krasovsky ellipsoid. But the problem is again, how to calculate a good match? There will be people standing on the ellipsoid, someone standing under the ellipsoid, really headache. At this time, the geodesy introduced the Earth datum to measure the coincidence of the ellipsoid and the Earth. The geodetic datum is from the geoid, which refers to a closed surface obtained by the average sea level extending to the mainland. For example, when establishing the Beijing 54 coordinate system, experts will certainly choose a better ellipsoid to coincide with China's geoid. At this time, the ellipsoid is called the reference ellipsoid, and the coordinate system is called the core coordinate system, and the Beijing 54 and Xi ' an 80 coordinate systems are the reference coordinate system, which is a local scope coordinate system. However, this coordinate system is extremely inconvenient for the global positioning, the error is very big, so Uncle Sam took the lead in the GPS system designed for the global geodetic coordinates WGS-84 coordinate systems, the Earth origin is no longer the center of the reference ellipsoid, but the Earth's centroid. The relevant parameters of the WGS84 ellipsoid and the axes of the WGS84 coordinate system refer to the relevant professional books. China's existing National 2000 coordinate system is also a global geodetic coordinate system, which is slightly different from the WGS-84 coordinate system.

Here are the ellipsoid parameters for several common coordinate systems:

The Beijing 54 coordinate system and Xi ' an 80 coordinate system are the core coordinate system, while the WGS-84 coordinate system and the National 2000 coordinate system are the geocentric coordinate system, the coordinates origin is the Earth centroid.
OK, so you understand the definition of the coordinate system, first of all, the need to define a reference ellipsoid, with a reference ellipsoid also requires a geodetic plane (global geodetic coordinate system is not), and then need to define the coordinate system origin and the axis point. Such a coordinate system has been established, later find sister more convenient, global positioning bar, haha!

2, why should projection?

People will think, with the coordinates on the line, why do you want to make a confusing projection? Hehe, we talked about the ellipsoid as a reference for space positioning, not intuitive, if one day you and sister paper dating, sister paper said she was in ( -2850017.472,4690744.523,3237959.973) or (112°e,38°n), the pit Father, This is in which country, how far away from my brother, I do not know Ah, not to take a ruler to test it. At this time, the ladies have come up with a method, the spherical projection to a plane, with a plane coordinate (x, y) to represent the location of the ground point, two points between the distance is not very easy ah? At this time you will find that sister is not the girl next door, 200 meters not to (embarrassed!) haha). Of course, the biggest goal of projection is not to facilitate the sister paper, but the map. So the projection is the transformation of spherical coordinates into planar coordinates, that is, 3D to 2D.

There are many kinds of projections, by nature, such as conformal projection, equal product projection, isometric projection, arbitrary projection and so on. As we all know, the spherical surface expands into a plane, certainly is a not tight (also can say imperfect) process, will have different degree of deformation. How to choose? For example, in sailing, you need isometric projection, if the direction is wrong, it will be a lot worse, I guess if Columbus knew that these would not run to the Americas and thought to India. If you need to measure the area, it is necessary to choose the equal product projection.

3. What are the means of measuring coordinates?

Common measurement coordinates include geodetic coordinates (B, L, h), spatial Cartesian coordinates (x, y, Z), planar coordinate (x, y, h). Refer to the relevant tutorials for specific reference.

4. Coordinate conversion

Finally, the key points, how to convert the various coordinates are the most concerned about. One thing to keep in mind:
Under the same reference ellipsoid, the conversion between geodetic and spatial Cartesian coordinates is rigorous (mathematical relationship correspondence), and their conversion to planar coordinates is not rigorous and requires a projection transformation (think also understand, the spherical surface into a plane that is stumped a lot of scientists AH). The coordinate conversion between the different reference ellipsoid is always strictly non-strict.
Principle of coordinate transformation:

(1) conversion under the same ellipsoid
Under the same ellipsoid, the transformations between the geodetic coordinates (B, L, H) and the spatial Cartesian coordinates (X, Y, Z) are strict, and the formula is:

The conversion of geodetic coordinates (B, L, H) to the Cartesian coordinate (X, Y, Z) is non-rigorous, and the projection of the spherical to the plane is chosen, and the spatial Cartesian coordinates are usually converted to the geodetic coordinate, and then the Gaussian positive and inverse equations are used to calculate between the geodetic coordinates and the plane cartesian coordinates.

(2) conversion under different ellipsoid

The transformation of coordinates in the different reference ellipsoid is the basis of the conversion. The conversion between the global benchmark used in space positioning technology and the local benchmark used by the ground network. The usual conversion models are the Bursa-Wolfe model and the Molodensky model. Both models are common and very similar, the BURSA model is more common in global or larger range, but the Molodensky model can overcome the problem of high correlation between rotation parameters and translation parameters in Bursa model.

The conversion of two coordinate systems usually has three-dimensional seven-parameter model and two-dimensional four-parameter model.
The BURSA model is also called a seven-parameter conversion, or a seven-parameter Helmert transformation. The model employs 7 parameters, namely three translation parameters (ΔX, ΔY, Δz) and three rotation parameters (Ωx, Ωy, ωz) and a scale parameter K.

The above formula is a Bursa model of spatial Cartesian coordinates converted to CGCS2000 under a WGS84, there are seven unknown parameters, simple solution, only 3 common points can be obtained, if we want to get a strict solution, we need more common points for the least squares adjustment calculation. For geodetic coordinates, it can be converted into space rectangular coordinate and then solved, and the BURSA model can be used directly.

5. Projection and coordinate system selection of remote sensing mapping

With regard to the coordinate system and projection of remote sensing imagery, it is common to hear the concept of the so-called Geographic coordinate system (geographic coordinate system) and projected coordinate system (Projection coordinate system). Opening the ArcGIS coordinate system folder will also find these two subfolders. A geographic coordinate system is a spherical coordinate system, expressed in latitude and longitude, and a projection coordinate system is a unit of meters or kilometers, which is a planar coordinate system represented by XY. The following are the definitions of the two coordinate systems in ArcGIS:

In the left figure A is the geographic coordinate system under WGS-84, we can see that it defines a WGS-84 ellipsoid, and then the Datum plane under WGS84. With Spheroid and Datum, you can use a geographic coordinate system. On the right, B is the projected coordinate system in XI ' an 80 coordinate system, and the projection method is Gaussian-gram gauss–krüger projection. As you can see, it also defines the Xian-1980 geographic coordinate system in addition to the Gauss-kruger projection parameters.

One would ask, why is a projected coordinate system with a geographic coordinate system? We know that the projection is the projection of the spherical surface to the plane, then the projection must be defined by which spherical coordinate system to project. For example, utm projection coordinate system, we are familiar with the WGS84 coordinate system to projection, in fact, we can also use the National 2000 coordinate system to project, as far as I know, in the lunar exploration process, people also used the UTM projection, and then the coordinate system used for projection is the lunar coordinate system.

The selection of common map projection in China:

In our country, the map of the medium-sized scale (≥1:50 million) is generally selected Gauss-gram gauss–krüger projection, Gauss-gram Gauss–krüger projection has 3° and 6° two kinds, 1:25,000 -1:50 million-scale topographic map using 6 degrees of deviation, 1:10,000 scale topographic map by the difference of 3 degrees. Small-scale maps (such as all-China maps) should be made with isometric positive-axis cut conic projections, which are Lambert projections (Lambert conformal conic), but small-scale charts are multi-select isometric positive-axis cylindrical projections, which are Mercator projections. In addition, we usually download the remote sensing images are mostly WGS-84 under the geographic coordinate system or UTM projection coordinate system.

Here is an example of the transformation of a geographic coordinate system into a projected coordinate system (projection selection):

For example: Beijing's central latitude roughly (117°e,40°n), then its 54 projection coordinate system in Beijing, the 6° should choose Beijing 1954 GK Zone 20.prj or Beijing 1954 GK Zone 20N.PRJ (the latter will be preceded by a band number in front of the horizontal axis), the central Meridian = band number (such as 20) *6-3. In Xi ' an 80 projection coordinate system, the 6° band should choose Xian 1980 GK Zone 20.prj. The UTM projection for remote sensing imagery in Beijing is generally chosen for WGS 1984 UTM Zone 50N, because the zone is 20*6-3 's central meridian is 117, left 114, right 120, which covers Beijing, while the Old World adds 30 (global 360/6 total 60 zones) so it is 50N, N represents the northern hemisphere. Also, it is important to note that a cross-band projection can cause large deformations. Many people download the global vegetation map, night lights, and so on, want to cut out their own area, the original data is often WGS84 under the geographic coordinate system, and the vector data is more than UTM or TM projection coordinate system, then need to transform the vector data into a geographic coordinate system and then cut, if the reverse of the global map projection, Will find it hard to see the deformation.

6, recommend some useful coordinate conversion tool
(1) Coordinate conversion tool: used a lot of coordinate conversion tool, also wrote, and now recommend a: GPS toolbox, found it very easy to use, precision is also good, this is: http://download.csdn.net/detail/rsyaoxin/5611283. Probably everyone will usually use more is coord this software, but I found that it is always wrong, the following is a few software comparison, the first is a GPS toolbox, the second is a small software I wrote, the third is coord, the result is obviously wrong, I do not know is not the download coord have problems. As for the tool I wrote myself, I will share it with you when I have time to improve it.

(2) Open source coordinates and projection conversion library: Proj4. Its functions mainly include the transformation of latitude and longitude coordinates and geographical coordinates, the transformation of coordinate system, including datum transformation. This is the official website: http://trac.osgeo.org/proj/, can be downloaded to the source code and documentation, the source code is written in C + +, need to compile to integrate into your program to use. Here is a version of my build: http://download.csdn.net/detail/rsyaoxin/5611299

A discussion on the relevant knowledge of coordinate system and projection