Knowledge about coordinate system and projection

Looking back, I have been in touch with remote sensing for several years, and now I am moving away from remote sensing. I suddenly want to sort out the remote sensing knowledge in my mind. The first thing that comes to mind is the coordinate system and projection. I think this is bothering more than 80% of practitioners in the field of surveying, remote sensing, and GIS. People in this group often ask me that I was also confused, what earth coordinate system, Earth coordinate system, Gaussian projection, and UTM projection are all big headers. However, spatial information is the soul of remote sensing data, if you are not sure about the positioning, you can only view the images as landscape paintings. Well, let's take a look at it. The basic things are still needed. After some exploration, coupled with some work dedicated to coordinate transformation last year, it is clearer and clearer, here I will share some of my insights with you. You are welcome to come and talk about cainiao and experts. Now let's get down to the truth and start an adventure in the coordinate system.

1. What is a coordinate system?

Maybe many people understand this concept, but they do not quite understand it. What is a coordinate system? People describe a point or a location in a space, usually using coordinates. But how can we calculate the coordinates? Who is it for reference? If China defines the coordinates of the Central South China Sea (2012, 2012) and the United States defines the coordinates of the White House (,), which day the dark horse will say that we should hit the Central South China Sea, then it's possible to cook it yourself. Therefore, you must establish a reasonable coordinate system ~~, This is a far-fetched reason ).

The coordinate system consists of the origin and coordinate axes. There are many types of coordinate systems. We must have learned Cartesian coordinate systems, Polar Coordinate Systems, spherical coordinate systems, and Cylindrical Coordinate Systems in mathematics,In the field of learning, the most used is the plane coordinate system, the space Cartesian coordinate system (the first two are Cartesian coordinate systems) and the spherical coordinate system.For example, the coordinate of a point is (-2850017.472, 4690744.523, 3237959.973), which refers to the Cartesian coordinate of a space. We often see the coordinate of a point on Google Earth (37 ° 20' 17 "N, 112 ° 33 '20 "E) refers to the spherical coordinate.

In terms of measurement, how is the coordinate system defined? The earth is an irregular elliptical type. How to express it in a strict mathematical manner should be the peak pursued by surveying and painting experts. To represent the location of each point on the earth, should we establish a unified world coordinate system? Do you need to determine the coordinate origin and coordinate axis when creating a coordinate system? So how to establish it? The surveyors treat the Earth as a rule elliptical, and this is much easier to handle. The center of the elliptical is the origin, and the short axis of the long axis is the coordinate axis, so a coordinate system will come out. But some people may ask, how does this elliptical form represent it? Well, I also want to ask, it turns out that scientists have used astronomical observations, and different scientists have different elliptical shapes. For example, A person named craasovsky engaged in a crasovski elliptical, there are people engaged in what IUGG-1975, WGS-84, grs80 elliptical, they are mainly characterized by the long half axis and flat rate is different. However, some people may ask (a lot of questions about y) Why are there so many elliptical objects. Well, we know that there must be an error in the tight elliptical shape of the earth. Some countries have to make their own countries match the elliptical sphere (we 'd better all stand on the elliptical sphere ), in this way, different reference regions are defined based on their respective situations. For example, the 54 coordinate system in Beijing uses the clasovski sphere of the Soviet Eldest Brother. But the problem is coming again. How can we make a good fit? Someone is standing on the elliptical sphere, and someone is standing under the elliptical sphere, which is really a headache. At this time, surveyors have introduced the to measure the coincidence between the elliptical and the earth. The is derived from the, and refers to a closed surface obtained by extending the average sea level to the mainland. For example, when building the 54 coordinate system in Beijing, experts will certainly choose an elliptical shape that fits well with the geoid in China. In this case, the elliptical system is called the reference elliptical system, and the established coordinate system is called the reference coordinate system. The Beijing 54 and Xi'an 80 coordinate systems in china are both the reference coordinate system and a local range coordinate system. However, this coordinate system is extremely inconvenient for the global positioning, the error is very large, so Uncle yamu took the lead in designing the global coordinate system WGS-84 Coordinate System for the GPS system, then the Earth origin is no longer reference the center of the elliptical, it is the center of the Earth. For details about the parameters of the WGS84 elliptical body and the coordinate axes of the WGS84 coordinate system, see related professional books. China's existing national 2000 coordinate system is also a global coordinate system, which is slightly different from the WGS-84 coordinate system.

The following are the elliptical parameters of several common coordinate systems:

The Beijing 54 coordinate system and the Xi'an 80 coordinate system are coordinate systems, while the WGS-84 coordinate system and the national 2000 coordinate system are coordinate systems, and the coordinate origin is the center of the Earth.

Well, now you understand the definition of the coordinate system. First of all, you need to define the reference elliptical body. If you have a reference elliptical body, you also need the (the Global ), then you need to define the coordinate system origin and coordinate axis point. Such a coordinate system is created, and it will be much easier to find a girl later. For global positioning, haha!

2. Why projection?

Everyone will think that we can just get the coordinates. Why do we need to create a confusing projection? Well, what we mentioned above is Space Positioning Based on the elliptical body, which is not intuitive at all. If you date your sister-in-law paper one day, sister-in-law said she was there (-2850017.472, 4690744.523, 3237959.973) or (112 ° E, 38 ° N), Nima, where is the country? How far is it from my brother? I don't know. I won't take a ruler to test it. At this time, the girl master came up with a way to project the sphere to a plane and use a plane coordinate (x, y) to represent the location of the ground point, is it easy to find the distance between two points? At this time, you will find that girl is not the girl next door, less than 200 meters (sorry! Haha ). Of course, the biggest purpose of projection is not to facilitate the delivery of sister paper, but to map.Therefore, projection is to convert the spherical coordinates into the plane coordinates, that is, the transformation from 3D to 2D.

There are many types of projection, which are classified by properties, such as equal-angle projection, equal-product projection, same-distance projection, and arbitrary projection. As we all know, expanding a sphere into a plane is definitely a very tight (or imperfect) process with varying degrees of deformation. How to choose? For example, in sailing, we need angular projection. If the direction is wrong, it will be much worse. I guess if Columbus knew that at that time, he would not go to the Americas and think that he would go to India. If you need to measure the area, you need to select an equal product projection.

3. What are the Representation Methods of the measurement coordinates?

Common measurement coordinates include Earth coordinates (B, l, h), Space Cartesian coordinates (x, y, z), and plane coordinates (x, y, H ). For more information, see related tutorials.

4. Coordinate Transformation

At last, the focus is on how to convert coordinates. First, remember:

Under the same reference elliptical coordinate, the conversion between the Earth coordinate and the space Cartesian coordinate is strict (the mathematical relationship corresponds), and the conversion between them and the plane coordinate is not strict, projection conversion is required (think about it and understand that it is difficult for many scientists to develop the sphere into a plane ). The coordinate transformation between different reference regions is always not rigorous.

Coordinate Conversion principle:

• Transformation under the same elliptical shape

The conversion between the geocoordinate (B, l, H) and the Space Cartesian coordinate (x, y, z) under the same elliptical is rigorous. The formula is as follows:

However, the conversion between the geocoordinate (B, L, H) and the Space Cartesian coordinate (X, Y, Z) to the plane Cartesian coordinate is not rigorous, projection from the sphere to the plane is required. Normally, the space Cartesian coordinates are converted to the Earth coordinates, and then the Gaussian positive calculation and Inverse calculation formulas are used between the Earth coordinates and the plane Cartesian coordinates.

• Transformation under different elliptical shapes

The coordinate transformation under different reference regions is essentially a benchmark conversion. For example, the conversion between the global benchmark used by the Space Positioning Technology and the local benchmark used by the ground network. The usual conversion models include the bosa-Wolff model and the moroginski model. These two models are commonly used and very similar. Bosa models are commonly used globally or within a large range, however, the moroginski model can overcome the high correlation between rotation parameters and translation parameters in the Bosa model.

The transformation between two coordinate systems usually involves the three-dimensional seven-parameter model and the two-dimensional four-parameter model.

The bosha model is also called a seven-parameter conversion or a seven-parameter helm transformation. The model uses seven parameters: Three translation parameters (△x, △y, and △z) and three rotation parameters (ω X, ω Y, and ω Z) and a scale parameter k.

The above formula is a bosha model in which the space Cartesian coordinates under WGS84 are converted to the space Cartesian coordinates under CGCS2000. It has seven unknown parameters and is simple to solve, you only need three public points. If you want to obtain a rigorous solution, you need more public points for the Least Square adjustment solution. For the Earth coordinates, you can convert them into space Cartesian coordinates before solving them, or you can directly use the Bosa model.

5. Remote sensing plotting projection and Coordinate System Selection

With regard to the coordinate system and projection of remote sensing images, we often hear the concepts of geographic coordinate system and projection coordinate system.Open the Arcgis coordinate system folder and you will find these two subfolders. The geographical coordinate system is represented by longitude and latitude. It is a spherical coordinate system, and the projection coordinate system is in meters or kilometers. It is a plane coordinate system represented by xy. The following are definitions of two coordinate systems in Arcgis:

 

(A) geographic coordinate system (B) Projection Coordinate System

In the left figure a is the geographic coordinate system under the WGS-84, we can see that it defines a WGS-84 elliptical body, then is the reference level under WGS84. With Spheroid and Datum, you can use the geographic coordinate system. Figure B on the right is the projection coordinate system under the Xi'an 80 COORDINATE SYSTEM, and the projection method is Gaussian-gram projection. It can be seen that in addition to the Gauss-Kruger projection parameters, it also defines the geographic coordinate system of Xian-1980.

Someone may ask, why does the projection coordinate system contain a geographic coordinate system? We know that the essence of projection is to project the sphere to a plane, so the projection must define which spherical coordinate system is used for projection. For example, in the UTM projection coordinate system, we are familiar with the WGS84 Coordinate System for projection. In fact, we can also use the national 2000 Coordinate System for projection. As far as I know, during Lunar Exploration, UTM projection is also used, and the coordinate system used for projection is the lunar coordinate system.

Selection of commonly used map projection in China:

In China, a map with a large scale (≥1: 50 thousand) usually uses Gaussian-gram projection,Gaussian-gram projection has two types: 3 ° and 6 °. the terrain map of the 50 thousand-scale adopts a longitude difference of 6 degrees, and the terrain map of the scale adopts a longitude difference of 3 degrees.A map of Small Scale (such as a map of all China) should adopt an equal-angle positive axis Cut Cone projection, that is, Lambert projection
Conformal Conic), but for small-scale charts, you can select an equal-angular positive-axis cylindrical projection, that is, mocato projection. In addition, the remote sensing images we usually download are mostly the geographic coordinate system under the WGS-84 or UTM projection coordinate system.

The following is an example of the conversion from the geographic coordinate system to the projection coordinate system (projection selection ):

 
For example, if the longitude and latitude of the center in Beijing are roughly (117 ° E, 40 ° N), Beijing 1954 GK Zone 20 should be selected for the 6 ° split band in the Beijing 54 projection coordinate system. prj or Beijing
1954 GK Zone 20N. prj (the latter will add the belt number before the x-axis), the central longitude line = the belt number (such as 20) * 6-3. In the projection Coordinate System of Xi'an 80, Xian 1980 GK Zone should be selected for the 6 ° split. The UTM projection of remote sensing images in Beijing generally selects WGS 1984 UTM Zone 50N, because the central longitude line of Zone 20*6-3 is 117, left 114, right 120, and exactly covers Beijing, the Eastern Hemisphere requires 30 (60 zones in total in 360/6), so it is 50N, and N indicates the northern hemisphere. In addition, it should be noted that cross-band projection will cause large deformation. Many people download remote vegetation maps and night lighting maps from around the world and want to crop the desired area. The raw data is usually the geographic coordinate system under WGS84, vector Data is usually a projection coordinate system such as UTM or TM. In this case, the vector data needs to be converted to the geographic coordinate system and then cropped. If the global map is projected in turn, the deformation will be hard to see.

6. Some useful coordinate conversion tools are recommended.

(1) Coordinate Conversion Tool:I have used many coordinate conversion tools and wrote them myself. Now I recommend one for you:GPS ToolkitIt is easy to use and has good precision. This is:Http://download.csdn.net/detail/rsyaoxin/5611283.Maybe we usually use the Coord software, but I find that the result is always incorrect. Below is a comparison of several software. The first is the GPS toolbox, the second is a small software I wrote, and the third is Coord. The result is obviously incorrect. I don't know if I have a problem with the downloaded Coord. As for the tool I wrote, I will share it with you later.

(2) Open-source coordinate and projection conversion Library: proj4.Its functions mainly include the conversion of longitude and latitude coordinates and geographical coordinates, and the transformation of coordinate systems, including the benchmark transformation. This is an official website:Http://trac.osgeo.org/proj/You can download the source code and documentation. The source code is written in C ++ and must be compiled before it can be integrated into your program. The following is a compiled version:Http://download.csdn.net/detail/rsyaoxin/5611299

Postscript:Okay, I have said a lot. If there is something wrong, please also point out that you can leave a message directly or contact QQ Group 94935830.