Triangulation - what is it? Triangulation of a mobile phone in a cellular network. Method of triangulation

What is a triangulation? It should be noted that this word has several meanings. So, it is used in geometry, geodesy and information technologies. Within the framework of the article, attention will be paid to all topics, but the most popular will be the most popular direction - use in technical equipment.

In geometry

So, we begin to disassemble what istriangulation. What is it in geometry? Let's say we have an undeveloped surface. But it is necessary to have an idea of ​​its structure. And for this you need to deploy it. Sounds impossible? And here not! And the triangulation method will help us in this. It should be noted that its use makes it possible to build only an approximate sweep. The method of triangulation involves the use of adjacent one to the second triangle, where you can measure all three corners. At the same time, coordinates of at least two points must be known. The rest are to be determined. In this case, either a solid network or a chain of triangles is created.

To obtain more accurate data, useelectronic computers. Separately, we should mention the moment like Delaunay's triangulation. Its essence is that with the existing set of points, with the exception of vertices, they all lie outside the circle, which is described around the triangle. This was first described by the Soviet mathematician Boris Delone in 1934. His developments are used in the Euclidean problem of the traveling salesman, bilinear interpolation and the finite element method. That's what Delaunay's triangulation is.

In geodesy

In this case, it is envisaged thatpoint of triangulation, which is subsequently included in the network. And the latter is built in such a way that it looks like a group of triangles on the terrain. The obtained figures measure all the angles, as well as some basic sides. The way the triangulation of the surface will be performed depends on the geometry of the object, the qualification of the performer, the available instrument cluster and the technical and economic conditions. All this and solves the level of complexity of work that can be implemented, as well as the quality of their conduct.

In information networks

And gradually we come to the most interestinginterpretation of the word "triangulation". What is it in information networks? It should be noted that there are a large number of different options for interpretation and use. But within the limits of the article, due to the limitation of its size, only GPS (global positioning system) and mobile network will receive attention. Despite a certain similarity, they are quite different. And now we will find out what exactly is.

Global Positioning System

It's been more than a decade since GPSwas launched and successfully operates. The global positioning system consists of a central control station located in Colorado and observation posts around the world. During the time of its work several generations of satellites had already changed.

Now GPS is a worldThe radio navigation system, which is based on a number of satellites and earth stations. Its advantage is the ability to calculate the coordinate of the object to within a few meters. How can triangulation be represented? What is it and how does it work? Imagine that every meter on the planet has its own unique address. And if there is a user receiver, you can request the coordinates of your location.

How does this work in practice?

Conventionally, there are four mainstage. Initially, the triangulation of satellites is carried out. Then the distance from them is measured. An absolute measurement of time and the determination of satellites in space is carried out. And finally, differential correction is carried out. This is briefly. But it is not entirely clear how triangulation works in this case. That this is not good, it is understandable. Let's detail.

So, initially we measure the distance tosatellite. Found that it is 17 thousand kilometers. And the search for our location is significantly narrowed. It is precisely known that we are at a specific distance, and we need to search in that part of the terrestrial sphere, which is located 17 thousand kilometers from the detected satellite. But that is not all. We measure the distance to the second satellite. And it appears that we have been removed from it by 18 thousand kilometers. So, we should be sought in a place where the spheres of these satellites intersect at a specified distance.

Appeal to the third satellite will allowfurther reduce the search territory. And so on. The location is determined by at least three satellites. The exact parameters are determined according to the set data. Let's assume that the radio signal moves at a speed close to light (that is, a little less than 300 thousand kilometers per second). The time for which it passes from the satellite to the receiver is determined. If the object is at an altitude of 17 thousand kilometers, it will be about 0.06 seconds. Then the position in the space-time coordinate system is set. Thus, each satellite has a clearly defined orbit of rotation. And knowing all these data, the technique and calculates the location of the person.

The specifics of the global positioning system

According to the documentation, its accuracy varies fromrange from 30 to 100 meters. In practice, the use of differential correction allows you to obtain detailed data up to centimeters. Therefore, the scope of the global positioning system is simply enormous. It is used to track the transportation of expensive goods, helps to accurately land aircraft, guide the vessel in foggy weather. Well, the most famous is the application in car navigation systems.

Algorithms of triangulation due to theiruniversality and coverage of the whole planet allows you to travel freely even in unfamiliar places. In this case, the system itself paves the way, indicates where it is necessary to roll in order to reach the established final goal. Due to the gradual reduction in the price of GPS, there are even car alarms based on this technology, and now if a car is stolen, it will not be difficult to find and return it.

And what about the mobile connection?

Here, alas, not everything is so smooth. If GPS can determine the coordinates to within a meter, then triangulation in the cellular communication of this quality can not provide. Why? The point is that in this case the base station is the reference point. It is believed that if there are two BSs, you can get one of the coordinates of the phone. And if there are three, then the exact location is not a problem. This is partly true. But the triangulation of a mobile phone has its own characteristics. But here comes the question of accuracy. Before that, we considered a system of global positioning, which can reach phenomenal accuracy. But, in spite of the fact that mobile communication has much more equipment, it is not necessary to talk about any qualitative correspondence. But first things first.

Looking for answers

But first let's formulate questions. Can the distance from the base station to the phone be determined using standard tools. Yes. But will this be the shortest distance? Who deals with measurements - phone or base station? What is the accuracy of the data? During the conversation, the base station measures the time it takes for the signal to reach the telephone. But only thus it can be reflected, say, from buildings. It should be understood that the distance is taken in a straight line. And remember - only during the process of maintaining the call.

Another significant disadvantage is that it is rathersignificant level of error. So, it can reach a value of five hundred meters. The triangulation of the mobile phone is further complicated by the fact that the base stations do not know what devices are in their territory. The device catches their signals, but does not inform themselves. In addition, the phone is able to measure the signal of the base station (which, incidentally, it constantly does), but the amount of attenuation is unknown to him. And here there is an idea!

Base stations know their coordinates and powertransmitters. The phone can determine how well it hears them. In this case, it is necessary to detect all the stations that are working, exchange data (this requires a special program that sends out the verification packets), collect the coordinates and, if necessary, transfer them to other systems. It would seem everything, it's a hat. But, alas, for this it is necessary to implement a number of modifications, including sim cards, access to which is not guaranteed at all. And in order for a theoretical opportunity to turn into a practical one, it is necessary to work substantially.

Conclusion

Despite the fact that there are almostall people, to assert that a person can easily be tracked, still should not be. After all, this is not such an easy thing, as it may seem at first glance. More or less confidently you can talk about luck only when using a global positioning system, but it requires a special transmitter. In general, after reading this article, we hope that the reader no longer has questions about the relative nature of triangulation.