GPS coordinates, From Zero to IDK

technical

gis

easy

G -> Global
P -> Positioning
S -> System

Literally, it’s the thing that lets you know where you are and works anywhere in the world. Originally created as a U.S. defense project, it has spread in later years for civilian purposes, so much so that by now anyone can tell you what it is without ever having studied it.

The common person, however, knows only what it is, and not how it works. In this article I want to summarize what I learned while working on an enterprise software project involving OpenStreetMap and Google Maps geographic data: I built it on these basic concepts and took them to the next level of complexity.

Projections

When working with geographic data, the root problem is approximation. There are so many ways, perhaps even infinite ways, to represent the Earth coordinates, whether it is on a 2D plane, or through the use of some geometric figure, such as a sphere, or even a cube!

Long live the cubic Earth, checkmate flat-earthers!

Each of these representations of the Earth is called a projection. One of the most famous is surely Mercator’s, which you may have already heard of and which dates back to the 1500s/ 1600s.


Ancient Mercator’s Map

Here for example there is a list of projections, each with its own distinguishing characteristics, there is the one that distorts the representation of the Earth at the 2 poles the most, or perhaps the one that is perfect for representing Antarctica but becomes horrible at any other location.


Random projections

The problem of approximation

How do you think you can perfectly represent an (almost) spherical planet like Earth using a 2D surface? It’s impossible! Indeed, it is, which is why on advanced computer systems such as GPS no such projection is used.

Let’s use a sphere!

Easy, we can approximate the Earth as if it was a sphere as they did in the plastic globe and it will surely work…. It shouldn’t be too inaccurate. Wrong. In order to use it in real life, we want an accuracy of less than 10 meters from the actual position, which cannot be reached by a sphere.

Real shape of Earth

Wait? Isn’t the earth a sphere? But then they lied to me.

You don’t fool me this time, the earth is a geoid, it is identical to a sphere but flattened at the 2 poles (north and south).

Well yes, but actually no, that’s not it either…. No matter how hard we may try to assign the Earth a geometric shape, it remains a planet, and therefore it will be full of irregularities.

See for example the photo below (right), which shows the true shape of the Earth, and on the left instead you can see an approximation of it as a geometric shape (which, however, remains only an approximation).


Earth shape (Right) and its approximation (Left)

THE projection

WGS-84, a dream, a religion, a standard, everyone uses it, so many hate it, a projection to rule them all.

~ Mahatma Gandhi

And it’s only at this point that we can talk about WGS-84. It’s a projection, whose acronym stands for World Geodetic System 1984, what year do you think it was invented?


Are you sure it’s just a coincidence?

This specific projection is used by virtually anyone dealing with geographic data saved on computer systems (so-called GIS), we find it everywhere, in Google Maps, OpenStreetMap, GPS coordinates, Pokemon Go and probably any other map app you can think of.

But why is it so popular?

Popularity

It’s quite accurate
It’s a widespread standard
Read 2 again

Everyone uses this format for geographical data, what could be more convenient than downloading existing data and using it directly without having to convert it to other proprietary formats?

But why can we say that it’s quite accurate?

Precision

WGS-84 approximates the Earth using the ellipsoid, using measurements precise enough to achieve the approximation that was set as a target.


WGS-84 Earth Ellipsoid

The geometric figure that approximates the Earth is constructed with almost absolute precision. In the image you see above, the smallest axis (let us assume it’s Z) measures 6356752.314245 meters in this representation, which is a measurement that achieves a precision of 0.001 millimeters (Read more).

You have to think of this projection as a 3D model of the Earth, and a coordinate is simply a point on the outer surface of the geometric figure. Because accuracy is critical, using a 3D projection of the world instead of a 2D one is essential if we want to have accurate calculations when you manipulate GIS data, we cannot do otherwise.

Coordinates are relative

Well, I’m italian, so let’s take the most famous monument in the world as an example, the Colosseum in Rome, Italy.


Colosseum in WGS-84 coordinates

And, as we can see, it perfectly coincides with the satellite view, because it uses WGS-84 coordinates too.


Colosseum in satellite image

So since Google Maps uses the WGS-84 projection, we know that in this projection the coordinates of the Colosseum are 41.89026 North and 12.49226 East.

Here is a permanent Google Maps URL, perfectly centered as it should be.

Please note, these are WGS-84 coordinates, if we use another projection we may need to do a conversion between the two measurement systems. I have a China story about this that I will probably tell in the future….

Meanwhile you can use this simple converter tool or you can do the same using a PostGIS function in a Postgres query: here you are the PostGIS documentation.

Good luck dealing with this!

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It ain’t much, but it’s honest work