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The GNSS satellites follow an elliptical orbit, one focus of which is the centre of mass of the Earth. It's fairly natural to specify each satellite's position relative to that point. ECEF format uses cartesian (x, y, z) coordinates measured in metres from that centre. So the coordinates are "Earth Centred".
The axes are "Earth-Fixed" because they run through the centre of the Earth and they are fixed to the lines of longitude and latitude:
The positive Z axis runs from the centre of the Earth and through the North Pole at latitude 90°. The negative Z axis runs through the South Pole at latitude -90°.
The positive X axis runs through the intersection of the Prime Meridian and the Equator at latitude 0° longitude 0°. The negative X axis runs through the opposite side of the Earth at latitude 0°, longitude 180° (close to the Gilbert Islands in the Pacific Ocean).
The Y axis is perpendicular to the other two. The positive Y axis runs through the Equator at latitude 0° longitude 90°, close to Sumatra in the Indian Ocean. The negative Y axis runs through the Equator at latitude 0° longitude -90°, close to the Galapagos Islands in the Pacific. For more details of ECEF see here .
As we've seen, the position of the poles, equator and Prime Meridian depend on which terrestrial reference frame you are using, so the same goes for ECEF coordinates. When using cartesian coordinates, you need to know which terrestrial reference frame the axes are bound to.
If two positions are specified in ECEF coordinates it's easy to figure out the distance between them. A GNSS devices works by measuring the distances to satellites and knowing their position, so it makes sense to specify the positions of the satellites in ECEF coordinates. The receiver figures out its position within the same system.
However, surveyors find latitude, longitude and height more useful, so all of my survey devices display their position in that form. The map application on my Apple iPhone does the same.
I also have a Garmin Etrex, which is a hiker's SatNav. It assumes that you are used to UTM coordinates (easting, northing and height above sea level) and it displays its position in that form.
Behind the scenes, all these devices are working in ECEF coordinates and converting to some more convenient form before displaying the result.
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