GPS altitude
 

Hi,
I am in the middle of studying GPS navigation and I can't figure out how the reciever calculates it's altitude.

After recieving the NM and the CA code the reciever calculates its position by looking at the time delay between the sending and recieving of signal.

However, surely the altitude of the reciever will affect the range to the satalite and therefore its position, whether the unit is up a 40m mast on a ship, a 2000m mountain or an aircraft at 35000ft.

Am I right in thinking that the pseudorange is a 3d sphere?

Anyone help me out?
cheers

.. undeleted as it is useful for this to be revisited from time to time ...

That and with reference to the speed of light. The receiver calculates these and applies errors first for each of the information received from 3 satellites (for a 2D solution) and 4 satellites (for 3D solution). Newer GPS receivers have 12 channels so in addition to the 4 used to lock onto the satellites, the other 8 is used to lock onto additional satellites for more accuracy.

I am not sure but I think the pseudo range is calculated first using 3 satellites, thus a 2D sphere. Only after azimuth and elevation data received from the 3 satellites and error corrections are made for the 2D position, information from additional satellites are used for 3D modelling.

Correct me if I am wrong.

Basically, GPS will provide you with a 3D fix, with may or may not be on Earth. Imagine this: You have multiple magic footballs (the soccer ones, for all you americans!), that can join into each other.

Take one, and there is an infinite number of points all along the surface, all equidistant from the center of the ball.

Place ball number two in such a manner that the two balls intersect. The intersection will be a circle, right? You still have an infinite number of points, though.

Now, ball number three goes anywhere it will cross the circle earlier mentioned. It will cross at two points. One probably being in space, and one on Earth. We have narrowed it down to two possible positions.

Now, place ball number four in such a manner that it will intersect either of the two points. You have your position.


Now, this far, we havn't included the Earth. It may or may not be at the point where all our four balls intersect. If it is, you are on the surface. If not, you are in the air somewhere. Let's remember that the GPS reciever only knows only the position of the different satelites in relation to Earth and it's own charts, and will calculate it's own position based on this. It knows where it is, it knows where the Earth is, and the rest basically comes down to trigonometry :)

A further question, of course, is whether the altitude so derived is accurate. It seems to me that, given the GPS unit's onboard database size limits, there is little chance that relief data is available to make this altitude even close to reality.

A good point.

I'm not intimately familiar with the GPS system, but from it's principle of operation, it would seem that it's altitude capability is just as accurate as it's lateral positioning. I would think (think, that is!) that the biggest source of inaccuracy would be the charts. We all know that by now, our plain old 2D charts are very accurate, but how accurate is the terrain elevation data? Not compared to adjacent terrain, but in relation to the 3D universe the GPS reciever works in? Again, these are merely thoughts...

Edit: reading through your post again, I see that's pretty much what you were saying anyway. Bedtime for me! :)

jau
 

These pages are useful, although aimed at surveying + recreation users the theory is relevant. Bfisk's explanation of pseudoranges is there, with illustrations!

http://www.ordnancesurvey.co.uk/oswe...gps/index.html

GPS Alt
 

Hi, I used to work for a company that specialised in GPS software and hardware solutions and think I may be able to offer you an answer. I'll try to explain in a simple terms as possible!

GPS altitude is not that accurate. It takes a minimum 3 satellites to calculate a 2D fix, and 4 for a 3D fix. Obviously the more satellies, the more accurate. However, only the satellites closer to the horizon can play any part in calculating your altitude to a higher degree of accuracy. However, the Earth model used by the GPS system is based on an 'averaged' spheroid:

Earth is not a perfect sphere like a globe would lead you to believe, it is in fact slightly more elongated across the equator than between the two poles. Plus the fact that some of the surface is covered in high terrain, while the rest is at sea level. So, if you see where I'm coming from, the developers of the GPS system 'averaged' out Earth into a spheroid taking into account these factors. Thus, you may be in a position where you are calculated to be at altitude, when in fact you are standing on a beach. Likewise, you could be calculated at being at a negative-value altitude when standing at sea level, due to the averaged Earth surface used by the system.

The only truly accurate altitude reporting GPS's on the market are those with built in barometers.

Hope that this is of use to you and I haven't confused you further!

Atb, Tri

Re. altitude: in theory it is correct that the vertical component should be as precise as its horizontal counterparts. In practise this isn't so due to the fact that the satellites used will be clustered above the receiver (as they need to be above the horizon to be visible) thus most of the effect of the measurement uncertainties will be in the vertical direction.

Another thing to keep in mind is that GPS elevations are worked out with respect to the ellipsoid (a mathematical surface used to approximate the shape of the Earth) associated with the WGS84 datum (or more precisely, one of its refinements). This is not the same as the MSL elevations we see on the charts, which are measured relative to a different reference surface, known as the geoid--this latter surface is not mathematically developable due to its irregular shape (think of a rugby ball with bumps and dents), although it can be approximated analytically.

Such an approximation is called a geoid model, and can be used to calculate the distance between the geoid and a specific ellipsoid at a specific location--this distance is variously called "geoid undulation", "geoid correction", "geoid-ellipsoid difference" and various other names, and varies between about -100m to about +100m depending where on the Earth you are.

The bottom line is that this quantity which needs to be applied to an ellipsoidal height to obtain MSL also has an error, further degrading the vertical precision of a GPS-derived position fix. Depending on how accurate a geoid model you're using this error can range between a couple of centimetres (for a locally derived geoid model for a specific area) to a couple metres (for a low-precision global model).

A more serious concern, though, is to make sure you know whether you are reading ellipsoid or MSL heights, as that could make a serious difference--up to a couple hundred feet in parts of Europe. By the way, I do not know what consumer-grade navigation GPS receivers normally show, I would appreciate if someone could clue me up on this point.

Other than that, bfisk has provided an accurate and very clear explanation (unlike mine) of how a GPS position is calculated. Just to add, the reason why many units will give you a position with only three satellites is because they will assume the receiver to be near sea level (effectively they'll be using the Earth as a fourth football, if you like).

HTH.

Thanks for the replies re GPS altitude. I had a very strong belief already that the GPS altitude isn't worth a cracker after calling it up often on the ACMS and seeing what it read compared with our F/L. Even allowing for baro variations, it's still way out - in the order of 1500 - 2000 ft or so. So much of the inherent inaccuracy comes from the poor grazing angles of the SVs used for nav solutions. As it has been pointed out, nav solutions prefer SVs with a diferent sight line than altitude and that's what the GPS is optimised to do.

Baro-aiding is really only useful in the navigation solution itself. The altitude (or elevation) data provided by the airborne receiver is a "raw data" value that is, in itself, quite unreliable. It is possible to obtain survey quality elevation data, but this requires DGPS survey, followed by subsequent "massaging" of the data to account for errors in SV positions, among other errors.

And, of course, a correcyion must be applied to the assumed WGS84 spheriod, to be able to relate it to the real world earth.

AFAIK, Airborne receivers aren't (yet) capable of taking those extra steps that will yield an accurate elevation, thus the altimeter will be needed for another few years... or so...

I read somewhere before that the Pythagoras Theorem is used as well, in calculating the altitude.