# GPS does great horizontally

1. Dec 25, 2004

### tribdog

I've always been told that GPS does great horizontally, but not so great vertically. Is the reason simply because the earth is blocking any satellites that would provide info below the receiver? Is vertical precision 1/2 as reliable as horizontal?

2. Dec 25, 2004

### Grogs

One thing about it is that you need to be receiving a signal from more satellites to get your altitude as well as your position (4 instead of 3.)

My father owns a private planne that he flies a lot and he's gone over almost entirely to GPS for navigation. One of the features they've recently added for private GPS's is WAAS, which gives very accurate altitude information in addition to the position information previously available - dead on with the altimeter. Unfortunately, I have seen a few days where it was consistently off by ~200 feet, so if I were a pilot, I think I would continue to land with the ILS system until I was certain all the kinks were hammered out.

Unfortunately, I'm not really sure what's involved in the WAAS technology since my father isn't a very technical person. When I was learning how to use the military GPS back in the early 90's, I was told there was a 50 meter positional error built into the satellites. In order to get more accurate readings from the satellites (1m), you needed to load an electronic COMSEC (communications security) variable into the GPS. This has apparently gone away now and the new WAAS technology may be the same sort of thing.

In any event, the technology to accurately determine the altitude is certainly there. They may just have a few last bugs to work out of the system.

3. Dec 25, 2004

### Staff: Mentor

I think its just trigonometry: 2 gps satellites form a very long isocolese triangle with the reciever: moving side to side causes a more noticeable change in the triangle than moving up and down.

4. Jan 3, 2005

### enigma

Staff Emeritus
That doesn't make much sense to me.

GPS receivers _all_ use signals from at least 4 satellites now. You need the fourth sat to take transmission time due to general relativity into account so you can get around the cheap clocks that the receivers have. Putting high precision cesium clocks in every GPS receiver isn't exactly practical. As a side note, this is why I tell every crackpot who claims that relativity doesn't work to check out how GPS satellites work... not surprisingly, they never do.

Now, if you have a signal from 4 satellites and they are located in a very small arc of the sky, then you'll get errors. Still, unless you're flying in areas with mountains that block out the lower azimuths you should be able to get PRN (pseudo-random noise, what the GPS sat's broadcast) signals from more than 4 sats directly above you.

Like Grogs said, they have de-classified the precise signal which used to be broadcast for US military purposes. People had found ways to get around the coarse signal broadcast to get positions to within a meter from them, so maintianing security on them was sort of pointless

5. Jan 3, 2005

### Staff: Mentor

Well, my example was 2-dimensional and an oversimplification. Two satellites won't give any position at all - my example was just a 2-d analogy.
Right, and in doing so firms up the distance the signals traveled (I think) - which has more of an effect on the vertical position than the horizontal.
That's all I was trying to convey.

6. Jan 4, 2005

### enigma

Staff Emeritus
I was referring to the OP

I can't figure out why a modern GPS system would be having problems determining alititude unless it's operating in the Grand Canyon (or similar) which blocks out the lower azimuths.

The first part is correct. If you're getting a signal from -say- 20 degrees above the horizon, it's narrowing in differently.

All the GPS receivers do is take the time and direction to the satellites (which are at a known position for every time) and do a least squares regression to get the position and clock bias of the receiver.

Last edited: Jan 4, 2005
7. Jan 4, 2005

### LunchBox

How GPS works...

Well... let's go... here's the boiled down version of how GPS works...

The GPS satellites send basically 3 pieces of information... an almanac message, a broadcast message, and a precision message.

So, your receiver basically contains a glorified timex as its internal clock... much too inaccurate for use in precision time calculation... but that's okay.
The GPS satellites each have 4 atomic clocks onboard, so their time is EXTREMELY accurate.

So, the almanac signal basically contains the satellites orbital properties and it transmitted at 50 Hz at 50 bps, so it takes 12.5 min for the receiver to obtain. This gives the receiver a ~km idea of where the satellite is (not where it itself is). Now, the signals from the GPS satellites experience chipping (a doppler shift) based upon how they are moving relative to the receiver. The receiver takes the precision message (which is essentially the satellite broadcasting its onboard time) and compares it and the frequency shift due to chipping with the precision message and frequency shift of the other satellites in view and obtains a clock bias value for the receiver's onboard clock (the aforementioned glorified timex). The receiver now knows to a high level of accuracy the "actual" time. Now the fun can start...

The satellite's broadcast message contains the position of the satellite at the time it begins its precision message (the precision message is a repeating message unique to each satellite what begins at very precise intervals). The receiver notes what internal time it receives the beginning of this precision message. The time difference between when the receiver picks up the beginning of the precision message and when the satellite sent the beginning of the precision message is now the time of flight of the signal. Now, using the very simple formula:

$$v \times t = d$$ just speed times time equals distance

From this, the receiver now knows a sphere around the satellite with this distance as its radius that the receiver lies on. From the broadcast message, the receiver knows the position of the satellite. By combining the spheres from multiple satellites through a process known as trilateration (similar to 2D triangulation) the receiver knows very accurately where it is.

Publicly available GPS units contain the assumption that the receiver is on the terrestrial sphere (generally the WGS84 geoid) and adds this as an additional constraint. However, this is not necessary. Altitude could easily be determined by not assuming the receiver is on the geoid, but could compare the position to the geoid to obtain an altitude measurement.

But... there's always a but isn't there... there is something known as dilution of precision which is the fact that you can only know your position to a certain degree. So, generally speaking, you can know your position to within a 15m sphere if you have 3 or more satellites with a good spread between them.

8. Jan 6, 2005

### BobG

LunchBox covered how GPS works pretty well. GPS receivers don't so much work better for horizontal position than vertical position as much as the assumption the receiver is on the terrestrial sphere allows the receiver to figure horizontal position with only 3 satellites - in other words, it normally determines horizontal position quicker, not better than altitude.

The satellite geometry matters, as well. You get a better trilateralation if you have 3 satellites a little above the horizon (say 20 degrees or so) about 120 degrees apart with a fourth nearly overhead. You get four satellites all in within a couple of degrees of each other as viewed by you and they don't do squat for you - they may as well be 1 satellite. Bad geometry would be the exception where a GPS receiver would determine horizontal position better than vertical (only 3 satellites in good positions). With at least 24 satellites in the GPS constellation, you should usually get good satellite geometry for fixing your location in all 3 dimensions.

In other words, what tribdog has heard is more true than not (a better term would be that GPS is more reliable in consistently providing good horizontal position than it is in providing vertical position).

Last edited: Jan 6, 2005
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