GPS speed 3D or 2D?

[Orion84]

Since I will be taking my Vista HCx along on my snowboard trip later this winter, I was wondering...

 

The speed a GPSr records/logs/displays, is it the 3D speed, taking changes in elevation into account, or is it simply horizontal speed? While descending a steep slope, this could be quite different...

[+trainlove]

Go on a parachuting expedition to find out. Your horizontal speed there would be close to zero but your vertical speed could get up to 120MPH before you open your chute.

 

I think it's strictly horizontal. Since vertical position accuracy is 10x worse you couldn't expect them to want to include that in the calculation. Plus, it's based on the WGS84 model of the Earth which does not include elevations.

[+Red90]

Speed is horizontal as is distance.....

[+trainlove]

Speed is horizontal as is distance.....

Now if the GPS makers said velocity...

[timz2]

deleted

Edited December 10, 2008 by timz2

[timz2]

it's based on the WGS84 model of the Earth which does not include elevations.

GPS calculates X-Y-Z first, doesn't it? If so, it could calculate 3D speed from that-- and any elevation error would be irrelevant.

Edited December 10, 2008 by timz2

[Orion84]

Go on a parachuting expedition to find out. Your horizontal speed there would be close to zero but your vertical speed could get up to 120MPH before you open your chute.

I rather just ask the experienced experts here

 

I think it's strictly horizontal. Since vertical position accuracy is 10x worse you couldn't expect them to want to include that in the calculation.

You've got a good point there. Is it certain that a GPSr determines speed from current and last location and the time interval, or does it calculate it directly using doppler effect somehow? (Just a wild idea, don't know how I came up with it, it's probably just done simply by taking two positions and a time interval, but since I am always told that one can not ask stupid questions...)

 

Plus, it's based on the WGS84 model of the Earth which does not include elevations.

Don't exactly know what you mean by that?

 

it's based on the WGS84 model of the Earth which does not include elevations.

GPS calculates X-Y-Z first, doesn't it? If so, it could calculate 3D speed from that-- and any elevation error would be irrelevant.

 

Isn't Z the same as the elevation?

Edited December 10, 2008 by Orion84

[timz2]

You know how (x,y,z) three-dimensional rectangular coodinates work in general-- you have three planes, each perpendicular to each of the other two, and a point's x-coordinate is its distance from one plane, its y-coordinate is its distance from one of the other two planes, etc.

 

As I recall, the z-coordinate of a point on earth is its distance from the plane of the equator-- so no particular connection to its elevation.

[+Prime Suspect]

It's forward speed only, but not for the reasons mentioned above. It doesn't use GPS positioning to determine current speed, so the fact that GPS places your location is on an ellipsoid is irrelevant. A GPS unit determines its current speed by Doppler Shift detection. This is much more accurate (to 0.5 MPH) than continually checking your current position against the last position, and doing a speed calculation based on the time and distance.

[Hertzog]

Go on a parachuting expedition to find out. Your horizontal speed there would be close to zero but your vertical speed could get up to 120MPH before you open your chute.

I suggested this on a similar thread about a year or two ago, but if there were any takers they didn't report back on their results

[timz2]

A GPS unit determines its current speed by Doppler Shift detection.

So it first determines its "3D" speed, and somehow converts that to horizontal speed before displaying it?

[AngusOg]

As indicated previously the GPS receiver uses Doppler shift to determine its velocity expressed in three dimensions having a north, east, and down component.

 

See the following link for a more detailed explanation:

Velocity Vectors

 

Depending on the GPS receiver the speed can be reported as a 2D horizontal speed taking only the north and east vectors into account, a 3D speed using all three vectors, or vertical speed only using the down vector.

 

Garmin's as well as most GPS receivers will report speed as 2D horizontal speed (north/east). The various speed determination equations only require using the needed vector components, so in a sense the GPS does not need to calculate 3D speed and then 2D speed. But, obviously the GPS does derive the 3 velocity vector components initially from the Doppler.

 

So, any GPS receiver is capable of calculating 3D, 2D or 1D speeds its just a question of how and if this information is presented to a user.

 

Angus

[+julianh]

The 2D length between 2 points (with map coordinates E1 N1 and E2 N2 respectively) is given by

 

L2D = SQRT( (E2-E1)^2 + (N2-N1)^2)

 

If we also know the heights of the two points (Z1 and Z2 respectively), then the 3D distance between the same two points is given by:

 

L3D = SQRT( (E2-E1)^2 + (N2-N1)^2 + (Z2-Z1)^2)

 

The slope of the sector (i.e. the gradient) is given by:

 

Slope = (Z2-Z1) / L2D

 

Most roads have a gradient of less than 10% or so, but some very steep hills might get up to 20% or more. When you are skiing or snowboarding, you are probably generally on slopes of less than 50% gradient (1:2), but you might hit 100% gradient (1:1) in the really extreme stuff.

 

A bit of basic arithmetic gives the following relationship between gradient and the error between 3D velocity and 2D speed:

 

Gradient 3D Speed / 2D Speed

0% 1.000 (0.0% error)

5% 1.0012 (0.1% error)

10% 1.0050 (0.5% error)

15% 1.0112 (1.1% error)

20% 1.0199 (2.0% error)

25% 1.0311 (3.1% error)

30% 1.0448 (4.5% error)

40% 1.0797 (8.0% error)

50% 1.1245 (12.5% error)

 

It can be seen that for the kind of gradients you are likely to encounter while driving around, ,the difference between 2D distance and 3D distance is so small that it is not worth worrying about (generally less than 1% error).

 

On the other hand, when you plummet down a double black diamond ski slope, your GPSr could be understating your 3D speed by 10% or so.

 

Hope this helps!

[Orion84]

Ah, so I was correct about the doppler thing. Must have read that somewhere then

 

About the fact that the actual error will quite likely be not too large: Good point! And on the slopes that are steep enough (and long enough) to cause a serious error, I probably won't be going flat out anyway

 

Well, thanks for all the replies. I learned a thing or two again. If I won't forget (snowboard trip is somewhere in februari), I'll report back here with my experiences after I return from Austria

[+JSWilson64]

A GPS unit determines its current speed by Doppler Shift detection.

 

Then doesn't your doppler shift include your movement in the Z axis? Or does it somehow decompose your doppler-derived velocity into its component vectors?

[+Prime Suspect]

A GPS unit determines its current speed by Doppler Shift detection.

 

Then doesn't your doppler shift include your movement in the Z axis? Or does it somehow decompose your doppler-derived velocity into its component vectors?

This is a complete guess, but it seems that the unit would know the angles of the transmission waves, and it's compensating for that (since you're obviously not moving directly towards or away from a satellite). Any movement up or down would not register as a Doppler change, but simply as a inconsequential change to the angle of attack.

[timz2]

Then doesn't your doppler shift include your movement in the Z axis?

Your vertical movement, you mean? No doubt it does include that, until it removes it.

[timz2]

(since you're obviously not moving directly towards or away from a satellite)

Why not?