Science Questions

How accurate is GPS for measuring speed?

Sun, 28th Nov 2010

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Question

Andre Grobler asked:

Hi Dr. Smith

 

Would you be so kind to clarify this relating to GPS speed monitor on next week's show with Redi?

 

My thoughts are as follows, but they are ever so slightly incoherent.

 

In South Africa a good signal will allow a WAAS enabled GPS to be around 3m accurate on average, with a variation up to 15m for the horizontal plane this is usually trebled in the vertical plane - so 9 to 45m.

Most GPS, outdoors type GARMINS - "take a point" every second - it may be saved as a track or waypoint or not, so if you use it to monitor your speed at around 120km/h- where you travel roughly 33.3 m/s you can have a horizontal error of up to 30m but mostly the distance measured could vary from -6 to 6m from 33.3 which seems very inaccurate - contrary to the "evidence" on display

 

So what is the reason for the accuracy, pure averaging?

 

Or does the error follow a pattern? I.e two points taken directly after each other will err more or less in the same direction and extent. I ask this because there is apparently still some error introduced by governments and this may cause a "pattern following" error, or will the ionospheric and atmospheric and satellite delays for two consecutive measurements be roughly the same?

I'm not even considering the vertical plane, as my trig is non-existent, but you may

 

BTW car manufacturers err on the side of caution for speedometers but are spot-on for odometers, unless you change your tyre circumference or gearing.

Sincerely

 

Andre Grobler

Answer

Dave -   The two devices are measuring speed in very different ways.  The speedometer is measuring the number of times your wheels turn every second or every minute, and if you know the circumference of your wheels you can work out how fast you're going.  There can be errors on that because the tires will wear down, that will change the circumference of your wheels.  Quite often, I think they build speedometers to possibly slightly under-read which is quite good because that way, you get less speeding tickets.  Especially, old fashioned speedometers werenít as accurate as modern ones.  They werenít computerised and they just tended to be less sensitive at high speeds to have actually kind of fudged that back into modern computerised speedometers, because people expect it to be less sensitive at high speeds.

The GPS is basically measuring your position repeatedly and measuring how far you move over a certain period of time and then dividing that distance by the time itís averaged over, and then that will give your speed.  If youíre stationary, the GPS will quite often give you a speed, so the GPS is not at all accurate in giving a speed when you're going very, very slowly because the errors in position can be a few meters.  And the accuracy of the speed will depend on how long itís averaging over to get the speed.  So if itís averaging for 10 minutes the GPS will be more accurate, if itís averaging over 2 seconds the speedometer will certainly be.

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Andre Grobler asked the Naked Scientists: Hi Dr. Smith Would you be so kind to clarify this relating to GPS speed monitor on next week's show with Redi? My thoughts are as follows, but they are ever so slightly incoherent. In South Africa a good signal will allow a WAAS enabled GPS to be around 3m accurate on average, with a variation up to 15m for the horizontal plane this is usually trebled in the vertical plane - so 9 to 45m. Most GPS, outdoors type GARMINS - "take a point" every second - it may be saved as a track or waypoint or not, so if you use it to monitor your speed at around 120km/h- where you travel roughly 33.3 m/s you can have a horizontal error of up to 30m but mostly the distance measured could vary from -6 to 6m from 33.3 which seems very inaccurate - contrary to the "evidence" on display So what is the reason for the accuracy, pure averaging? Or does the error follow a pattern? I.e two points taken directly after each other will err more or less in the same direction and extent. I ask this because there is apparently still some error introduced by governments and this may cause a "pattern following" error, or will the ionospheric and atmospheric and satellite delays for two consecutive measurements be roughly the same? I'm not even considering the vertical plane, as my trig is non-existent, but you may BTW car manufacturers err on the side of caution for speedometers but are spot-on for odometers, unless you change your tyre circumference or gearing. Sincerely Andre Grobler What do you think? Andre Grobler , Sat, 27th Nov 2010

It is my understanding that a GPS takes a running average of data points with some smoothing function. This means that while you are speeding up or slowing down the GPS will be off a little, but at a constant speed it will be very accurate. Also, it isn't just position information that is used in the calculation, signal Doppler shift is also included.  SteveFish, Sat, 27th Nov 2010

See this thread, which is discussing the same question:

http://www.thenakedscientists.com/forum/index.php?topic=35426.0 chris, Sun, 28th Nov 2010

http://www.thenakedscientists.com/forum/index.php?topic=35426.msg332423#msg332423 maffsolo, Sun, 28th Nov 2010

I don't have a GPS in my car...
The paper maps do quite nicely...
And if I don't know where I'm at... 
It'll make a good adventure, and I'll eventually figure it out  :)

I've played around with the handheld GPS instruments a bit.  I think they're fairly accurate, at least in the wide-open. 
An error of a few yards should be ok as long as it is reproducible from one measurement to the next.
As mentioned, the vertical isn't as accurate, but I'm not sure about the reproducibility from one measurement to the next.

A base station helps with accuracy a lot, including vertical accuracy.  If Cell towers could be designed to broadcast GPS info, the accuracy for many locations could be sub-millimeter.  But, perhaps there would be no immediate economic benefit for such technology.

The problem is in the woods, one frequently looses signal, or connects to a sub-optimal number of satellites.  I would assume the same would be true in big cities.

The simplest way to program the device would be to connect the dots with straight lines.  But that would likely underestimate the distances, unless the calculations jumped around based on differing satellites. 
Adding a smoothing/interpolation algorithm would do a lot better with gentle corners as long as not too much time lapsed between location readings.
The best would be if one could actually access a map database and overlay one's actual travel over the known roads. 

Whether the current GPS devices are sophisticated enough to use all the available information, I don't know.  I doubt they do much more than curve smoothing and interpolation. CliffordK, Mon, 29th Nov 2010

I have a really cheap one (I do have a reputation to protect) and it always seems to be in agreement with the speedometer on my truck. It can also do something the speedometer can't - it alerts me when I'm speeding  Geezer, Tue, 30th Nov 2010

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