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## stuzzo

534 posts

Ultimate Geek

Suppose your GPS calculates your speed by taking a reading every 50 meters. The accuracy of your GPS (without ground-based augmentation) is about 5m to one standard deviation so if you take the standard deviation of the error at both ends you get about 7m, so the error will be about 14%.

Then there will be error allowing for a non-straight path and non-uniform speed. Decreasing the sampling distance will reduce these errors but increase the error from the GPS.

In any case I doubt the GPS could get accurate to better than 10% for speed.

Some errors due to atmospheric conditions are fairly uniform over short periods so this could help the accuracy a bit.

## diysteve

26 posts

Geek

The speedo on my BT50 reads 8% faster than my GPS and the road side radar signs. I'm glad the company I work for pays the RUC.

I drive 55000km per year at the GPS reading and haven't been stopped yet and I see lots of police cars on the road daily.

## stuzzo

534 posts

Ultimate Geek

Yes, I used to run a lot of commercial vehicles and found the speedos were generally a bit conservative, up to 10%, so the speedo might say 55 at 50 km/hr.

That might be the manufacturers covering themselves so doesn't necessarily mean the odometers are out by the same margin.

## richms

20445 posts

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They are out by an amount. I am guessing they do it for maintanance issues. Hard to prove GPS distances over anything but a straight line but I saw 20k's a week more in an older company car than my car, and mine is pretty much on what a GPS says. so thats only about 3-4% of my commute added, but that is still signifigant.

No idea if they could ping you for an odometer that read low, but for cert purposes when changing wheels you only have to provide documentation that the speedo has been corrected.

Richard rich.ms

## Oncop53

252 posts

Ultimate Geek

stuzzo: Suppose your GPS calculates your speed by taking a reading every 50 meters. The accuracy of your GPS (without ground-based augmentation) is about 5m to one standard deviation so if you take the standard deviation of the error at both ends you get about 7m, so the error will be about 14%.

Then there will be error allowing for a non-straight path and non-uniform speed. Decreasing the sampling distance will reduce these errors but increase the error from the GPS.

In any case I doubt the GPS could get accurate to better than 10% for speed.

Some errors due to atmospheric conditions are fairly uniform over short periods so this could help the accuracy a bit.

I query your assumptions here. My nuvi 265W does 1 second logs, so it must at least calculate speed from second intervals. At 100 km/h this would be every 27.8 m not 50 m.

A 2004 publication reported GPS accuracy of  0.2 m/s for 45% of the values with a further 19% lying within 0.4 m/s. these values equate to 0.72 km/h and 1.44 km/h respectively. There have been advances in GPS reciever sensitivity since then so we can assume that accuracy is currently at least that. Presumably the speed calulation software discards transient outliers.

When I overlay my 1 s track logs over google earth you can clearly and consistant see what side of the road I was driving on, which would suggest a real world accuracy greater than that of your calculation (which I realise was a near maximum since your were taking 1 sd at both ends).

## sarg

730 posts

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Most car speedos in my experience under read. I believe road side council operated radar speed warning signs give an accurate check against a cars speedo. Robinson Instruments can calibrate and test speedos in Auckland. http://www.robinsoninstruments.co.nz/index.html

that would be an ecumenical matter

## stuzzo

534 posts

Ultimate Geek

Oncop53:
stuzzo: Suppose your GPS calculates your speed by taking a reading every 50 meters. The accuracy of your GPS (without ground-based augmentation) is about 5m to one standard deviation so if you take the standard deviation of the error at both ends you get about 7m, so the error will be about 14%.

Then there will be error allowing for a non-straight path and non-uniform speed. Decreasing the sampling distance will reduce these errors but increase the error from the GPS.

In any case I doubt the GPS could get accurate to better than 10% for speed.

Some errors due to atmospheric conditions are fairly uniform over short periods so this could help the accuracy a bit.

I query your assumptions here. My nuvi 265W does 1 second logs, so it must at least calculate speed from second intervals. At 100 km/h this would be every 27.8 m not 50 m.

A 2004 publication reported GPS accuracy of  0.2 m/s for 45% of the values with a further 19% lying within 0.4 m/s. these values equate to 0.72 km/h and 1.44 km/h respectively. There have been advances in GPS reciever sensitivity since then so we can assume that accuracy is currently at least that. Presumably the speed calulation software discards transient outliers.

When I overlay my 1 s track logs over google earth you can clearly and consistant see what side of the road I was driving on, which would suggest a real world accuracy greater than that of your calculation (which I realise was a near maximum since your were taking 1 sd at both ends).

Obviously my 50 m assumption was just that, an assumption, to see how the error panned out. A while ago I looked into the accuracy of GPS as an exercise. It was hard to find any error information on manufacturer's websites so my guide was the information in Wikipedia which has quite a big discussion on errors, most of which are atmospheric related and independant of the sensitivity of the equipment.

As stated, the fact that atmospheric conditions are little changed over the time used to measure speed means that you get quite accurate observed readings ie The position readings may suffer from certain inaccuracies that are not as important when the measurement of interest is the difference in readings and this certainly appears to have more than the minor affect that I thought.

This also is likely why sports players running around with GPS for calculating distance travelled can be reasonably accurate.

## richms

20445 posts

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The errors reported by GPS recivers are worst case, It is almost always within 1m when I have tested it.

Something I did notice, was putting 2 GPS units side by side makes them both a little iffy. But with 2 in the car logging and then putting into google earth, you can almost see exactly where they were in the car with the lines being beside each other except when in the urban jungle when they go all over the place.

Richard rich.ms

## stuzzo

534 posts

Ultimate Geek

richms: The errors reported by GPS recivers are worst case, It is almost always within 1m when I have tested it.

So this is when you've had the opportunity to take readings from known trig points?

This does surprise a bit, the new Galileo system in Europe is designed to get accuracy down to the 1 metre level. Ground augmented GPS certainly can I believe.

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