OpenStreetMap

Position accuracy revised

Posted by Schwedenhagen on 23 July 2009 in English (English)

Hi everybody,

in my blog of 4. Mai 2009, 18:18 I described an attempted to check the accuracy of my Garmin Etrex Venture HC by putting the instrument on a fixed position with a nearly unrestricted view on the horizon while it was recording this position at a sampling rate of 1 second for about 700 seconds. The standard deviations around the mean position of latitude, longitude and height were all about 1.5 m within the recording time. In the subsequent discussion it became clear that the recording time was to small because it comprised the time scale of turbulent atmospheric fluctuations but not the time scale of substantial changes in satellite positions. Therefore I repeated the measurements by taking 19 measurements of the same position within a 0.1 m radius each separated by at least one day. The result was different to my first attempt as expected. The standard deviations around the mean position of elevation was 2.3 m, of latitude was 2.0 m, and of longitude was 1.1 m, respectively. Assuming a Gaussian distribution of the sampled values the accuracy of a single statistically independent measurement would be with a probability of 67% within a sphere with a radius of about 2 m, with a probability of 95% within a sphere with a radius of about 4 m, and with a probability of 99% within a sphere with a radius of about 6 m. The error of a mean value is proportioanl to the inverse of the square root of the number of statistically independent measurements. Hence, it would require at least 10 statistically independent measurements (separated by at least 1 day) in order to obtain an accuracy of the mean position close to 2 m radius with 99 % probability. This gives an estimate of how many repeated statistically independent mappings of a particular object are necessary if a given accuracy shall be obtained.

Location: Warnemünde, Ortsamt Nordwest 1, Rostock, Mecklenburg-Vorpommern, Germany

Comment from RichardB on 23 July 2009 at 20:30

If you do measurements at the same time on two consecutive days, the alignment of the satellites might not be much different - since the satellites orbit twice per siderial day (twice every roughly 23h 56m)

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Comment from Mungewell on 24 July 2009 at 00:27

As RichardB points out the constellation repeats on an approximately daily basis, but your specific location can affect the performance significantly.

In general you want to have a good sky view, with a fair number of satellites overhead. You can find out the orbits and plan the best time for your 'survey' with a tool such as:
http://www.sokkiagps.com/support/s_planning.php

Another factor would be obstructions around your horizon, which could block signals or cause multipath. The rotation of the receiver/antenna may have effect too.

Did you know you can actually get raw measurements out the Garmins (http://artico.lma.fi.upm.es/numerico/miembros/antonio/async/node3.html), but doing this you could post process the data to find out whether the accuracy is down to the antenna/RF frontend or the positional processing of the micro.

Add in a local reference station and you should be able to get really (for a cheap unit) accurate....
Cheers,
Simon

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Comment from ceyockey on 24 July 2009 at 00:40

Consider the interesting Excel function related at http://www.gps-practice-and-fun.com/gps-coordinates.html . Do you think that increasing the accuracy of the four measured points by multiple measurements would have significantly enhanced the end result extrapolated position of the '3rd steeple' in the example? What about replacing two of the four points with distance measures, such as one might do if one wanted to accurately place multiple objects in a relatively small area (e.g. sculpture garden, cemetery, accident site)? Distances could be measured using either a laser ranging instrument or a rolling linear measure.

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Comment from Mungewell on 24 July 2009 at 00:44

Oh, you'll need a recent almanac file:
http://www.navcen.uscg.gov/GPS/almanacs.htm

Simon.

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Comment from Mungewell on 24 July 2009 at 00:55

and.... when doing your stats you probably want to consider the horizontal plane seperately from the vertical. Elevation accuracy is weaker and will be approaching 2x the error of that for lat/long.

I believe that it is also 'valid procedure' to eliminate outlying data points from your data.

I'll stop typing now... ;-)
Simon.

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