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.