Global Positioning System Reference
In-Depth Information
Figure 16 illustrates FN curves before and after applying the algorithm for different temporal
resolutions with data originally collected every 10 seconds in Polk County. The graph
presents relatively parallel FN curves for all data collection frequencies. These curves show
that as temporal resolution increases, the percentages of FN data points decreases. FN
curves after applying the algorithm show lower percentages of FN data points compared to
before executing the algorithm. FN curves for Columbia and Portage counties behave
similarly with different sampling intervals. All county cases illustrate that larger amount of
FN points occur when using smaller buffers independent of data collection frequency.
Figure 17 shows the variation of solved cases as temporal resolution increases in Portage
County. Percentages of solved spatial ambiguities increase as data is collected at higher
frequencies, being the largest at a 50-foot buffer with 68%. This percentage decreases in
average for Columbia County data from approximately 80% to 20% as sampling intervals
increase from 5 to 30 second for all buffer sizes. The same behavior is apparent for solved
case percentages in Polk County as data is collected more frequently.
4.3.5 GPS error
GPS measurements are affected by both systematic and random errors. Their combined
magnitudes will affect the accuracy of the positioning results. Systematic errors obey
physical or mathematical law, and can be computed and applied to measurements to
eliminate their effects (Ghilani & Wolf, 2006). Random errors occur because of stochastic
noise in the measurement process producing different coordinates each time a measurement
is achieved, even during short intervals. This type of error is assumed to be Gaussian
affecting both latitude and longitude or X, Y coordinates. DGPS is a method that increases
the accuracy of CA code measurements by canceling some of the inherent systematic errors.
Any potentially remaining systematic errors were not modeled in this study, and only the
effects of random errors were examined.
Random errors were simulated by using a normal distribution random number generator
(Box & Muller, 1958) for known means and different standard deviations. If U1 and U2 are a
pair of independent uniformly-distributed random numbers from the rectangular density
function on the interval (0, 1), then a pair of independent random numbers (
X
1
and
X
2
) from
a normal distribution with mean zero and standard deviation σ are generated using
Equations 4 and 5.
X
1
= (-2 logU
1
)
1/2
cos(2πU
2
)
(4)
X
2
= (-2 logU
1
)
1/2
sin(2πU
2
)
(5)
Experiments conducted by the Wisconsin Winter Maintenance Concept Vehicle project
concluded that random DGPS errors were on the order of 2 to 5 meters, root-mean-square
(Vonderohe et al., 2001). Therefore, a mean value of zero and standard deviations of ±2 and
±5 meters were employed in this analysis. Speed range and number of consecutive points
values were held fixed as 2- and 5-meter standard deviation errors were introduced in the
DGPS data points.
Percentages for FN and solved cases were computed to compare the performance of the
algorithm for original and perturbed DGPS data points. Figure 18 presents variations in the
percentage of FN data points for original and perturbed data by county for a 40-foot buffer
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