## Why Every GPS Overestimates Distance Traveled

Why Every GPS Overestimates Distance Traveled - Runners, mariners, airmen, and wild trekkers beware: Your international positioning system (GPS) is flattering you, telling you that you simply have run, sailed, flown, or walked considerably farther than you truly have. And it’s not the GPS’s fault, or yours.

Blame the statistics of measure. Researchers at the University of metropolis (UoS), metropolis Forschungsgesellchaft (SFG), and also the earthenware University of Technology have done the maths to prove that the gap measured by GPS over a line can, on average, exceed the particular distance traveled. They additionally derive a formula for predicting however huge the error are going to be. The open-access paper was revealed within the International Journal of Geographical info Science; Associate in Nursing earlier version is on the market on Arxiv.

GPS course calculations ar subject to each interpolation error (a operate of the sampling interval) and measure error (the everyday contrariness of real-world physical systems). The metropolis team—including 1st author Peter Ranacher of UoS and senior author mythical being Reich of SFG—discovered a scientific bias in distance measure errors.

Measurement errors have several causes. The paper specifically cites: propagation delay (atmospheric fluctuations have an effect on the speed of the GPS signal); annual error (uncertainty within the precise position of the GPS satellite); satellite clock drift; error (the shortcomings of the terrestrial GPS unit); signal reflections (which will increase the length of the signal path); and unfavorable satellite pure mathematics (available GPS satellites ar too low within the sky or too close or too few, for example).

Put them along and you've got readings that scatter round the true position. The metropolis researchers found that distances derived from position measurements with haphazardly distributed errors can, on average, come back up longer than the particular separation between 2 points. There ar 3 parts to their calculation:

### Why Every GPS Overestimates Distance Traveled

The reference distance (d0): the particular geometrician distance between 2 points

The variance (Vargps): the “mean of the sq. minus the sq. of the mean” of the position error, Associate in Nursing index of however correct the position measure is. Variance is that the sq. of the quality deviation, σ2

The autocorrelation (C, maybe a lot of properly the autocovariance) of the measure error. this will vary from a most of Vargps (if the errors ar closely covariant) to zero (if they're random) to -Vargps (if there's Associate in Nursing inverse correlation).

The metropolis formula for the typical Overestimation of Distance (OED) is then,

OED = (d02 + Vargps - C)1/2 - d0

The variance is often positive, thus if the autocorrelation is not up to the variance, the overestimation of distance can forever be positive. and also the autocorrelation is mostly not up to the variance.

The problem becomes significantly acute once the user (or the GPS) calculates the whole distance traveled by adding along the lengths of multiple segments. The variations between verity and measured distance can fluctuate—sometimes short, however a lot of typically long. as a result of the GPS-measured distance skews long, though, the whole GPS distance error can tend to grow with every additional section.

Not content with mere calculation, Ranacher, Reich, and their colleagues went on to check their findings through an experiment. In Associate in Nursing empty automobile parking space, they staked out a sq. course ten m on a facet, reference-marked either side at precise 1-m intervals, and set a GPS-equipped pedestrian (a volunteer, one hopes) to run the perimeter twenty five times, taking an edge reading at every reference mark.

The researchers analyzed the information for section lengths of one meter and five meters. They found that the mean GPS measure for the one-m reference distance was 1.02 m (σ2 = zero.3) and also the mean GPS measure for the five-m reference distance was 5.06 m (σ2 = a pair of.0). They additionally ran an analogous experiment with cars on a extended course, with similar results.

Now, that pedestrian-course error of one.2 to a pair of % isn’t large. however it's sufficiently big that your GPS watch might tell you you’re crossing the line of a forty two,195-meter marathon whereas the important terminus is quite four hundred meters ahead.

That’s not a theoretic example. For years, runners have complained that their GPS watches and different devices have mismeasured the distances they’ve run over purportedly verified courses, or suddenly finding that they set personal record times the primary time they use a GPS to live their course. There are variety of assured explanations. Most concerned either interpolation error (measuring the gap between sequential plots as a line, which can seemingly report a shorter-than-actual distance over a crooked course) or the runner’s non-optimal selection of routes (adding to the verified distance on every leg, and reportage a extended actual distance traveled). perhaps they’ll like this rationalization higher.

The Ranacher team’s results don't mean that measure the lengths of complicated courses by GPS is futile. They means that moment-by-moment GPS speed measure isn't subject to a similar sources of error, so calculative distance traveled by integration speed ought to yield fairly correct results.

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