Vitorio Miliano
A Long Walk
Off a Short Pier
A Case Study of GPS Position Dither in Motion
Geographic Information Science & GPS
Peter H. Dana
Spring 2007
A Long Walk Off a Short Pier
WHILE it is generally accepted that stationary GPS location fixes will,
over time, produce a point cloud averaging down to the estimated
location of the receiver, there is a pervasive misconception that GPS
is somehow “more accurate” when in motion.
This case study involved an traversing a known, public, linear
path, over varying amounts of time, in a repeatable fashion, in an
effort to demonstrate the potential inaccuracies of GPS readings
even when in motion.
We will take a look at the collected data, the location it was
captured at and the methodology with which it was captured and
“I had that problem with my car. If I
parked, my position would jump
around by up to, like, ten feet. When I
was moving it was pretty accurate,
though,” remarked an acquaintance in
regards to this case study.
A Long Walk Off a Short Pier
A Long Walk
GIVEN a GPS track of fixed length measured in an exorbitant length
of time – specifically, approximately 950 feet measured in four
hours, forty-three minutes and sixteen seconds – one can visualize
excessive perturbations in the recorded line. As with multiple
stationary measurements, the effect is something akin to a point
cloud. However, as the receiver is indeed moving, the line
connecting these points loops back onto itself, adding substantial
length and detail.
We can take this path, its constituent points and its length, and
sample data from it at regular intervals to change the time scale
while preserving the overall character of the data. The following
graphs demonstrate the original time scale, the time scale reduced by
half (sampling every other point), reduced to a third (sampling every
third point), to a tenth (sampling every tenth point), to a fiftieth, to a
hundredth and to one two-hundredth of its original time for capture.
The crudest measure is length. GPS tracks measure length by
measuring the distance between points. These points were captured
in WGS84 and projected to the Texas State Plane Central NAD 83
survey feet coordinate system for length measurements. The original
measurement captured NMEA sentences every two seconds, for a
total of 8342 points. Connecting these points offered a length of
6337 feet. Compare to the sampled measure of 1/50 (five minutes,
forty seconds, a fast walk), a much more accurate 1398 feet.
GPS Track in Motion
Distance in Feet
Rendering of the total “long walk”
Elapsed Time
A Long Walk
It has been said that GPS position errors in motion have fractal
dimensions. Fractal dimension is a complexity measure: a measure
of the tortuousness (the opposite of straightness) of a line at various
scales – in our case, time. Fractal line measurements range from 1.0
(perfectly straight) to 2.0 (no longer a line, but a two-dimensional
plane). An increase in fractal dimension is an order of magnitude
increase in complexity. We see a fractal dimension of 1.27 at the
highest time scale, and this is preserved even when halving it. Even
a reduction to one-tenth of the time scale only reduces us to a fractal
dimension of 1.22. Only with dramatic reductions in sampled time
do we see values approaching 1.0, beginning at 1.09 for 00:05:40.
Fractal Dimension
GPS Track in Motion
“GPS position dither is very similar to
a complex path with fractal
dimensions at some walking rate.”
Peter H. Dana, March 2, 2007
“For each line, the fractal dimension
(D) is calculated as follows:
D = log(n) / ( log(n) + log(d/L) )
whereby n is the number of line
segments that make up the line, d is
the distance between the start and end
points of the line, and L is the total
length of the line, i.e. the cumulative
length of all line segments.”
Hawthorne Beyer
Elapsed Time
A more graceful indicator of perturbations within a line is
sinuosity. Sinuosity is the measure of back-and-forth variation in a
line, such as to add to its length in comparison to a straight line from
beginning to end. A straight line has a sinuosity of 1.0. Here, too, we
see dramatic increases in sinuosity as the measurement time
increases (6.9), just as with the raw length value. We only see values
approaching 1.0 with the more natural speeds, e.g. 1.5 at 00:05:40.
GPS Track in Motion
Elapsed Time
“For each line, sinuosity (S) is
calculated as follows:
S = Lt / Lsf
whereby Lt is the total length of the
line, i.e. the cumulative length of all
line segments, and Lsf is the distance
between the start and finish
locations.” Hawthorne Beyer
A Long Walk Off a Short Pier
It is readily apparently that slow traversal speeds can adversely
affect measurement quality, adding substantial noise to the system.
This comes at a substantial risk to accuracy: the length of the bridge
increased over seven times in our longest sample rate. So much error
is injected into the data stream at that point that even reducing the
data to ten percent of its original content is not enough to give a
reasonably straight, accurate line.
This is where drawing a statistical line becomes difficult. While
it is apparent from the graphs and figures that 10% is terribly
inaccurate, but 2% is fairly reasonable, this is difficult to translate
into minimum recommended traversal times, because the data
corruption due to the slow initial collection is pervasive:
Remeasuring the 950' path at a normal walking rate of
approximately eight minutes (and some two hundred points) yielded
an accurate length, a fractal dimension of 1.000969 and a sinuosity
of 1.005184, all essentially straight.
Given an average human walking speed of three miles per hour,
950' should be able to be traversed in under four minutes. Six
minutes gives a reasonable winnowing of inaccurate data. Eight
minutes of fresh data provides us a fairly accurate traversal, giving
us a third greater leeway over the poorer data. Thirty minutes of
poor data is far too long, plus 33% is forty minutes to provide an
upper bound on a maximum “too slow” measurement. It might not
be unreasonable, then, to suggest that taking 10x over an average
walking pace to record data would risk severe adulteration of a
position stream, and that no more than 5x an average pace should be
Data points:
Length (Feet)
A Short Pier
A Short Pier
THE Congress Avenue Bridge in downtown Austin, TX was built in
1910. It spans Town Lake (the Colorado River) between 1st Street
East (Cesar Chavez Street East) and Barton Springs Road. It
comprises three lanes of traffic in each direction with no bike lanes,
shoulders or median. Pedestrian sidewalks are available on each side
of the bridge (only the curb separates them from traffic), and a three
foot high metal railing bounds the pedestrian walkways from the
edge and the water.
A spray-painted utility service marker at the south end of the
bridge reads “1000' fence.” This is in line with the approximately
950' length of the supported portion of the bridge as measured
during the study.
The bridge was selected because of its safe, 24/7 availability (it
is a public thoroughfare and street lights illuminate it overnight); its
straight and linear path; and its substantially clear view of the sky
(including an essentially unencumbered view to the horizon to the
northwest and southeast from the middle of the bridge). These
attributes provide a practically best-case scenario for GPS
The suspended portion of the bridge has definitive beginning and
ending markers by way of the seams in the concrete on either side.
These markers were used to begin and end all measurements.
Six-inch true-color aerial
photography tile from the City of
Austin, showing the Congress Avenue
Bridge spanning Town Lake (2003)
A Long Walk Off a Short Pier
SCOUTING the location was fairly straight-forward given modern tools
such as online aerial and satellite photography. Google Maps was
used to quickly locate open areas within a short drive from the
University of Texas at Austin campus.
Paths needed to be at least 150 meters in length, so an
appropriate zoom level was set in Google Maps to make easy visual
comparisons against the stepped scale line. 150 meters was the
minimum to provide enough data even if GPS' estimated 15 meter
unaided accuracy was obtained (of course, finer resolution was
hoped for).
Parks, cemeteries, walking trails, bike paths and other similar
edifices were considered and rejected for various reasons: no defined
straight paths, overhanging foliage, potential for awkward social
interactions, etc. At under 290 meters, the aforementioned Congress
Avenue Bridge was additionally ideal from both availability and
repeatability perspectives.
GARMIN eTrex Legend GPS receivers are made available to students
of the Department of Geography and the Environment in the College
of Liberal Arts at the University of Texas at Austin. These blue, lefthanded units are in Garmin's “Mapping Handheld” product line, a
notch above their “Basic Handheld” series. These handhelds have
been noted by ESRI for their use with participatory and low-cost
mapping projects. With a suggested retail price of around US$160
and an online price of around US$125, it probably represents the
expected functionality of any amateur or financially restricted
collection effort.
The Garmin eTrex Legend 12-channel receiver is waterproof to
one meter for thirty minutes, supports real-time differential
correction through WAAS and via an external beacon receiver,
updates its position every second, can output NMEA sentences over
an RS-232 serial line, and runs for well over six hours on two
alkaline AA batteries.
The onboard data collection facility on the eTrex is limited to
waypoints, tracks and routes. Collecting waypoints requires at least
two button presses and you cannot see any other information
“A Cost-Effective Approach to
GPS/GIS Integration for
Archaeological Surveying.” ArcNews
Fall 2006 Issue. ESRI. Retrieved May
2, 2007.
“Mapping Handhelds.” Garmin |
Products. Garmin, Ltd. Retrieved
May 2, 2007.
“Garmin eTrex Legend GPS
Navigator.” Amazon.com:
Electronics. Amazon.com, Inc.
Retrieved May 2, 2007.
(direction, odometer, satellite configuration, etc.) while you are
collecting them. Once you have initiated a waypoint collection, the
waypoint location is not updated between the time of your initial
press and the time you press “OK” to save the location, even if your
location substantially changes.
The eTrex can store up to ten tracks plus one “Active” track,
which is the track currently being collected. Tracks can have up to
9999 points, which can be collected as frequently as once a second
(making for approximately two hours and fifteen minutes of
collection time at this highest rate). Once the active track is stored,
the track is simplified, causing dramatic data loss. A track of over
5600 points was reduced to approximately sixty points according to
the receiver's on-screen display and to two points – a beginning and
an end – when downloaded to a PC. Two different PC-based
applications, DNR Garmin and GPS TrackMaker reported the same
(lack of) data. Even downloading from the active track is
problematic, as the receiver seems to occasionally drop points during
the transfer. At least ten points went missing in each active track
download, but no indication was provided of which ones or when;
only that the total count reported by the receiver was different from
the total count received by the software.
Garmin, Ltd. eTrexLegend personal
navigator owner's manual and
reference guide. Taiwan, 2002.
It should be noted that for any
recreational use, smoothing these
essentially straight tracks to start and
end points is likely precisely what
would be desired.
DNR Garmin
GPS TrackMaker
Routes are limited to fifty points and so were not experimented
with for this study.
To avoid these issues, WGS84 NMEA sentences were chosen to
be collected for this long walk. However, this had its own pair of
concerns: the proprietary RS-232 serial cable (ultimately provided
by UT) and a serial data collection device that would survive the
desired length of collection: over six hours.
GLOBAL Positioning System satellites (NAVSTAR GPS) orbit the
Earth twice every sidereal day. Given the rotation of the Earth, they
rise and set over any particular location on the ground in a maximum
of six hours. This means to achieve the greatest amount of potential
irregularities (including experiencing the densest atmosphere at each
horizon), any distance measured would ideally be measured over a
precisely or greater than six hour span.
Few modern laptops enjoy even a five hour battery life, let alone
at least six during active data collection. Popular models, such as the
Apple MacBook and MacBook Pro (each advertising at least five
hours “depending on configuration and use”), do not feature serial
ports, requiring additional serial-to-USB adapters, which would
consume additional power. Taking six hours to drive along a major
thoroughfare with a machine plugged into a cigarette lighter would
have likely quickly incited the ire of a traffic officer. Laptops
supporting multiple batteries would still have required awkward
swaps in the middle of data collection, risking damage or lost data.
Bare serial data loggers start at US$60 (requiring assembly) and
work their way up from there.
It would have been particularly nifty
to model the estimated satellite
positions in the sky, perhaps using
software like SaVi and Geomview,
and use that to pick particular times
or even locations for measurement.
“Technical Specifications.” MacBook
and MacBook Pro. Apple, Inc.
Retrieved May 2, 2007.
cs.html> and
“Logomatic Serial SD Datalogger.”
SFE Widgets. Spark Fun Electronics.
Retrieved May 2, 2007.
A Long Walk Off a Short Pier
Instead, a Palm IIIxe PDA was obtained, second-hand, for US$5.
This handheld, originally released in 2000, was an 8MB upgrade to
the venerable Palm III line of PDAs. Battery life using standard,
replaceable, alkaline AAA batteries, was traditionally measured in
weeks of daily use or even months of casual use. 8MB of RAM
would ensure plenty of storage for NMEA sentences. The Palm IIIxe
docks and synchronizes over a serial port using a cradle, which was
cannibalized to produce just the internal cable for ease of use and
transportation. Software availability was practically assured due to
the popularity of the Palm III line.
For those readers unfamiliar with the
hardware, Dale DePriest, author of A
GPS User Manual: Working with
Garmin Receivers, has lots of great
links and information on using older
Palm devices for GPS at his
“Navigation and the Palm OS” site.
A 9-pin male-to-male null-modem adapter was required to
couple the two female serial cables together (as they were intended
to connect to PCs, not to other serial devices); one was assembled
from off-the-shelf adapters from a major electronics chain for
Several Palm III-compatible GPS logging applications are
available, including a few free applications, out of which NMEA
Monitor was selected. NMEA Monitor can record a single NMEA
sentence type, or all sentences, to Memos, which end up as plain text
files after synchronizing to a PC. As total storage capacity was
untested (individual memos are limited to four kilobytes each and
while NMEA Monitor creates new memos every 4K, it is unknown
if there is a limit to the total number of possible memo files), only
$GPGGA sentences were logged. These were captured at a rate of
one every two seconds.
LONG walk data was collected over the course of four hours and
forty-three minutes at a relatively constant, awkward shuffle. The
intent was to move no more than half an inch a second (which would
have made the under-300 meter trip over six hours in length), but
without external monitoring of distance traversed, this proved to be
As the eTrex receiver is intended for left-handed use, it was
placed on the western (south-bound traffic) railing of the pedestrian
sidewalk at the south end of the bridge and, with a stiff arm, slowly
slid forward as the operator shuffled north.
Short walk data was collected over the course of eight minutes in
the same manner, at a relaxed walking pace, after the long walk.
DATA was synchronized to a desktop PC running Palm Desktop 4.1.4
per the requirements of the Palm IIIxe. NMEA data was manually
copied and pasted from the multiple Memo files into a single text
file, one for each walk.
All NMEA sentences reported a DGPS fix due to real-time
WAAS correction.
Nearly half the points in the long walk reported ten or eleven
NMEA Monitor
$GPGGA sentences are Global
Positioning System Fix Data
messages, providing time, latitude,
longitude, quality of the reading
(invalid, GPS or DGPS), number of
satellites in view, relative horizontal
accuracy (HDOP) and other data less
relevant to this study.
satellites in view and 99% had at least seven. More than half the
points had an HDOP of 1.0 or less, with 96% at 1.4 or under.
All of the points in the short walk reported at least eight satellites
in view, with more than half reporting at 10. More than half recorded
an HDOP of 1.1 or below.
The NMEA sentence files were converted into GPX format using
GPS Babel, one file for each walk containing both waypoints and
tracks. The date was supplied as $GPGGA sentences have none.
The GPX files were converted into ESRI shapefiles using
gpx2shp. This created both a point shapefile and a line shapefile,
sparing the need to connect-the-dots (over eight thousand of them)
within ArcMap.
gpsbabel.exe -p "" -w -i
nmea,date=20070429 -f
"nmealongwalk.txt" -x
transform,wpt=trk,del=n -o gpx -F
gpx2shp.exe longwalk.gpx