ACCURATE VELOCITY ESTIMATES FROM INACCURATE GPS DATA
Norman J. Cimon, Systems Analyst
Michael J. Wisdom, Wildlife Biologist,
United States Forest Service, Pacific Northwest Research Station
Forestry & Range Sciences Lab
1401 Gekeler Lane, La Grande, Oregon
email: ncimon@fs.fed.us
ABSTRACT
We used an empirical technique to obtain an accurate velocity estimate from inaccurate GPS data. It relies on everincreasing time-differences to reduce the relative error component in distance measurements based on GPS position
data error. The technique was used to derive estimate the average velocity for four sets of recreation visitor trials on
a rural forest road system: for hikers, bikers, horseback riders, and all terrain vehicle users.
THE RECREATION STUDY
ATV riding, mountain biking, horseback riding, and hiking were used as experimental treatments during 2002
and 2003 in an area closed to all human activities except the treatments. Each activity was randomly selected and
run on trails and primitive roads for a given 5-day period, followed by a 9-day period of rest (no human activity).
This pattern was repeated from spring through fall. Responses of animals to each activity versus rest periods were
analyzed in a variety of ways, including movement rates, flight responses, and habitat selection.
As part of this recreation-use study (Wisdom et al. 2004), conducted at the Starkey Experimental Forest and
Range (Cimon et al. 2004), we collected GPS position observations at one-second intervals for each of four series of
recreation trials: all-terrain vehicles, hikers, bikers, and horseback riders. Then, for each of the trial types, an average
velocity, defined as the average speed of each recreation activity in meters per minute, was obtained. These velocity
estimates will eventually be used to derive recreation density and to obtain estimates of equivalent recreation use
and its impact on deer and elk movements (Wisdom et al. 2004).
The GPS units were programmed to use all available satellites when finding a location regardless of the number
and geometry of those satellites. To date we have collected about 4 million GPS locations as part of 498 trials in the
two years of the study.
At the one-second sampling frequency, distance estimates based on differences between position measurements
often include large error components (the discrepancy between true location and estimated location) which biases
the resulting velocity estimates. We needed a method to calculate the average velocity under these conditions. As
one example, hikers move relatively slowly, and the GPS error can easily overwhelm their movement at the onesecond sampling frequency.
METHODS
We decided to calculate the average velocity for different time lags between GPS locations for a given
recreation trial. Our reasoning was that we could reduce the effect of the GPS error for a trial if we used a longer
time lag between GPS locations. We calculated the velocity using 1, 5, 10, 15, 20 and 25-second differences. A
graphical example for the first two of these is shown in Figure 1.
Remote Sensing for Field Users
Proceedings of the Tenth Forest Service Remote Sensing Applications Conference
Salt Lake City, Utah ΠApril 5-9 2004
Figure 1. One and five second GPS differences used for calculating average velocity
After calculating the average velocity using each of set of time-lagged points, we examined the results. As we
expected, the greater the lag size, the more the calculated average asymptotically approached what we assume is the
true mean.
The key to the analysis was the use of a relational database to store and analyze the data. Rapid application
development techniques were used to prototype then build an application1 that transfers the data from the dBase files
created by the Trimble2 GPS units directly into one of the Forest Service Oracle instances. The application also
tracks which specific trials had previously been loaded, and notified us if there were any conflicts (Appendix 3).
The complete details of the loading and analysis process are too lengthy to describe in this paper, but a block
diagram
of
the
general
process
is
shown
in
1
For more information on this application, please contact the Starkey data administrator Norm Cimon at
ncimon@fs.fed.us.
2
Mention of products or sources is given for information only. It does not constitute endorsement of the authors or
their employers.
Remote Sensing for Field Users
Proceedings of the Tenth Forest Service Remote Sensing Applications Conference
Salt Lake City, Utah ΠApril 5-9 2004
Appendix 1. The data, once in Oracle, were immediately made available through a library in the SAS system. A SAS
macro (Appendix 4) then created a series of datasets: one for each lagged velocity average grouped by trial. Our
initial decision to create a sequential key (called ID) for each GPS location as it was loading into the relational DB
allowed us to easily join two copies of the table via the correct offset3 which greatly simplified this process.
Additional macros were used to merge datasets, to fit different trial curves to the resulting velocity estimators,
to find trials with certain properties, to plot asymptotes, and to perform other analytical tasks4.
RESULTS AND DISCUSSION
To gain an understanding of the trend for each trial – and between trials of the same type – we plotted the
velocity averages as a function of the lag for each of them in SAS. A cross-section of these trials was also exported
to SigmaPlot for graphing. These are shown in Appendix 2 along with a trial-specific curve-fit that approximates the
velocity trend well, and the asymptote for each curve.
These trend lines were also calculated using the facilities of SAS. Two different non-linear models were fit to
the six lagged averages we’d calculated for each of our individual trials using models suggested by the data itself.
The first is:
vˆ ( L) = a ⋅ e − bL + c
where a , b and c are the constants of the fit, and L is the number of lag points. The second:
a
vˆ ( L) = + b
L
where a and b are constants and L , again, is the number of lag points. A second paper, currently in preparation will
provide a theoretical justification for the selection we made of the proper model and an examination of the errors
associated with it.
There is a caveat: the path of any GPS unit will rarely be straight, and any will affect the computation of the
distance and thus the velocity if the lag window becomes large (or the GPS unit is traveling very rapidly).
Nonetheless, the technique represents a new way of looking at GPS data. Even with relaxed requirements on the
precision of individual GPS locations, it is possible to obtain a very precise estimate of the velocity of the path the
GPS unit is traveling, a property of the entire point-set.
An added benefit is that the technique could, in theory, be incorporated directly into the units themselves, as it
requires only minimal storage to compute a series of running averages. The logic to determine the non-linear
regression parameters would also have to be programmed into the unit. The device would then provide very accurate
velocity data from relatively inaccurate location information.
LITERATURE CITED
Cimon, N., D. White, and N. Negulescu. Starkey Facilities,
Http://www.fs.fed.us/pnw/starkey/starkey_details/index.shtml. 2004.
Wisdom, M. J., A. A. Ager, N. J. Cimon, B. K. Johnson, and H. K. Preisler. Effects of off-road recreation on mule
deer and elk. Transactions of the North American Wildlife and Natural Resources Conference 69. 2004.
3
The WHERE clause in each proc SQL (Appendix 4) includes the necessary statements to join the two copies of
the table including the last AND with the ID field offset by the correct number of data points for the given time-lag.
4
For copies of these macros, please contact the Starkey data administrator Norm Cimon at ncimon@fs.fed.us.
Remote Sensing for Field Users
Proceedings of the Tenth Forest Service Remote Sensing Applications Conference
Salt Lake City, Utah ΠApril 5-9 2004
Appendix 1. Block diagram of GPS data processing
Remote Sensing for Field Users
Proceedings of the Tenth Forest Service Remote Sensing Applications Conference
Salt Lake City, Utah ΠApril 5-9 2004
Appendix 2. Cross-section of trial analyses for each recreation type
Remote Sensing for Field Users
Proceedings of the Tenth Forest Service Remote Sensing Applications Conference
Salt Lake City, Utah ΠApril 5-9 2004
Appendix 3. Starkey ATV study RAD application (top: loading data / bottom: trials in the DB)
Remote Sensing for Field Users
Proceedings of the Tenth Forest Service Remote Sensing Applications Conference
Salt Lake City, Utah ΠApril 5-9 2004
Appendix 4. SAS proc SQL code for 1 and 5 second time-lagged velocity estimates
proc sql;
CONNECT TO ORACLE AS StkyDBMS
(user=STKYDBA pw=xxxxxxxx path='idb' connection=global);
/*
* Query to produce the average speed (SPEED) in meters/second by
* Transport Type (TRANSPORT) and day (DAY) for the StarkeyATV
* study.
*/
CREATE TABLE StkyRec.AvgSpd01 AS
SELECT * FROM connection to StkyDBMS
(SELECT T1.TRANSPORT
"Transport",
T1.OBSDATE
"TrialDate",
T1.SECTION
"Section",
T1.TIMEOFDAY
"AM/PM",
T1.SEQUENCE
"Sequence",
1
"lag pts",
SUM(SQRT(POWER(T1.NORTHING-T2.NORTHING,2)+POWER(T1.EASTING-T2.EASTING,2)))/
(86400*SUM(NEW_TIME(T1.GPS_TIME,'GMT','PDT')-NEW_TIME(T2.GPS_TIME,'GMT','PDT'))) "Avg
Speed"
FROM
STKY_ATV_POSNPNT T1,
STKY_ATV_POSNPNT T2
WHERE T2.TRANSPORT = T1.TRANSPORT
AND
T2.OBSDATE = T1.OBSDATE
AND
T2.SECTION = T1.SECTION
AND
T2.TIMEOFDAY = T1.TIMEOFDAY
AND
T1.SEQUENCE = T2.SEQUENCE
AND
T2.ID = T1.ID-01
GROUP BY T1.TRANSPORT, T1.OBSDATE, T1.SECTION, T1.TIMEOFDAY, T1.SEQUENCE);
proc sql;
CONNECT TO ORACLE AS StkyDBMS
(user=STKYDBA pw=xxxxxxxx path='idb' connection=global);
/*
* Query to produce the average speed (SPEED) in meters/second by
* Transport Type (TRANSPORT) and day (DAY) for the StarkeyATV
* study.
*/
CREATE TABLE StkyRec.AvgSpd05 AS
SELECT * FROM connection to StkyDBMS
(SELECT T1.TRANSPORT
"Transport",
T1.OBSDATE
"TrialDate",
T1.SECTION
"Section",
T1.TIMEOFDAY
"AM/PM",
T1.SEQUENCE
"Sequence",
5
"lag pts",
SUM(SQRT(POWER(T1.NORTHING-T2.NORTHING,2)+POWER(T1.EASTING-T2.EASTING,2)))/
(86400*SUM(NEW_TIME(T1.GPS_TIME,'GMT','PDT')-NEW_TIME(T2.GPS_TIME,'GMT','PDT'))) "Avg
Speed"
FROM
STKY_ATV_POSNPNT T1,
STKY_ATV_POSNPNT T2
WHERE T2.TRANSPORT = T1.TRANSPORT
AND
T2.OBSDATE = T1.OBSDATE
AND
T2.SECTION = T1.SECTION
AND
T2.TIMEOFDAY = T1.TIMEOFDAY
AND
T1.SEQUENCE = T2.SEQUENCE
AND
T2.ID = T1.ID-05
GROUP BY T1.TRANSPORT, T1.OBSDATE, T1.SECTION, T1.TIMEOFDAY, T1.SEQUENCE);
proc sql;
Remote Sensing for Field Users
Proceedings of the Tenth Forest Service Remote Sensing Applications Conference
Salt Lake City, Utah ΠApril 5-9 2004