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Geo-Positioning,
GPS, DGPS, and Positioning Accuracy
Assigned
Reading:
Please read Chapter 2
"Positioning Systems" in The
Precision-Framing Guide for Agriculturists, by Deere & Company.
On the Web http://www.trimble.com/gps/index.htm
study the following:
How GPS works
Differential GPS
Putting GPS to work
Scan http://nespal.cpes.peachnet.edu/home/links/pa/gps_resources.asp
to see items that may interest you at that site (no assigned
reading at this time).
Please read http://tycho.usno.navy.mil/gpsinfo.html
and answer the following:
1. The general population has access to Standard
Positioning Service (SPS). Give
the expected accuracy specification with Selected Availability on for
a.
Horizontal____________
b.
vertical ______________
c.
time ________________
GPS
Signal Characteristics
1. The
precision of a measurement is limited by the wavelength.
The shorter the wavelength, the more accurate the measurement.
If we use as a rule of thumb that measurements using with phase
shift relationships, (http://www.sfu.ca/sonic-studio/Phase-Shift.html)
we can measure to 1% of the wavelength, what are the missing wavelengths
and expected limits of accuracy for each of the following.
Note
frequency*wavelength=speed of light, MHz=106Hz or 106cycles/second.
The speed of light is 300,000,000 meters per second
|
Frequency
band
|
frequency
|
Wavelength
(meters)
|
Expected
accuracy centimeters
|
|
L1
|
1575.42MHz
|
0.190
|
0.19
|
|
L2
|
1227.6MHz
|
0.244
|
____
|
|
C/A
|
1.023MHz
|
____
|
____
|
|
P
|
10.23MHz
|
____
|
____
|
This example explains
how receivers based on the C/A frequency band only are less accurate that
those that use L1 and C/A for measurement.
Systems that use C/A are sometimes called GIS receivers.
The best accuracy for this class is a little better than one meter.
Most of the units used for precision agriculture are of this class.
Those that use the carrier wave (L1) have the capability of being
more accurate and are sometimes called surveying receivers with an
accuracy of one centimeter. The
most expensive of this class use both L1 and L2.
This adds the ability to better account for errors caused by the
atmosphere and increases the speed with which the unit can achieve
centimeter accuracy. These
differences will be explored more later when you study the specifications
of available equipment.
2.
How long is the C/A code pattern (i.e. period).
Selective
availability
3.
Selective availability reduction is accomplished by changing which
two items?
a._______________
b._______________
GPS
system segments
4.
How long is a sidereal day? ____________________
http://pegasus.phast.umass.edu/a100/handouts/sidday.html
5.
How does this cause the satellites to appear 4 minutes earlier each
day?
6.
Approximately how many times a day does a GPS satellite circle the
earth.
Clock
accuracy
If a clock had a timing error
of one microsecond, what would be the error in the distance measurement?
(This exercise is to impress you on the quality of the clocks on the
satellites)
7. What would be the
error for 1 nanosecond clock error? _______________
Where
are the satellites and how many are available at any given time?
The first thing to understand
is how to change our time to Greenwich Mean Time.
http://www.greenwich2000.com/time/info/time.htm
Reading Greenwich
Mean Time on this page will help you understand what time to enter to find
where the satellites are in your area at this time.
To make some sense of
these numbers look up your location on a globe. http://cliffie.nosc.mil/~NATLAS/index.html
and click world. For example San Luis Obispo, CA has an approximate
location of -120 degrees. (120 degrees west of Greenwich (0 degrees))
Since it takes 12 hours for the earth to rotate one half way (180
degrees) Greenwich is hours ahead of San Luis Obispo in time.
Then go to http://www.trimble.com/satview/index.htm
and look at satellite locations for your area at the time you are
observing the web page.
Note that an azimuth is the clockwise angle from north.
Understanding
GPS specifications
Read the definitions of 2DRMS,
RMS and CEP at
http://www.redhorsetech.com/aggps/NFlinks.html and compare to
page 24 and 25 of text. Then
use the following to relate it to statistics.
(Note if you like the
presentation below, the total publication is for sale)
Go to the following web site:
http://www.tellduxbury.com/seestatframeset.htm
click tour seeing statistics (twice)
click table of contents (on the side)
click Normal Distribution
click 7.0.1 and click through the pages to read what you need to
understand 7.3.1
click 7.3.1
Use the
calculator to calculate the error circle as one changes the accuracy
specification
2DRMS
Middle (on
bottom)
mean =0
Standard deviation (Std Dev) = 50
Z score = 2
Press enter.
The program calculates that the range of error is +/- 100 meters. Recall your answer to question 1.
RMS
Z score = 1 Enter
Error circle = 50 meters Percent
of the time the answer is right 68.3%
CEP
Probability
(prob.)= .5 (Percent of the time the answer is right 50%)
Error circle = 34 meters
Thus a
manufacturer can increase the apparent accuracy of his equipment (from 100
meters to 34 meters) by reducing the amount of time that the answer must
be right.
8. Assume
that the measurement is accurate within 30 meters 2DRMS with selective
availability off. (standard
deviation = 15)
Selective Availability is discussed at
http://www.csi-dgps.com/library/docs/articles/sa.htm
Note it is a controversial subject.
Find what
the manufacturer's accuracy specification would be for RMS and CEP for the
two blanks in the table.
|
Name of
statistic
|
Probability
Fraction of
time the answer is right
|
Error circle
(meters) with selective availability on
|
Error circle
(Meters) with selective availability off
|
|
2 s
2DRMS
|
.954
|
100
|
30
|
|
1 s
RMS
|
.683
|
50
|
___
|
|
CEP
|
.5
|
34
|
___
|
Note that quoting an
accuracy as CEP (wrong 50% of the time) and selective availability off are
the easiest way for a manufacturer of inexpensive equipment to look better
than expensive equipment to the uneducated eye.
Equipment
to be used in laboratories at Cal Poly
Collecting positions
with the Trimble ProXL
Contouring a vineyard
with the Trimble 4600LS. Real
time position corrections come from the base station located on the tripod
in the right center of the picture. The
corrections are sent via the radio antenna at the right of the picture.
The Ph the field was
measured using a grid pattern with the Trimble 4600LS.
The contours were drawn with Terramodel and added to ArcView with
CivilView. Terramodel and
CivilView are products of Spectra Precision.
CivilView is listed on Spectra Precision web page under
Spectra Precision Software Tools For ArcView
http://www.spectraprecisionatl.com/
The variable rate
sprayer demonstration unit uses an Ashtech AgNavagator. The real time differential correction is provided from a
Coast Guard Beacon correction signal received on the second antenna.
Sources
of Real Time GPS
Read http://www.navcen.uscg.mil/faq/dgpsfaq1.htm#How
go to http://www.navcen.uscg.mil/ADO/DgpsSelectStatus.asp
click
on Coverage plot and select your area (pick one of the first five choices
for an overview then pick your state for more complete information)
Is your area covered? __________________
What is the name of the site nearest you? ________________
For
worldwide information see http://joe.mehaffey.com/dgps.htm
http://www.csi-dgps.com/library/docs/articles/dgps.htm
and select
A WHITEPAPER ON DGPS
(IN PDF) to see what is planed for the future for your area. (not
required)
Reading
the specifications of the equipment used in the laboratory at Cal Poly.
Read http://www.redhorsetech.com/aggps/NFdefinitions.html
Download the file
agnav596.pdf.
Go to http://www.trimble.com/
and click Mapping and GIS Systems
Click the work products in the second paragraph.
At the side bar click GPS Pathfinder Pro XR/XRS
Download the Product Datasheet: PDF
Click home on the
side and Land Survey
Click on "Trimble
GPS Total Station® 4700"
On the side click on 4600LS
Download the Product Datasheet: PDF
This
exercise is to help you read the specification sheet on the equipment.
For the AgNavigator
look at the section Measurement Features
Single point position:* 25m(rms)
*with Selective Availability off
This says that 68.3% of the time that the receiver with no differential
corrections will be within 25 meters of the correct location when
selective availability is off. This
is consistent what was estimated above.
DGPS Position:
< 1 m (rms, PDOP<4)
With differential correction (from the Coast Guard for example) the
accuracy should be better than 1 meter 68.3 % of the time.
The satellites should not be all in one part of the sky.
See page 26 of your text.
Time to first
fix: Typically>1 minute.
When you turn on the unit it does not know where the satellites
are. It probably knows
approximately where in the world it is because of previous readings.
Under these conditions it will be able to obtain it location in 1
minute or less. For some
receivers, if the previous location is not stored in the instrument, it
can take a long time to initialize.
Tracks 12 satellites
simultaneously.
This should be enough to track all satellites in view.
Inexpensive instruments may track only one or two satellites and
have to cycle between satellites causing slower response.
Carrier-smoothed
pseudo range.
The basic measurement is made with the C/A code.
The carrier wave is used to improve the measurement but the integer
number of carrier waves to the satellite are not measured.
Half second update
rate
The GPS position is updated ever one half second.
At 5 miles per hour you would move 3.66 feet in one half second.
Note your speed will help determine your require update rate
Real time
Differential (RTCM 104)
This is the format required for a unit supplying the correction
information.
In
group discussion, discuss your interpretation of the specifications of the
other two GPS receivers.
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