Leica GPS Basics User Manual
50
403020
GPS Basics
Introduction to GPS (Global Positioning System)
Version 1.0
English
Contents
Preface ........................................................... 4
1. What is GPS and what does it do ? .......... 5
2. System Overview ....................................... 6
2.1 The Space Segment ............................................... 6
2.2 The Control Segment .............................................. 8
2.3 The User Segment ................................................. 9
3. How GPS works ....................................... 10
3.1 Simple Navigation .................................................. 11
3.1.1 Satellite ranging .................................................... 11
3.1.2 Calculating the distance to the satellite ................. 13
3.1.3 Error Sources ........................................................ 14
3.1.4 Why are military receivers more accurate ? ........... 18
3.2 Differentially corrected positions (DGPS) ................19
3.2.1 The Reference Receiver ........................................ 20
3.2.2 The Rover receiver ................................................. 20
3.2.3 Further details ....................................................... 20
3.3 Differential Phase GPS and Ambiguity Resolution ... 22
3.3.1 The Carrier Phase, C/A and P-codes .................... 22
3.3.2 Why use Carrier Phase? ....................................... 23
3.3.3 Double Differencing............................................... 23
3.3.4 Ambiguity and Ambiguity Resolution ...................... 24
4. Geodetic Aspects ..................................... 26
4.1 Introduction ...........................................................27
4.2. The GPS coordinate system .................................28
4.3 Local coordinate systems ......................................29
4.4 Problems with height .............................................30
4.5 Transformations .....................................................31
4.6 Map Projections and Plane Coordinates ................. 34
4.6.1 The Transverse Mercator Projection ...................... 35
4.6.2 The Lambert Projection ......................................... 37
5. Surveying with GPS ................................ 38
5.1 GPS Measuring Techniques .................................. 39
5.1.1 Static Surveys ........................................................ 40
5.1.2 Rapid Static Surveys .............................................. 42
5.1.3 Kinematic Surveys ................................................. 44
5.1.4 RTK Surveys .......................................................... 45
5.2 Pre-survey preparation ........................................... 46
5.3 Tips during operation .............................................46
Glossary ....................................................... 48
Further Reading .......................................... 59
Index ............................................................. 60
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Preface
1. What is GPS and what does it do?
2. System Overview
3. How GPS works
4. Geodetic Aspects
5. Surveying with GPS
Glossary
Index
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Preface
Why have we written this book and
who should read it?
Leica manufactures, amongst other
things, GPS hardware and software.
This hardware and software is used by
many professionals in many applications. One thing that almost all of our
users have in common is that they are
not GPS scientists or experts in Geodesy. They are using GPS as a tool to
complete a task. Therefore, it is useful to
have background information about what
GPS is and how it works.
This book is intended to give a novice or
potential GPS user a background in the
subject of GPS and Geodesy. It is not a
definitive technical GPS or Geodesy
manual. There are many texts of this sort
available, some of which are included in
the reading list on the back pages.
This book is split into two main sections.
The first explains GPS and how it works.
The second explains the fundamentals
of geodesy.
Preface
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1. What is GPS and what does it do ?
GPS is the shortened form of NAVSTAR
GPS. This is an acronym for NAVigation
System with Time And Ranging Global
Positioning System.
GPS is a solution for one of mans
longest and most troublesome problems. It provides an answer to the
question Where on earth am I ?
One can imagine that this is an easy
question to answer. You can easily
locate yourself by looking at objects that
surround you and position yourself
relative to them. But what if you have no
objects around you ? What if you are in
the middle of the desert or in the middle
of the ocean ? For many centuries, this
problem was solved by using the sun
and stars to navigate. Also, on land,
surveyors and explorers used familiar
reference points from which to base their
measurements or find their way.
These methods worked well within
certain boundaries. Sun and stars
cannot be seen when it is cloudy. Also,
even with the most precise measurements position cannot be determined
very accurately.
After the second world war, it became
apparent to the U.S. Department of
Defense that a solution had to be found
to the problem of accurate, absolute
positioning. Several projects and
experiments ran during the next 25 years
or so, including Transit, Timation, Loran,
Decca etc. All of these projects allowed
positions to be determined but were
limited in accuracy or functionality.
At the beginning of the 1970s, a new
project was proposed GPS. This
concept promised to fulfill all the requirements of the US government, namely
that one should be able to determine
ones position accurately, at any point on
the earths surface, at any time, in any
weather conditions.
GPS is a satellite-based system that
uses a constellation of 24 satellites to
give a user an accurate position. It is
important at this point to define accurate. To a hiker or soldier in the desert,
accurate means about 15m. To a ship in
coastal waters, accurate means 5m. To
a land surveyor, accurate means 1cm or
less. GPS can be used to achieve all of
these accuracies in all of these applications, the difference being the type of
GPS receiver used and the technique
employed.
GPS was originally designed for military
use at any time anywhere on the surface
of the earth. Soon after the original
proposals were made, it became clear
that civilians could also use GPS, and
not only for personal positioning (as was
intended for the military). The first two
major civilian applications to emerge
were marine navigation and surveying.
Nowadays applications range from incar navigation through truck fleet management to automation of construction
machinery.
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What is GPS and what does it do ?
System Overview
2. System Overview
2.1 The Space Segment
The total GPS configuration is com-
prised of three distinct segments:
The Space Segment Satellites
orbiting the earth.
The Control Segment Stations
positioned on the earths equator to
control the satellites
The User Segment Anybody that
receives and uses the GPS signal.
The Space Segment is designed to
consist of 24 satellites orbiting the earth
at approximately 20200km every 12
hours. At time of writing there are 26
operational satellites orbiting the earth.
GPS Satellite Constellation
The space segment is so designed that
there will be a minimum of 4 satellites
visible above a 15° cut-off angle at any
point of the earths surface at any one
time. Four satellites are the minimum
that must be visible for most applications. Experience shows that there are
usually at least 5 satellites visible above
15° for most of the time and quite often
there are 6 or 7 satellites visible.
GPS satellite
Each GPS satellite has several very
accurate atomic clocks on board. The
clocks operate at a fundamental frequency of 10.23MHz. This is used to
generate the signals that are broadcast
from the satellite.
System Overview
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The satellites broadcast two carrier
waves constantly. These carrier waves
are in the L-Band (used for radio), and
travel to earth at the speed of light.
These carrier waves are derived from the
fundamental frequency, generated by a
very precise atomic clock:
• The L1 carrier is broadcast at 1575.42
MHz (10.23 x 154)
• The L2 carrier is broadcast at 1227.60
MHz (10.23 x 120).
The L1 carrier then has two codes
modulated upon it. The C/A Code or
Coarse/Acquisition Code is modulated
at 1.023MHz (10.23/10) and the P-code
or Precision Code is modulated at
10.23MHz). The L2 carrier has just one
code modulated upon it. The L2 P-code
is modulated at 10.23 MHz.
GPS receivers use the different codes to
distingush between satellites. The
codes can also be used as a basis for
making pseudorange measurements
and therefore calculate a position.
Fundamental
Frequency
10.23 Mhz
×154
×120
GPS Signal Structure
L1
1575.42 Mhz
L2
1227.60 Mhz
÷10
C/A Code
1.023 Mhz
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P-Code
10.23 Mhz
P-Code
10.32 Mhz
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System Overview
2.2 The Control Segment
The Control Segment consists of one
master control station, 5 monitor stations and 4 ground antennas distributed
amongst 5 locations roughly on the
earths equator.
The Control Segment tracks the GPS
satellites, updates their orbiting position
and calibrates and sychronises their
clocks.
A further important function is to determine the orbit of each satellite and
predict its path for the following 24
hours. This information is uploaded to
each satellite and subsequently broadcast from it. This enables the GPS
receiver to know where each satellite
can be expected to be found.
The satellite signals are read at Ascension, Diego Garcia and Kwajalein. The
measurements are then sent to the
Master Control Station in Colorado
Springs where they are processed to
determine any errors in each satellite.
The information is then sent back to the
four monitor stations equipped with
ground antennas and uploaded to the
satellites.
Colorado Springs
Haw aii
Ascension
Control Segment Station Locations
Kw ajalein
Diego G arcia
System Overview
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2.3 The User Segment
The User Segment comprises of anyone
using a GPS receiver to receive the GPS
signal and determine their position and/
or time. Typical applications within the
user segment are land navigation for
hikers, vehicle location, surveying,
marine navigation, aerial navigation,
machine control etc.
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System Overview
3. How GPS works
There are several different methods for
obtaining a position using GPS. The
method used depends on the accuracy
required by the user and the type of GPS
receiver available. Broadly speaking, the
techniques can be broken down into
three basic classes:
Autonomous Navigation using a single stand-alone receiver. Used by
hikers, ships that are far out at sea and the military. Position Accuracy is
better than 100m for civilian users and about 20m for military users.
Differentially corrected positioning. More commonly known
as DGPS, this gives an accuracy of between 0.5-5m. Used for
inshore marine navigation, GIS data acquisition, precision
farming etc.
Differential Phase position. Gives an accuracy of 0.5-20mm.
Used for many surveying tasks, machine control etc.
How GPS works
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3.1 Simple Navigation
3.1.1 Satellite ranging
This is the most simple technique
employed by GPS receivers to instantaneously give a position and height and/
or accurate time to a user. The accuracy
obtained is better than 100m (usually
around the 30-50m mark) for civilian
users and 5-15m for military users. The
reasons for the difference between
civilian and military accuracies are given
later in this section. Receivers used for
this type of operation are typically small,
highly portable handheld units with a
low cost.
All GPS positions are based on measuring the distance from the satellites to the
GPS receiver on the earth. This distance to each satellite can be determined by the
GPS receiver. The basic idea is that of resection, which many surveyors use in their
daily work. If you know the distance to three points relative to your own position, you
can determine your own position relative to those three points. From the distance to
one satellite we know that the position of the receiver must be at some point on the
surface of an imaginary sphere which has its origin at the satellite. By intersecting
three imaginary spheres the receiver position can be determined.
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A Handheld GPS Receiver
GPS Basics -1.0.0en
Intersection of three imaginary spheres
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How GPS works
The problem with GPS is that only
pseudoranges and the time at which the
signal arrived at the receiver can be
determined.
Thus there are four unknowns to determine; position (X, Y, Z) and time of travel
of the signal. Observing to four satellites
produces four equations which can be
solved, enabling these unknowns to be
determined.
At least four satellites are required to obtain a
position and time in 3 dimensions
How GPS works
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3.1.2 Calculating the distance to the satellite
In order to calculate the distance to each
satellite, one of Isaac Newtons laws of
motion is used:
Distance = Velocity x Time
For instance, it is possible to calculate
the distance a train has traveled if you
know the velocity it has been travelling
and the time for which it has been
travelling at that velocity.
GPS requires the receiver to calculate
the distance from the receiver to the
satellite.
The Velocity is the velocity of the radio
signal. Radio waves travel at the speed
of light, 290,000 km per second
(186,000 miles per second).
The Time is the time taken for the radio
signal to travel from the satellite to the
GPS receiver. This is a little harder to
calculate, since you need to know when
the radio signal left the satellite and
when it reached the receiver.
Calculating the Time
The satellite signal has two codes modulated upon it, the C/A code and the
P-code (see section 2.1). The C/A code is based upon the time given by a
very accurate atomic clock. The receiver also contains a clock that is used to
generate a matching C/A code. The GPS receiver is then able to match or
correlate the incoming satellite code to the receiver generated code.
The C/A code is a digital code that is pseudo random or appears to be
random. In actual fact it is not random and repeats one thousand times
every second.
In this way, the time taken for the radio signal to travel from the satellite to
the GPS receiver is calculated.
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How GPS works
3.1.3 Error Sources
Up until this point, it has been assumed
that the position derived from GPS is very
accurate and free of error, but there are
several sources of error that degrade the
GPS position from a theoretical few
metres to tens of metres. These error
sources are:
1. Ionospheric and atmospheric
delays
2. Satellite and Receiver Clock
Errors
3. Multipath
4. Dilution of Precision
5. Selective Availability (S/A)
6. Anti Spoofing (A-S)
1. Ionospheric and Atmospheric delays
As the satellite signal passes through
the ionosphere, it can be slowed down,
the effect being similar to light refracted
through a glass block. These atmospheric delays can introduce an error in
the range calculation as the velocity of
the signal is affected. (Light only has a
constant velocity in a vacuum).
The ionosphere does not introduce a
constant delay on the signal. There are
several factors that influence the amount
of delay caused by the ionosphere.
How GPS works
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a. Satellite elevation. Signals from low
elevation satellites will be affected more
than signals from higher elevation
satellites. This is due to the increased
distance that the signal passes through
the atmosphere.
b. The density of the ionosphere is
affected by the sun. At night, there is
very little ionospheric influence. In the
day, the sun increases the effect of the
ionosphere and slows down the signal.
The amount by which the density of the
ionosphere is increased varies with
solar cycles (sunspot activity).
Sunspot activity peaks approximately
every 11 years. At the time of writing, the
next peak (solar
max) will be
around the year
2000.
In addition to this,
solar flares can
also randomly
occur and also
have an effect on
the ionosphere.
Ionospheric errors
can be mitigated
by using one of
two methods:
- The first method
involves taking an
average of the
effect of the reduction in velocity of light
caused by the ionosphere. This correction factor can then be applied to the
range calculations. However, this relies
on an average and obviously this
average condition does not occur all of
the time. This method is therefore not
the optimum solution to Ionospheric
Error mitigation.
- The second method involves using
dual-frequency GPS receivers. Such
receivers measure the L1 and the L2
frequencies of the GPS signal. It is
known that when a radio signal travels
through the ionosphere it slows down at
a rate inversely proportional to its
frequency. Hence, if the arrival times of
the two signals are compared, an
accurate estimation of the delay can be
made. Note that this is only possible
with dual frequency GPS receivers. Most
receivers built for navigation are single
frequency.
c. Water Vapour also affects the GPS
signal. Water vapor contained in the
atmosphere can also affect the GPS
signal. This effect, which can result in a
position degradation can be reduced by
using atmospheric models.
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How GPS works
2. Satellite and Receiver clock errors
3. Multipath Errors
Even though the clocks in the satellite
are very accurate (to about 3 nanoseconds), they do sometimes drift slightly
and cause small errors, affecting the
accuracy of the position. The US Department of Defense monitors the satellite
clocks using the Control Segment (see
section 2.2) and can correct any drift that
is found.
Multipath occurs when the receiver
antenna is positioned close to a
large reflecting surface such as a
lake or building. The satellite signal
does not travel directly to the antenna
but hits the nearby object first and is
reflected into the antenna creating a
false measurement.
Multipath can be reduced by use of
special GPS antennas that incorporate a ground plane (a circular,
metallic disk about 50cm (2 feet) in
diameter) that prevent low elevation
signals reaching the antenna.
Choke-Ring Antenna
For highest accuracy, the preferred solution is
use of a choke ring antenna. A choke ring
antenna has 4 or 5 concentric rings around
the antenna that trap any indirect signals.
Multipath only affects high accuracy, surveytype measurements. Simple handheld
navigation receivers do not employ such
techniques.
How GPS works
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4. Dilution of Precision
The Dilution of Precision (DOP) is a
measure of the strength of satellite
geometry and is related to the spacing
and position of the satellites in the sky.
The DOP can magnify the effect of
satellite ranging errors.
The principle can be best illustrated by
diagrams:
Well spaced satellites - low uncertainty
of position
Poorly spaced satellites - high
uncertainty of position
The range to the satellite is affected by
range errors previously described. When
the satellites are well spaced, the
position can be determined as being
within the shaded area in the diagram
and the possible error margin is small.
When the satellites are close together,
the shaded area increases in size,
increasing the uncertainty of the position.
Different types of Dilution of Precision or
DOP can be calculated depending on
the dimension.
VDOP Vertical Dilution of Precision. Gives accuracy degradation in vertical direction.
HDOP Horizontal Dilution of Precision. Gives accuracy degradation in horizontal direction.
PDOP Positional Dilution of Precision. Gives accuracy degradation in 3D position.
GDOP Geometric Dilution of Precision. Gives accuracy degradation in 3D position and time.
The most useful DOP to know is GDOP
since this is a combination of all the
factors. Some receivers do however
calculate PDOP or HDOP which do not
include the time component.
The best way of minimizing the effect of
GDOP is to observe as many satellites
as possible. Remember however, that
the signals from low elevation satellites
are generally influenced to a greater
degree by most error sources.
As a general guide, when surveying with
GPS it is best to observe satellites that
are 15° above the horizon. The most
accurate positions will generally be
computed when the GDOP is low,
(usually 8 or less).
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How GPS works
3.1.4 Why are military receivers more accurate ?
5. Selective Availability (S/A)
Selective Availability is a process
applied by the U.S. Department of
Defense to the GPS signal. This is
intended to deny civilian and hostile
foreign powers the full accuracy of GPS
by subjecting the satellite clocks to a
process known as dithering which
alters their time slightly. Additionally, the
ephemeris (or path that the satellite will
follow) is broadcast as being slightly
different from what it is in reality. The end
result is a degradation in position
accuracy.
It is worth noting that S/A affects civilian
users using a single GPS receiver to
obtain an autonomous position. Users
of differential systems are not significantly affected by S/A.
Currently, it is planned that S/A will be
switched off by 2006 at the latest.
6. Anti-Spoofing (A-S)
Anti-Spoofing is similar to S/A in that its
intention is to deny civilian and hostile
powers access to the P-code part of the
GPS signal and hence force use of the
C/A code which has S/A applied to it.
Anti-Spoofing encrypts the P-code into a
signal called the Y-code. Only users with
military GPS receivers (the US and its
allies) can de-crypt the Y-code.
Military receivers are more accurate
because they do not use the C/A code to
calculate the time taken for the signal to
reach the receiver. They use the P-code.
The P-code is modulated onto the carrier
wave at 10.23 Hz. The C/A code is
modulated onto the carrier wave at 1.023
Hz. Ranges can be calculated far more
accurately using the P-code as this code
is occurring 10 times as often as the C/A
code per second.
The P-code is often subjected to Anti
Spoofing (A/S) as described in the last
section. This means that only the
military, equipped with special GPS
receivers can read this encryted P-code
(also known as the Y-code).
For these reasons, users of military GPS
receivers usually get a position with an
accuracy of around 5m whereas, civilian
users of comparable GPS receivers will
only get between about 15-100m
position accuracy.
How GPS works
A military handheld GPS receiver
(courtesy Rockwell)
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3.2 Differentially corrected positions (DGPS)
Many of the errors affecting the measurement of satellite range can be completely eliminated or at least significantly
reduced using differential measurement
techniques.
DGPS allows the civilian user to increase position accuracy from 100m to
2-3m or less, making it more useful for
many civilian applications.
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DGPS Reference station broadcasting to Users
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How GPS works
3.2.1 The Reference Receiver
3.2.2 The Rover receiver
3.2.3 Further details
The Reference receiver antenna is
mounted on a previously measured
point with known coordinates. The
receiver that is set at this point is known
as the Reference Receiver or Base
Station.
The receiver is switched on and begins
to track satellites. It can calculate an
autonomous position using the techniques mentioned in section 3.1.
Because it is on a known point, the
reference receiver can estimate very
precisely what the ranges to the various
satellites should be.
The reference receiver can therefore
work out the difference between the
computed and measured range values.
These differences are known as corrections.
The reference receiver is usually attached to a radio data link which is used
to broadcast these corrections.
The rover receiver is on the other end of
these corrections. The rover receiver has
a radio data link attached to it that
enables it to receive the range corrections broadcast by the Reference
Receiver.
The Rover Receiver also calculates
ranges to the satellites as described in
section 3.1. It then applies the range
corrections received from the Reference.
This lets it calculate a much more
accurate position than would be possible if the uncorrected range measurements were used.
Using this technique, all of the error
sources listed in section 3.1.3 are
minimized, hence the more accurate
position.
It is also worthwhile to note that multiple
Rover Receivers can receive corrections
from one single Reference.
DGPS has been explained in a very
simple way in the preceding sections. In
real life, it is a little more complex than
this.
One large consideration is the radio link.
There are many types of radio link that
will broadcast over different ranges and
frequencies. The performance of the
radio link depends on a range of factors
including:
Frequency of the radio
Power of the radio
Type and gain of radio antenna
Antenna position
Networks of GPS receivers and powerful
radio transmitters have been established, broadcasting on a maritime
only safety frequency. These are known
as Beacon Transmitters. The users of
this service (mostly marine craft navigating in coastal waters) just need to
purchase a Rover receiver that can
receive the beacon signal. Such systems have been set up around the
coasts of many countries.
How GPS works
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