Transcript REAL-TIME SURVEYING WITH GPS

REAL-TIME SURVEYING
WITH GPS
Important Phone Numbers
Trimble support
Technical Assistance Center
(hardware and software support)
Computer Bulletin Board
System Operator (David Elms)
Coast Guard Navigation Center
Recorded message
Live voice
Computer Bulletin Board
ftp://ftp.trimble.com
www.trimble.com
1-800-SOS-4TAC
1-800-767- 4822
408-732-6717
408-481-6049
www.navcen.uscg.mil
703-313-5907
703-313-5900
703-313-5910
National Geodetic Survey
www.ngs.noaa.gov
Information Center
Computer Bulletin Board
301-713-3242
301-713-4181 or 4182
GPS some background
• Satellite based positioning in development since mid 1960’s
• NAVSTAR GPS
• NAVigation Satellite Timing And Ranging
• Global Positioning System
• NAVSTAR GPS - Merging of two military programs in 1973
• Naval Research Laboratory - TIMATION program
• Air Force - 621B Project
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Managed by the Department of Defense
System tested with Ground Transmitters (pseudo-satellites)
First test satellites (Block I) launched in 1978
Operational satellites began launching in 1989 (Block II & Block IIA)
• Block II & Block IIA launched by Delta II rockets from Cape Canaveral
• Next generation of satellites (Block IIR) are already on contract
GPS the segments
Space Segment
Monitor Stations
Diego Garcia
Ascension Is.
Kwajalein
Hawaii
User Segment
Colorado Springs
Control Segment
Control / Monitor Segment
• 5 Stations world-wide
• Monitored by Department of Defense
• All perform monitor functions
• Receive all satellite signals
• Collect Meteorological data ( used for ionospheric modelling )
• Transmit data to MCS
• Master Control Station
• Upload to Satellites
• Orbital prediction parameters
• SV Clock corrections
• Ionospheric models
(Basically everything in NAVDATA)
• SV commands
Space Segment
• 25 satellites in final constellation
• 6 planes with 55° rotation
• each plane has 4/5 satellites
• Very high orbit
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20,183 KM, 12,545 miles
approximately 1 revolution in 12 hours
for accuracy
survivability
coverage
Copied from “GPS Navstar User’s Overview” prepare by
GPS Joint Program Office, 1984
User Segment
• Surveyors
• Anyone with GPS equipment
• Hardware and Software can be application specific
Vehicle Tracking
Navigation
Mapping
Hydrographics
Aircraft Approach and Landing
Dredging
Sunken ship salvage
Oil Exploration
Ambulances
Police
Cruise Ships
Courier Services
Hikers
Working surfaces
A Datum is described by a specifically oriented reference
ellipsoid defined by 8 elements
• Position of the network (3 elements)
• Orientation of the network (3 elements)
• Parameters of the reference ellipsoid (2 elements)
Ellipsoid
fitting
Europe
th a
r
o
N eric
Am
Euro
pe
Geoid
Regional Datums are designed so that the ellipsoid conforms to
the geoid over the desired region rather than the whole Earth
Ellipsoid fitting
North America
Earth-Centered, Earth Fixed System
• Z axis = Mean rotational
axis (Polar axis)
• X axis = 0 longitude
• X axis in plane of equator
• Y axis = 90 E longitude
• Y axis in plane of equator
Elements of an ellipse
• a = semi-major axis
b = semi-minor axis
• f = flattening = (a-b)/a
• Parameters used most often: a and 1/f
SEMI-MINOR AXIS
SEMI-MAJOR AXIS
Ellipse in 3-D: an Ellipsoid
• Rotate ellipse about semi-minor (polar) axis to obtain 3-d ellipsoid
• Semi-major axis is equatorial axis
SEMI-MINOR AXIS
SEMI-MAJOR AXIS
Common ellipsoids in surveying
• WGS-84 (Datum = WGS-84)
• a = 6378137.000
b = 6356752.310
1/f = 298.2572235630
• GRS-80 (Datum = NAD83)
• a = 6378137.000
b = 6356752.310
1/f = 298.2572221010
• Clarke 1866 (Datum = NAD27)
• a = 6378206.400
b = 6356583.800
1/f = 294.9786982000
• NOTE SIMILARITY BETWEEN WGS-84 AND GRS-80
Datum (WGS 84)
Datum (NAD 27)
Datum
One point can have different sets of coordinates depending on
the datum used
x
Coordinate Systems
Z
P
H
Cartesian coordinates (X, Y, Z)
Ellipsoidal coordinates (f, l, H)
Z
l
Y
f
X
Y
X
Altitude Reference
• Ellipsoid
• A smooth, mathematically defined model of the earths surface
• Geiod
• A surface of equal gravitational pull (equipotential) best fitting the average sea
surface over the whole globe
HAE
MSL
Earths Surface
Ellipsoid
Geoid
Notes about the geoid
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The geoid approximates mean sea level
The geoid is a function of the density of the earth
The geoid is a level surface which undulates
Conventional levels are referenced to the geoid
Reference Surfaces
B.M. “A” elevation 84 ft
B.M. “ B ” elevation 73 ft
Earths Surface
50 ft
Ellipsoid Height = H
H = 41 ft
Ellipsoid
34 ft
Geoid
Height = N
84 ft
Orthometric Height = h
h = 73 ft
Geoid
DE = B.M “A” - B.M. “B” =
ORTHOMETRIC 84 ft - 73 ft = 11 ft
ELLIPSOID
50 ft - 41 ft = 9 ft
N = 32 ft
Conditions for surveying with GPS
• At least 2 receivers required
• At least 4 common SV’s must be tracked from each station
• Visibility to the sky at all stations should be sufficient to track
4 SV’s with good geometry
• Data must be logged at common times (sync rates, or epochs)
• Receivers must be capable of logging carrier phase
observables (not just C/A code)
• At some point in the survey, at least one point must be
occupied which has known coordinates in the datum and
coordinate system desired
• 2 horizontal and 3 vertical control points are required for
complete transformation to the desired datum
What the surveyor gets in GPS
• 2 Types of Measurements:
• Change in phase of the code
• Change in phase of the carrier wave
• 2 Types of Results:
• Single point positioning and navigation -- from code
• Baseline vectors from one station to another (post-processed or processed as
“real time”)--from carrier wave
WHAT IS A VECTOR?
Z
Station1
on ground distance
Vector: Reference to Station1
geodesic
Reference
Y
X
Satellite Signal Structure
• Two Carrier Frequencies
• L1 - 1575.42 Mhz
• L2 - 1227.6 MHz
• Three modulations
• Two PRN codes
• Civilian C/A code
 L1
-160 dBw
 Option for L2 in future
• Military P code (Y code if encrypted)
 L1
-163 dBw
 L2
-166 dBw
• Navigation message (NAVDATA)
• L1
• L2
• Spread Spectrum
Who uses the code?
• Code-based applications:
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Rough mapping
GIS data acquisition
Navigation
Any applications able to tolerate accuracies in range of sub-meter - 5 meters
Measure Ranges to the satellites
• Use the simple formula: Distance = Rate X Time
• Distance = RANGE to the satellite (Pseudorange)
• Time = travel time of the signal from the satellite to the user
• When did the signal leave the satellite?
• When did it arrive at the receiver?
• Rate = speed of light
SV Time
SV Time
User Time
How do we know when the signal left
the satellite?
One of the Clever Ideas of GPS:
• Use same code at receiver and satellite
• Synchronize satellites and receivers so they're generating
same code at same time
• Then we look at the incoming code from the satellite and see
how long ago our receiver generated the same code
measure time
difference between
same part of code
from satellite
from ground receiver
The Integer Ambiguity--What is it?
• Receiver measures partial
wavelength when it first logs on
• Receiver counts successive
cycles after this
• Receiver does not know whole
number of wavelengths behind
that first partial one, which
exists between the receiver and
the SV
• This unknown, N, is called the
integer ambiguity or bias (also
called phase ambiguity or bias)
How carrier waves produce baselines
• At least 4 common SV’s must be observed from at least 2
separate stations
• The processor uses a technique called “differencing”
• Single difference compares data from 2 SV’s to 1 station, or
from 1 SV to 2 stations
• Double difference combines these two types of single
differences
• Single and double differences performed at specific epochs in
time
• Triple difference combines double differences over successive
epochs in time (every 10th epoch normally)
Sequence in processing carrier waves
• Begin with a code estimate of receiver locations
• First generate the triple difference solution
• Based on triple difference processing, find and correct cycle
slips
• Using improved estimate of dx,dy,dz from triple difference
solution, compute double difference float solution
• Set estimates of N from float solution to integers and recompute baseline: double difference, fixed integer solution
• Final result of processing is baseline vector, dx,dy,dz,
estimated to centimeter-level or better precision
Calculate your position
With range measurments to several satellites you can figure your
position using mathematics
• One measurement narrows down our position to the surface of
a sphere
11,000 miles
4 unknowns
Latitude
Longitude
Height
Time
Need 4 equations
We are somewhere
on the surface of
this sphere.
Calculate your position cont’d
Second measurement narrows it down to intersection of two
spheres
11,000
Miles
12,000
Miles
Intersection of two
spheres is a circle
Calculate your position cont’d
Third measurement narrows to just two points
Intersection of three
spheres is only two
points
In practice 3 measurements are enough to determine a position.
We can usually discard one point because it will be a ridiculous
answer, either out in space or moving at high speed.
Calculate your position cont’d
Fourth measurement will decide between the two points.
Fourth measurement
will only go through
one of the two points
The fourth measurement allows us to solve for the receiver
clock bias.
Dilution of precision (DOP)
An indication of the stability of the resulting position
• DOP is dependent upon the geometry of the constellation
• DOP is a magnification factor that relates satellite
measurement noise (input) to solution noise (output)
• The lower the DOP, the more accurate the position is.
• The higher the DOP, the less accurate the position is.
• In surveying, we care most about PDOP and RDOP
• PDOP = Position dilution of precision--refers to instantaneous SV geometry
• RDOP = Relative dilution of precision--refers to change in SV geometry over
the observation period
• For all DOP’s, the lower, the better
Dilution of precision (DOP)
• Relative position of satellites can affect error
4 secs
6 secs
idealized situation
Dilution of precision (DOP)
Real situation - fuzzy circles
6 ‘ish secs
4 ‘ish secs
uncertainty
uncertainty
Point representing position is really a box
Dilution of precision (DOP)
Even worse at some angles
Area of uncertainty
becomes larger as satellites get closer together
Dilution of precision (DOP)
Can be expressed in different dimensions
• GDOP - Geometric dilution of precision
• PDOP - Position dilution of precision
• HDOP - Horizontal dilution of precision
• VDOP - Vertical dilution of precision
• EDOP - East dilution of precision
• NDOP - North dilution of precision
• TDOP - Time dilution of precision
• GDOP2 = PDOP2 + TDOP2
• PDOP2 = HDOP2 + VDOP2
• HDOP2 = EDOP2 + NDOP2
Selective Availability (S/A)
Govt. introduces artificial clock and ephemeris errors to throw
the system off.
• Prevents hostile forces from using it.
• When turned up, it's the largest source of error
• Selective Availability is the sum of two effects:
• Epsilon, or data manipulation term - ephemeris “fibbing”
• Epsilon term changes very slowly - rate change once/hour
• Dither, or clock variations
• Dither term has cyclical variations from 1 cycle every 4 minutes to once
every 15 minutes
Error Budget
• Typical observed errors
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satellite clocks
ephemeris error
receiver errors
tropospheric/iono
S/A Range error
2 feet
2 feet
4 feet
12 feet
100 feet
• No S/A Total (rt sq sum)
Satellite Clocks
Ephemeris
Receivers
Tropo/Iono
13 feet
S/A
0
• Then multiply by HDOP (usually 2-3)
which gives a total error of:
• typical good receiver 25-40 feet (7-10 meters)
• with S/A Total (rt sq sum) 100 feet
• Multiply by HDOP (usually 2-3)
• which gives a total error of:
• typically 200-300 feet (60 to 100 meters)
20
40
60
Feet
80 100
DGPS
• DGPS = “Differential” GPS
• Generally refers to real-time correction of code-based
positions
• Real-time capabilities presume radio link between receivers
• The “differential” is the difference between a GPS code
position and a known position at a single receiver
Differential Correction
• If you collect data at one location
there are going to be errors
• Each of these errors are tagged with
GPS time
BASE
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t+1
Time, t
Differential Correction (Cont.)
ROVER
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t+1
Time, t
• At the same time, the errors
occurring at one location are
occuring everywhere within the
same vicinity
Differential Correction (Cont.)
ROVER
BASE
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t+1
Time, t
Satellites Used
1234
1356
Any Combination of Base SV's
t+1
Time, t
Satellites Seen
123456
GPS Error Sources
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Dilution of Precision (DOP)
Satellite ephemeris
removed by differencing
Satellite clock drift
removed by differencing
Ionospheric delay
removed by differencing
Tropospheric delay
removed by differencing
Selective Availability
removed by differencing
Multipath
Receiver clock drift
Receiver noise
Unhealthy Satellites
Summary
• 3 Segments of GPS
• Space
• Control
• User
• GPS Signals
• L1 - c/a code, P-code
• L2 - P-code
• Differentials
• Code - sub-meter precision
• Carrier - cm precision
• Integer Ambiguity
Real-Time vs. Post-Processed
• Results are available in the field, so checks can be verified
immediately
• Staking out is now possible
• One base receiver supports multiple rovers (unlimited)
• No post-processing time required in office
• Transformation parameters needed prior to survey, for proper
relationship between GPS WGS84 and local system
Conditions for Real-Time Surveying
• At least 2 receivers required
• At least 5 common SV’s must be tracked from each station
• Visibility to the sky at all stations should be sufficient to track
5 SV’s with good geometry (4 SV’s required for baseline
solution, but 5 are required for initialization)
• Initialization must take place at beginning of survey
• Radio link must be available between base and rover
• “Lock” to SV’s must be maintained, or re-initialization must
occur
• Transformation parameters must be available to get from GPS
WGS84 LLH to local NEE
What Happens in Real-Time
• Data is logged simultaneously at base and rover
• Base data is transmitted via radio link to radio antenna at
rover
• Survey is “initialized” using data from both base and rover
(data is processed inside roving receiver)
• Survey is conducted, with processing within roving receiver
continuing throughout
• Results of processing are sent to TDC1 for logging and
viewing (results normally 2 seconds behind actual reception)
• Results viewed may be either lat/long/ellipsoidal height or
northing, easting, elevation, depending on whether sufficient
information exists in TDC1 for transformation
What is Initialization?
• Determination of integer wavelength counts up to the
satellites
• Required at beginning of all real-time surveys
• Required in the middle of surveys, if continuous tracking of at
least 5 SV’s (in common with the base) has been interrupted
Types of Initialization
• Fixed Baseline
• Survey Controller (SC) option: “RTK Initializer” (“mini”
fixed baseline)
• SC option: “Known point” -- should be previously
surveyed with GPS
• Automatic Initialization
• While static -- SC option: “New point”
• While moving -- SC option: “Moving” (often referred to as
“OTF”, or on-the-fly)
• NOTE: “Survey Controller” is firmware inside TDC1
Fixed baseline vs. Automatic
• Fixed baseline initialization may be performed with all
receivers
• Automatic initialization requires dual frequency receivers
(4000 SSE)
• Automatic initialization while moving is additional option to
basic 4000SSE real-time configuration
• Survey Controller recognizes capability of receivers in survey,
and presents only those options supported by your receivers
Components of RTK system
• BASE
• Receiver with RTK firmware -- may be single or dual
frequency; internal memory (GPS data logging capability)
not required
• GPS antenna
• TRIMTALK 900 radio
• Radio antenna (7db recommended)
• Battery
• Cables
• 2 Tripods (one for GPS antenna, one for TRIMTALK
antenna) and 1 tribrach (radio antenna has mounting
bracket with 5/8 thread)
Components of system -- cont.
• ROVER
• Receiver -- may be single or dual frequency; internal
memory not required
• RTK firmware
• TDC1 with Survey Controller firmware
• TRIMTALK 900
• GPS antenna
• Radio antenna
• Battery
• Cables
• Recommended: backpack and range pole with bipod
The Radio Link
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Range of TrimTalk 900, with average conditions, is 1-3 km
Maximum range, with idealconditions, up to 10 km
Repeaters can be used to extend range
Base and rovers set on “Reference/Rover”settings
Repeaters must be set on separate, individual settings
All radios, including repeaters, must be on same (internal)
channel
• One base radio can be received by unlimited rovers
• Rover can receive real-time data from only one base
Real Time Surveying Applications
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Control
Topographic mapping
Construction stakeout
Cadastral surveying
Sources of error in RTS
• Multipath (deflected GPS signal which can give erroneous
results -- watch for reflective surfaces in survey area)
• Poor PDOP -- weak satellite geometry (PDOP should be less
than 7)
• Erroneous antenna heights
• Interference with radio link -- select a different channel
within the TrimTalk
Multipath at Station
Direct Signal
Reflected Signal
Cycle Slips and Loss of Lock
• Cycle slip = interruption of GPS signal, due to:
• Obstructions
• Radio or other electromagnetic interference
• Loss of lock = Known integer biases on fewer than 4 SV’s
• i.e. Cycle slips on so many SV’s that fewer than 4 integer biases are resolved
• NOTE: if satellite tracking is reduced to 4 SV’s, then resulting
PDOP may be too poor (i.e. high) to resolve integer biases on
other SV’s -- may require a re-initialization
Grid coordinates
• Initial result of GPS survey is precise network based on
(possibly) inaccurate coordinates
• WGS-84 coordinates must be transformed to meaningful local
system
• 2 horizontal and 3 vertical control points with values in
desired coordinate system and vertical datum are minimum
required for transformation
• In RTS, 4-6 control points are minimum number
recommended, and up to 10-15 may be desirable for large
areas
Grid coordinates -- continued
• Control points are first located with GPS to determine WGS84 values
• WGS-84 values and known NEE on control points are used to
generate proper transformation parameters from GPS system
to local grid
• After transformation parameters have been determined (in the
office), they are uploaded to TDC1 and used for all
subsequent field work, which can now be performed in local
grid system
Steps in Calibration
• Locate control points in the field
• Occupy control points using GPS
• Enter control (NEE) and GPS-derived coordinates (WGS-84
LLH) into TRIMMAP
• Perform GPS calibration in TRIMMAP
• Upload results of GPS calibration (by creating a new “DC”,
or data collector, file) to TDC1
• Continue field survey, which can now be performed in local
grid system
GPS Calibration in TRIMMAP
GPS
WGS84: Latitude, Longitude,
and Ellipsoidal Height
Local M ap Proje ction
Local Ellips oid
1
Local Latitude, Longitude,
and Ellipsoidal Height
Northing, Easting, Height
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3
Local Grid
Northing, Easting, Elevation
1
3 or 7 Parameter Datum Transf ormation (PDT)
2
Projection
3
2D Transf ormation and Height Adjustment
Another view of GPS Calibration
• CALIBRATION IS 2-STEP PROCESS
• 1. Deriving GPS coordinates for local control points (in
the field)
• 2. Computing calibration parameters for the project using
TRIMMAP (in the office)
• 4 POSSIBILITIES:
• GPS to LLH on Local Datum:
Datum Transformation
• Local LLH to Local NEH:
Mapping Projection
• Local NEH to Local NEE:
2-D Transformation
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and Height Adjustment
• NOTE: a Mapping Projection must be selected when
creating a project in TRIMMAP, while the remaining three
are optional (and will normally be performed)
Summary
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Carrier waves and integer ambiguity
Real Time Surveys
Process of the Real Time Surveys
Initalizations
• Fixed
• Automatic
• Components of RTS
• Base
• Rover
• Radio