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      WITH GPS
  Important Phone Numbers
Trimble support
   Technical Assistance Center
   (hardware and software support)   1-800-SOS-4TAC
                                     1-800-767- 4822
   Computer Bulletin Board           408-732-6717
   System Operator (David Elms)      408-481-6049
Coast Guard Navigation Center
   Recorded message                  703-313-5907
   Live voice                        703-313-5900
   Computer Bulletin Board           703-313-5910
National Geodetic Survey   
   Information Center                301-713-3242
   Computer Bulletin Board           301-713-4181 or 4182
GPS some background
• Satellite based positioning in development since mid 1960’s
     • 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
•   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
User Segment                                                  Diego Garcia
                                                               Ascension Is.

                               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
    •   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                     Ambulances
 Navigation                           Police
 Mapping                              Cruise Ships
 Hydrographics                        Courier Services
 Aircraft Approach and Landing        Hikers
 Sunken ship salvage
 Oil Exploration
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)

                                              Euro                  Ellipsoid fitting
 Ellipsoid                     orth rica
                              N e                 pe                North America
 fitting                       Am


   Regional Datums are designed so that the ellipsoid conforms to
   the geoid over the desired region rather than the whole Earth
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
Datum (WGS 84)
Datum (NAD 27)
One point can have different sets of coordinates depending on
 the datum used

Coordinate Systems

         Z       P

                             Cartesian coordinates (X, Y, Z)

                             Ellipsoidal coordinates (f, l, H)


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

MSL                        HAE
                                                                 Earths Surface

Notes about the geoid
 •   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

                84 ft
              Orthometric Height = h                         h = 73 ft
    34 ft                                            Geoid                    N = 32 ft
 Height = N
                      DE = B.M “A” - B.M. “B” =
                      ORTHOMETRIC 84 ft - 73 ft = 11 ft
                      ELLIPSOID                 50 ft - 41 ft = 9 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


  on ground distance           Station1

                                          Vector: Reference to Station1



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:
    •   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
 • Single and double differences performed at specific epochs in
 • 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
 • 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 re-
   compute 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         We are somewhere
                                             on the surface of
4 unknowns                                   this sphere.

Need 4 equations
  Calculate your position cont’d

Second measurement narrows it down to intersection of two


  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

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


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              Satellite Clocks
   •   satellite clocks    2 feet           Ephemeris
   •   ephemeris error     2 feet
   •   receiver errors     4 feet
   •   tropospheric/iono   12 feet         Tropo/Iono
   •   S/A Range error     100 feet
• No S/A Total (rt sq sum)            13 feet
   • Then multiply by HDOP (usually 2-3)            0     20   40     60   80 100
     which gives a total error of:                                  Feet
   • 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)
• DGPS = “Differential” GPS
• Generally refers to real-time correction of code-based
• 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    BASE
    there are going to be errors             .
  • Each of these errors are tagged with
    GPS time

                                           Time, t
Differential Correction (Cont.)
         ROVER         • At the same time, the errors
             ?           occurring at one location are
                         occuring everywhere within the
                         same vicinity

           Time, t
Differential Correction (Cont.)
           ROVER                        BASE
                ?                          .

                    t+1                        t+1
              Time, t                    Time, t

    Satellites Used            Satellites Seen
       1234                      123456
Any Combination of Base SV's
GPS Error Sources
 •   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

• 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
 • 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
 • 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
• 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
 • 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
 • 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
Components of RTK system

  • 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.

   • 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
 • 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)
 • One base radio can be received by unlimited rovers
 • Rover can receive real-time data from only one base
Real Time Surveying Applications
 •   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
 • 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
Grid coordinates -- continued
 • Control points are first located with GPS to determine WGS-
   84 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                           Local Ellipsoid                Local Map Projection
WGS84: Latitude, Longitude,           Local Latitude, Longitude,          Northing, Easting, Height
      and Ellipsoidal Height           and Ellipsoidal Height
                               1                                   2


                                                                              Local Grid
                                                                         Northing, Easting, Elevation

         1    3 or 7 Parameter Datum Transformation (PDT)

         2    Projection

         3    2D Transformation and Height Adjustment
Another view of GPS Calibration
    • 1. Deriving GPS coordinates for local control points (in
      the field)
    • 2. Computing calibration parameters for the project using
      TRIMMAP (in the office)
    • GPS to LLH on Local Datum:         Datum Transformation
    • Local LLH to Local NEH:            Mapping Projection
    • Local NEH to Local NEE:             2-D Transformation
    •                                     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)
•   Carrier waves and integer ambiguity
•   Real Time Surveys
•   Process of the Real Time Surveys
•   Initalizations
     • Fixed
     • Automatic
• Components of RTS
     • Base
     • Rover
     • Radio

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