REAL-TIME SURVEYING WITH GPS

Important Phone Numbers Trimble support Technical Assistance Center ftp://ftp.trimble.com www.trimble.com (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 www.navcen.uscg.mil Recorded message 703-313-5907 Live voice 703-313-5900 Computer Bulletin Board 703-313-5910 National Geodetic Survey www.ngs.noaa.gov Information Center 301-713-3242 Computer Bulletin Board 301-713-4181 or 4182 Point out the handout in the grey folder. Point out that all the about GPS Information Providers are accessable by voice, modem (BBS) or internet. The Coast Guard provides information on the status of the GPS constelation. (Show the students a sample copy of a NANU) The NGS provides you with the Precise Ephemeris, which can be used for very precise position over long baselines.

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 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 Ground Transmitter ( GT ) testing started in mid 1970’s - 1975? U.S. Army Yuma Proving Grounds ( YPG ) Yuma, Arizona Inverted Range Control Center ( IRCC ) with 4 GT’s Proof of concept testing, Phase I, II, III testing. Tanks, Jets, Helicopters, Jeeps.

GPS the segments Space Segment User Segment Monitor Stations Diego Garcia Ascension Is. Kwajalein Hawaii 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 Colorado Springs -- MCS Diego Garcia Ascension Islands Kwajalein Hawaii Onizuka - Backup Control Station control SA/A-S selective availability/anti-spoof

Space Segment 25 satellites in final constellation Very high orbit 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 Dredging 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) Ellipsoid fitting North America Ellipsoid fitting Europe Font change?? more Datum slides ?? Geoid 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-MAJOR AXIS SEMI-MINOR 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-MAJOR AXIS SEMI-MINOR 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 Cartesian coordinates (X, Y, Z) P H Cartesian coordinates (X, Y, Z) Ellipsoidal coordinates (f, l, H) Z Y f l X Y X

Altitude Reference Ellipsoid Geiod 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 Notes on Heights: GPS gives heights, or changes in heights, above the WGS-84 ellipsoid Conventional elevations and levels are referenced to mean sea level, or the geoid Conventional elevations generally considered to be orthometric heights Ellipsoid and geoid are not necessarily coincident or parallel Difference between the two surfaces is Geoid Separation, or N Estimates of N can be obtained from geoid models Geoid 90 and Geoid 93 based on 5-km grid Basic equation: Ortho hgt = Ellipsoidal hgt - Geoid separation or h = H - N BEWARE: use of h and H is not consistent throughout geodetic and GPS literature. KNOW WHAT YOU’RE LOOKING AT! BEWARE also the use of term “Geoid Hgt”: it is height of geoid above or below the ellipsoid Ellipsoid Geoid

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 Earths Surface 50 ft Ellipsoid Height = H H = 41 ft B.M. “A” elevation 84 ft B.M. “ B ” elevation 73 ft Earths Surface 50 ft Ellipsoid Height = H H = 41 ft Ellipsoid 84 ft h = 73 ft Orthometric Height = h Notes on Heights: GPS gives heights, or changes in heights, above the WGS-84 ellipsoid Conventional elevations and levels are referenced to mean sea level, or the geoid Conventional elevations generally considered to be orthometric heights Ellipsoid and geoid are not necessarily coincident or parallel Difference between the two surfaces is Geoid Separation, or N Estimates of N can be obtained from geoid models Geoid 90 and Geoid 93 based on 5-km grid Basic equation: Ortho hgt = Ellipsoidal hgt - Geoid separation or h = H - N BEWARE: use of h and H is not consistent throughout geodetic and GPS literature. KNOW WHAT YOU’RE LOOKING AT! BEWARE also the use of term “Geoid Hgt”: it is height of geoid above or below the ellipsoid 34 ft N = 32 ft Geoid Geoid 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 Note that this begins a confusing discussion: code vs. carrier Ultimately we don’t care about single-point positioning, but we need to get the basics anyway

WHAT IS A VECTOR? Notes on Vectors: GPS vectors computed from carrier phase observations Vectors have magnitude and direction Vectors expressed as dx, dy, dz in ECEF coordinate system, from one station to another

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 Spread Spectrum: Use wider bandwidth than needed to transmit data - protects against jamming and noise interference.

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 redo slide 1. Use the simple formula Distance = Rate X Time Rate = speed of light Time = travel time of the signal from the sv to the user 2. We need the travel time to get travel time we need : time that the signal left the sv and time that the signal arrived at the user. 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 from satellite from ground receiver measure time difference between same part of code

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 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 this sphere. 4 unknowns Latitude Longitude Height Time Need 4 equations

Calculate your position cont’d Second measurement narrows it down to intersection of two spheres 11,000 Miles 12,000 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 GDOP: Geometry of SV’s cause the mathematics that relate the satellite measurements to user position to be indeterminant or a divergent set of equations. Need explaination of URA

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 No S/A Total (rt sq sum) 13 feet Tropo/Iono Receivers Ephemeris Satellite Clocks 20 40 60 80 100 Typical observed errors satellite clocks 2 feet ephemeris error 2 feet receiver errors 4 feet tropospheric/iono 12 feet S/A Range error 100 feet No S/A Total (rt sq sum) 13 feet 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)

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 BASE If you collect data at one location there are going to be errors Each of these errors are tagged with GPS time . t+1 Time, t

Differential Correction (Cont.) ROVER Time, t t+1 ? At the same time, the errors occurring at one location are occuring everywhere within the same vicinity

Differential Correction (Cont.) ROVER Time, t t+1 ? BASE . t+1 Time, t Satellites Used Satellites Seen 1 2 3 4 5 6 1 2 3 4 1 3 5 6 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 ephemeris, sv clock drift, ionospheric, and tropospheric delay - seen over a relatively short period (10-20 min) are seen as relatively constant bias errors in receiver position data Can be removed by DGPS Ephemeris: errors in the satellite position ( usually <3 m, can be >30 m) Ionospheric delay: Modeled for L1 or taken out for L1/L2 (20-30 m day 3-6 m night Tropospheric delay: 2-3 m in zenith direction, 20-30 m at 5 deg elevation - depending on temperature, humidity, pressure, user height, terrain below SV signal Models can take out most of it 1 -3 m difference from Ref to User S/A: C/A code 100 m accuracy absolute Dither - alter freq and phase of SV signal Epsilon - alter ephemeris data Can be eliminated or reduced by DGPS Corrections lose accuracy over time Multipath interference Signal bounces off other objects and interferes with straight line signal Good receivers use advanced signal processing and good antenna

Summary 3 Segments of GPS GPS Signals Differentials Integer Ambiguity 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 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 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 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

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 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 Carrier waves and integer ambiguity Real Time Surveys Process of the Real Time Surveys Initalizations Fixed Automatic Components of RTS Base Rover Radio