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GEOG 425/525 GPS Concepts and Techniques. John Benhart, Ph.D. Indiana University of PA Dept. of Geography & Regional Planning. What Are Global Positioning Systems (GPS)?. What is GPS Used For?. The Historical Context of the Global Positioning System (GPS). The origins of surveying:

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geog 425 525 gps concepts and techniques

GEOG 425/525GPS Concepts and Techniques

John Benhart, Ph.D.

Indiana University of PA

Dept. of Geography & Regional Planning

the historical context of the global positioning system gps
The Historical Context of the Global Positioning System (GPS)
  • The origins of surveying:
    • Efforts to measure distance on the earth’s surface
    • Efforts to specify location on the earth’s surface
    • Efforts to determine property/land boundaries
  • How?
the basics of surveying
The Basics of Surveying
  • Definition: The science of measuring and mapping relative positions above, on, or below the surface of the earth; or establishing such positions from a technical plan or title description
  • Types:
    • Plane surveying: Does not take into account the curvature of the earth
    • Geodetic surveying: measurements covering larger distances where the curvature of the earth must be taken into account
surveying history
Surveying: History
  • Evidence of surveying has been recorded as early as 5,000 years ago
  • Ancient Egyptian surveyors called harpedonapata (“rope stretcher”
    • Ropes and knots were tied at pre-determined intervals to measure distances
    • The 3-4-5 triangle (later formalized by Pythgoras) was discovered to derive a right angle easily by using a rope knotted at 3,4, and 5 units
    • Early Egyptian levels that were essentially plumb lines were derived
surveying history1
Surveying: History
  • Surveying inventions
    • Lodestone used to identify magnetic north
    • Thomas Diggs invents an instrument used to measure angles called the theodolite in the mid-1500s
    • Jean Praetorius invents the plane table in 1610
    • W.J. Young invents the transit based on the theodolite, which “flips” to allow back sighting in 1831
the basics of surveying1
The Basics of Surveying
  • Starting from a position with a known location and elevation, known as a “benchmark,” the distance and angles to the unknown point are measured
    • Using a leveled theodolite or total station
    • Distance: previously chains, now lasers
    • Horizontal angle: from compass on theodolite
    • Vertical Angle: sighted in on a measuring or leveling rod at the location in question
the historical context of the global positioning system gps1
The Historical Context of the Global Positioning System (GPS)
  • 1978 – launch of first GPS satellite
  • 1982 – macrometer prototype tested at MIT
  • 1984 – geodetic network densification in Montgomery, Co. PA
  • 1989 – Launch of first Block II satellite; Wide Area GPS concept tested
  • 1990 – GEOID90 for NAD83 datum established
  • 1993 – Real-time kinematic GPS implemented
  • 1996 – First US GPS policy expressed in presidential directive
  • 1999 – US GPS modernization initiative
  • 2000 – Selective availability (SA) deactivated
overview of gps logic
Overview of GPS - Logic
  • A continuous coverage of satellites exists within view of virtually every location on the earth’s surface (NAVSTAR)
  • These satellites launch signals at recorded times on specific frequencies that can be “received” by units on the earth’s surface
  • By calculating the amount of time it takes the signals from 4 satellites to reach a receiver on the earth surface, it is possible to determine the distance between the receiver and any satellite (pseudoranges)
  • By using the intersection of the radii from 4 satellites, it is possible to determine exactly where a GPS receiver is located on the earth’s surface (trilateration)

** A huge amount of science and technology has to be applied for any of these conditions above to exist…

overview of gps objectives
Overview of GPS - Objectives
  • The GPS was “conceived as a ranging system from known positions in space to unknown positions on land, at sea, in air and space.” (p.11)
  • The original objectives of GPS were “instantaneous determination of position and velocity (i.e. navigation), and the precise coordination of time (i.e. time transfer).”
  • “The global NAVSTAR Global Positioning System (GPS) is an all-weather space-based navigation system under development by the DoD to satisfy the requirements of the military forces to accurately determine their position, velocity and time in a common reference system, anywhere on or near Earth on a continuous basis.”
overview of gps
Overview of GPS
  • GPS can be conceptually be divided into 3 segments:
    • Space Segment: the constellation of satellites
    • Control Segment: tracking and monitoring of the satellites
    • User Segment: varying user applications and receiver types
overview of gps1
Overview of GPS
  • Space Segment
    • The NAVSTAR constellation: 24 evenly-spaced satellites in 12-hour orbits inclined 55 degrees to the equatorial plane…each is assigned a pseudorandom noise code # (PRN code)
      • Types: Block I, Block II, Block IIA, IIR, IIF, and Block III
    • Continuous signal coverage of every location on the earth’s surface
    • Satellite signals: launched at extremely-precisely recorded times (atomic clocks), and travel at the speed of light (through earth atmosphere) to receivers on the earth’s surface
      • L1: 1575.42 MHz, L2: 1227.60 MHz
overview of gps2
Overview of GPS
  • Control Segment
    • Master control station: located at the Consolidated Space Operations Center at Shriver Air Force Base, Colorado Springs, CO
      • Collects monitoring data from global stations
      • Calculates satellite orbits and clock parameters for each satellite…passed to ground control stations
      • Responsibility for satellite control
overview of gps3
Overview of GPS
  • Control Segment
    • Monitoring Stations: Five located at Colorado Springs, Hawaii, Ascension Island (South Atlantic), Diego Garcia (Indian Ocean), Kwajalein (North Pacific)
      • Precise atomic time standard
      • Continuous calculation of satellite pseudoranges
      • Official network for determining broadcast ephemerides
    • Ground Control Stations
      • Also located at Ascension, Diego Garcia, and Kwajalein
      • Communication links to upload ephemeris, and clock information to NAVSTAR satellites
overview of gps4
Overview of GPS
  • User Segment
    • Military Users
      • Original envisioned users; have access to precise P-code satellite signals
    • Civilian Users
      • Range from recreational to GIS and survey grade applications – all made possible by federal infrastructure
    • Receiver Types
      • C/A code pseudorange; C/A code carrier phase; P-code carrier phase; Y-code carrier phase
gps summary
GPS Summary
  • The system is predicated on:
    • A constantly monitored constellation of satellites
    • Very accurate time measurement
    • The ability to determine satellite location
    • The use of unique radio signals on specified wavelengths launched from satellites and received by receivers on the earth’s surface
    • The ability to translate pseudoranges into recognized coordinates through trilateration
reference systems
Reference Systems
  • GPS satellites are orbiting earth and launching signals with time stamps…we are usually trying to determine locations on earth…to do this we have to define suitable coordinate and time systems
  • 3 Types of reference systems that are relevant in the context of GPS
    • Earth-fixed reference: the international terrestrial reference system
    • Space-fixed reference: the international conventional celestial reference system
    • Geodetic reference system
the earth and its axis of rotation
The Earth and Its Axis of Rotation
  • The Earth’s axis of rotation changes over time
  • Why? 1) Mainly caused by the gravitational forces of the moon and the sun…as well as other celestial bodies 2) changes in the mass of earth-based phenomena
    • Precession – a slight change in the direction of the axis of the rotating earth
    • Nutation - a slight irregular motion in the axis of rotation of an axially symetrical body (planet)
    • Polar Motion - the movement of the earth’s axis across its surface (~ 20 m westward since 1900)…due to motions in the earth’s core and mantle, and redistribution of water mass
  • Who Cares? These factors cause the position of the earth in its orbit (revolution) around the sun to change over time (equinoxes and solstices)


  • Nutation
  • Polar Motion

Precession: Cause

The gravitational pull of the sun on the closest part of the oblate spheroid is stronger…

reference systems and reference frames
Reference Systems and Reference Frames
  • Reference Systems: the complete specification of a coordinate system, such as the origin, coordinate axes, coordinate units, etc.
  • Reference Frames: consist of a set of identifiable points along with their coordinates, which serve as a realization of the reference system
international conventional celestial space reference system
International (Conventional) Celestial (Space) Reference System
  • The celestial reference system adopted by the International Astronomical Union (IAU) for high-precision positional astronomy
  • Characteristics: Origin at the solar system barycenter (center of mass) and “space fixed” axis directions
  • Has been chosen by the IAU as the “most appropriate coordinate system for expressing reference data on the positions and motions of celestial objects.”
international conventional celestial space reference system1
International (Conventional) Celestial (Space) Reference System
  • A set of specifications based on space-fixed axes defining the location of bodies in space
  • For example, the base plane of the system is the extension of the earth’s equatorial plane at J2000.0 (Jan. 1, 2000)
  • Locations (of planets and stars) are specified based on declination (north-south) and right ascension (east)
earth centered earth fixed reference
Earth-Centered Earth-fixed Reference
  • The mass center of the earth is used as a reference
  • Conventional Terrestrial Reference System: X axis is identical to the mean Prime (Greenwich) Meridian; Z axis is identical to the earth’s mean rotational axis (also called the Conventional International Origin (CIO)); Y axis points to the mean equatorial parallel
  • See (the International Earth Rotation and Reference Systems Service)

International Union of Geodesy and Geophysics (1991) Resolution on the Conventional Terrestrial Reference System

  • The International Union of Geodesy and Geophysics,
  • Considering the need to define a Conventional Terrestrial Reference System (CTRS) which would be unambiguous at the millimeter level at the Earth's surface and that this level of accuracy must take account of relativity and of Earth deformation, and
  • noting the resolutions on Reference Systems adopted by the XXIst General Assembly of the International Astronomical Union (IAU) at Buenos Aires, 1991, endorses the Reference System as defined by IAU at the XXIst General Assembly at Buenos Aires, 1991 and recommends the following definitions of the CTRS:
    • 1) CTRS to be defined from a geocentric non-rotating system by a spatial rotation leading to a quasi-Cartesian system,
    • 2) the geocentric non-rotating system to be identical to the Geocentric Reference System (GRS) as defined in the IAU resolutions,
    • 3) the coordinate-time of the CTRS as well as the GRS to be the Geocentric Coordinate Time (TCG),
    • 4) the origin of the system to be the geocenter of the Earth's masses including oceans and atmosphere, and,
    • 5) the system to have no global residual rotation with respect to horizontal motions at the earth's surface.
the international terrestrial reference frame
The International Terrestrial Reference Frame
  • The Earth is constantly changing shape, because of plate tectonics and regional subsidence and/or used to represent the Earth when measuring its rotation in space.
  • To be understood in context, when the motion of the Earth's crust is observed, it must be referenced. A Terrestrial Reference frame provides a set of coordinates of some points located on the Earth's surface. It can be used to measure plate tectonics, regional subsidence or loading and/or used to represent the Earth when measuring its rotation in space.
the international terrestrial reference frame1
The International Terrestrial Reference Frame
  • This rotation is measured with respect to a frame tied to the celestial reference frame. The International Earth Rotation and Reference Systems Service (IERS) was created in 1988 to establish and maintain a Celestial Reference Frame, the ICRF, a Terrestrial Reference Frame, the ITRF.
  • The Earth Orientation Parameters (EOPs) connect these two frames together. These frames provide a common reference to compare observations and results from different locations
  • Reference locations are periodically evaluated for position change to re-define the reference frame
  • The ITRF is regularly updated by the IERS…the latest frame is ITRF 2005
earth centered earth fixed reference1
Earth-Centered Earth-fixed Reference
  • World Geodetic System of 1984 (WGS84)
    • The reference system utilized in GPS
    • Provides the basic reference frame and geometric figure for the earth, based on the USDMA (Defense Mapping Agency’s) measurements and modeling of the earth from a geometric, geodetic, and gravitational standpoint, using techniques and technology available in 1984
earth centered earth fixed reference2
Earth-Centered Earth-fixed Reference
  • World Geodetic System of 1984
    • WGS84: a = 6,378137 m, f = 1/298.2572236
    • Geocentric coordinate system originally realized from the coordinates of approx. 1500 reference stations derived from TRANSIT observations
    • Uniform specification of the earth’s size, shape, geoid surface characteristics, and reference station coordinates (unlike ITRF)
reference systems1
Reference Systems
  • Time – 3 major systems are used in GPS
    • Sidereal time: a measure of the earth’s rotation…defined as the hour angle of the vernal equinox (ie.
    • Dynamical time: a uniformly-scaled time used to describe the motion of bodies in a gravitational field
      • Terrestrial dynamic time may be used to describe satellite motion without taking into account the gravitational field of the sun
    • Atomic time: time systems kept and defined by atomic clocks such as International Atomic Time (IAT)
      • Uniformly-scaled time used in earth-centered coordinate systems
      • Because of the slowing of the earth’s rotation with respect to the sun, “leap seconds” are used to create the Coordinated Universal Time System (UTC)
      • In most cases UTC and GPS time are synonymous….it is the basis of GPS time calculations
reference systems time systems
Reference Systems – Time Systems
  • GPS Calendar references
    • Julian Date (JD): defines the number of mean solar days elapsed since January 1, 4713 BC
    • Modified Julian Date (MJD): obtained by subtracting 2,400,000.5 days from JD
      • Saves digits and has MJD start at midnight instead of noon
    • GPS standard epoch (time, calendar): the atomic time scale implemented by the atomic clocks in GPS ground control stations and satellites
      • GPS standard epoch was initiated on Jan. 6th, 1980
      • Current GPS reference to January 1, 2000 (J2000.0)
inertial frame of reference
Inertial Frame of Reference
  • A reference frame in which…
    • Newton’s first and second laws of motion are valid: inertia; acceleration
  • Newton’s laws are valid in an environment that is nether rotating nor accelerating relative to other bodies
  • By contrast, bodies may be subject to forces that result from the acceleration of the reference frame itself….
earth fixed non inertial frame of reference
Earth-Fixed (Non-Inertial)Frame of Reference
  • One in which a body violates Newton’s law of Motion….that is, it is rotating or accelerating
    • An example of an non-inertial frame is an earth-fixed coordinate reference, as the earth is rotating and body (satellite) motion is measured with respect to it
inertial vs earth fixed reference
Inertial vs. Earth-fixed Reference
  • The inertial frame of reference is theoretical….
  • Therefore, a satellite’s orbit, and it relational location to the earth, must be translated into an earth-fixed reference
  • One that takes into account the movement of the earth, including rotation, gravity impacts, etc.

Johannes Kepler – 1571-1630

Scientist and Astronomer

Developed important theories (laws) regarding planetary orbits…

terms relating to keplerian motion
Terms Relating to Keplerian Motion
  • Perigee: closest approach of a satellite with respect to the earth’s center of mass
  • Apogee: most distant position (in an orbit) ” “
  • Nodes: intersections between the equatorial and orbital planes
  • Anomaly: instantaneous position of a satellite within its orbit
what are we saying
What are we Saying?
  • The orbits of satellites around the earth can be described by an ellipse…that has the following characteristics (parameters):
    • Right ascension of the ascending node
    • Inclination of the orbital plane
    • Argument of the perigree
    • Semimajor axis of the orbital ellipse
    • Numerical eccentricity of the ellipse
    • Epoch of the perigree passage
  • Orbits do not occur in an inertial environment
keplerian motion and perturbed motion
Keplerian Motion and Perturbed Motion
  • Perturbed motion is “characterized by the temporal variations of orbital parameters.”
    • Caused by: gravitational forces (sun, moon), solar radiational pressure, eclipse periods, etc.
  • Perturbed motion also causes the Keplerian orbit model specification to be modified
  • A data file that contains the approximate orbit information of all satellites, which is transmitted by each satellite within its Navigation Message. It is transmitted by a GPS satellite to a GPS receiver, where it facilitates rapid satellite signal acquisition within GPS receivers.
broadcast ephemeris
Broadcast Ephemeris
  • The "Broadcast Ephemeris (or Ephemerides)" for a satellite are the predictions of the current satellite position and velocity determined by the Master Control Station, uploaded by the Control Segment to the GPS satellites, and transmitted to the user receiver in the Data Message.
sources of error

Typical amount of Error (per Satellite)

Sources of Error

Beyond quality of equipment/size of antennea, etc.

1.5 m

2.5 m

5.0 m

0.5 m

0.3 m

0.6+ m

  • Satellite Atomic Clock Errors
  • (corrected periodically)
  • Satellite Orbit (Position) Errors
  • (corrected periodically)
  • Earth’s ionosphere (charged particles)
  • Earth’s troposphere (moisture)
  • Receiver Noise (local conditions, radio interference)
  • Multipath Errors (bounce off buildings, etc.)
  • Local Weather (moisture in air, lightning)
  • Poor Satellite Geometry (GDOP)
  • Receiver Clock Errors (corrected by 4th + Satellites)
  • Satellite Atomic Clock Errors
  • (corrected periodically)
  • Satellite Orbit (Position) Errors
  • (corrected periodically)
  • Earth’s ionosphere (charged particles)
  • Earth’s troposphere (moisture)
  • Receiver Noise (local conditions, radio interference)
  • Multipath Errors (bounce off buildings, etc.)
  • Local Weather (moisture in air, lightning)
  • Poor Satellite Geometry (GDOP)
  • Receiver Clock Errors (corrected by 4th + Satellites)
gps masks pdop elevation snr
GPS Masks: PDOP, Elevation, SNR

Allow the user to control the quality of the data accepted at the time

of data collection (unacceptable readings are filtered out)

PDOP Mask: Allows the recording of positions only when there is

acceptable satellite geometry. Typically considers both quantity

and quality of satellites (e.g., 4 satellites with good precision, or

6 with reasonable precision, or 8 with average precision)

Elevation Mask: Sets minimum elevation above horizon for satellites to

be used. The lower on the horizon a satellite is the more

atmosphere the signal must pass through, thus the greater the

potential for signal diffraction (inaccurate estimations of

time/distance), as well as greater chance of multi-path errors.

Also, with Differential Correction, insures that all satellites used

are visible to base station as well as the field receiver.

SNR (Signal to Noise Ratio) Mask: (higher is better, stronger signal)

Filters out signals with excessive noise, using only those

satellites with low noise (more accurate). SNR ranges from 0-35;

10-15 is typical, less than 5 is generally considered unusable.

differential correction
Differential Correction
  • Can improve accuracy by up to 20 m. (50-90%)
  • Requires local Base Station (w/in 100 miles)
  • Requires “post-processing” (back in the lab) OR can be done on-the-fly using Real-Time DGPS
  • Need better data – longer recording period, better GDOP
  • More Base Stations near coasts (navigation)
  • No effect on multi-path and/or receiver errors
differential correction1
Differential Correction

Compare GPS data file from Rover file (handheld unit) with a data file from a Base Station (at a known coordinate) for the exact same time period. Relies on the fact that receivers located relatively close together, will record similar errors from the same constellation of satellites.

Uses the apparent “error” of the base station file to correct the corresponding error of the Rover file.

differential correction 2
Differential Correction 2


Estimated Location

Actual (Known) Position

GPS Receiver

Estimated Location

Differentially Corrected Estimated Position




(unknown Location)

Base Station

(w/known coordinates)

gps data collection procedure using trimble terrasync
GPS Data Collection Procedure Using Trimble TerraSync
  • Once you start the unit up and check status (navigation screen)
  • You will open a new data collection file
    • .SSF file (default DDMMYYHH.SSF)
  • A .DDF file is required data collection in an .SSF file (data dictionary)
    • A default is provided if one is not selected
  • The .DDF file becomes the template for the positional definition of features


  • Each Satellite transmits two carrier waves
  • L1 - frequency of 1575.42 MHz and a wavelength of approx 19cm
  • L2 - frequency of 1227.60 MHz and a wavelength of approx 24cm
  • The following satellite-specific signals, called the pseudo random noise (PRN) codes are modulated on the carrier waves:
  • On L1: C/A (Coarse/Acquisition) code λ = approx 300m
        • - Accessible to civilian users
        • - Consists of a series of 1023 binary digits (called chips) that are unique to each satellite.
        • - The chip pattern is repeated every millisecond
  • P (precise) code λ = approx. 30m
      • - Accessible only to military equipment
  • On L2: P code only

SVs transmit two microwave carrier (carry information) signals

L1 (1575.42 MHz): carries navigation message; SPS code

(SPS: standard positioning service)

L2 (1227.60 MHz): measures ionospheric delay

3 binary codes shift L1 and/or L2 carrier phases

C/A code (coarse acquisition) modulates L1 carrier phase

…repeating 1 MHz pseudo random noise (PRN) code

…pseudo-random because repeats every 1023 bits or

every millisecond…each SV has its own C/A code

…basis for civilian SPS

P-code (precise) modulates both L1 and L2

…long (7 days) pseudo random 10 MHz noise code

…basis for PPS (precise positioning service)

…AS (anti-spoofing) encrypts P-code into Y-code

(need classified module for receiver)

navigation message modulates L1-C/A; 50 Mhz signal

….describes satellite orbits, clock corrections, etc.


GPS receiver produces replicas of C/A and/or P (Y) code

receiver produces C/A code sequence for specific SV


C/A code generator repeats same 1023 chip

PRN code sequence every millisecond

PRN codes defined for

32 satellite ID numbers

modern receivers usually store complete set

of precomputed C/A code chips in memory

gps satellite signals
GPS Satellite Signals
  • (Coarse Acquisition or C/A) Code Phase
    • Based on each satellite’s unique pseudo Random Noise Code (PRN)
    • Each satellite’s PRN code is totally unique, and can be replicated by GPS receivers
    • The receiver “slides” its code later and later in time until it matches up with the satellite’s code (code correlation)
    • This is called “code phase lock”…however, even if this is achieved, there can be significant error
      • Because the PRN codes are not that complicated (large cycle width ~ microsecond ~ 300 m. of error)
      • Even with highly accurate code phase lock, error can be 5-10 meters (with the signal traveling at 180,000 miles per second)

Code Signal Positioning

Subframe of message

Receiver Signal


Matching Subframe

DelayedSatellite Signal

The ‘mis-match’ between the code patterns is a measure of the time the signal has taken to travel from satellite to receiver.

gps observables code phase
GPS Observables – Code Phase
  • The Pseudorange: The GPS receiver measures the distance between the satellite and antenna by measuring the time the signal takes to propagate from the satellite to the receiver…the pseudorange is the time offset multiplied by the speed of light
code pseudorange
Code Pseudorange
  • Based on travel time between when signal is sent and when it is received
  • Time data also includes errors in both satellite and receiver clocks
    • Δt = tr – ts = [tr(GPS)-δr] – [ts(GPS) – δs]
  • Pseudorange given by R = c Δt = ρ + cΔδ
    • Pseudo because of cΔδ (where Δδ = δs – δr) factor
code phase acquisition
Code Phase Acquisition
  • Code phase estimation
  • PRN code characteristics
    • Maximum autocorrelation at lag 0
    • Minimum auto-correlation in all other cases
    • Minimum cross-correlation in all cases
  • Generate local PRN code
  • Perform circular correlation to obtain code phase
  • Code phase is the circular shift of the local code that gives maximum correlation

receiver slides replica of code in time until

finds correlation with SV signal

(codes are series of digital numbers)


if receiver applies different PRN code to SV signal

…no correlation

when receiver uses same code as SV and codes begin to align

…some signal power detected


when receiver and SV codes align completely

…full signal power detected

usually a late version of code is compared with early version

to insure that correlation peak is tracked







0 1 2 3 4 5 6 7

code tracking
Code tracking
  • Enhance the accuracy of code phase obtained by acquisition
  • Generate three local PRN codes 0.5 chips apart
    • Early
    • Prompt
    • Late
  • Correlate the local codes with incoming code
  • Adjust code phase according to result of correlation
code tracking1
Code tracking

Incoming code








Delay in chips






gps satellite signals1
GPS Satellite Signals
  • Carrier Phase
    • The carrier signal has a much higher frequency than the PRN code, and therefore if “matched” has a much higher level of accuracy
    • The carrier signal is ambiguous…that is it is much less differentiated than the PRN code
    • The code correlation is used to “narrow down” the time frame of signal travel…then the carrier signal is used to very accurately determine signal travel time
    • Used for high end mapping grade and survey grade GPS
carrier phase
Carrier Phase
  • Based on the number of cycles (wavelengths) between satellite and receiver
  • Phase data will include errors in both the satellite and receiver as well as an initial integer number, N
combinations of code and carrier phase
Combinations of Code and Carrier Phase
  • “Smoothing” of the code pseudorange using carrier phase correlation
  • Several different algorithms
carrier phase acquisition
Carrier Phase Acquisition
  • Acquisition purpose
    • Estimate coarse value of PRN code phase
    • Estimate coarse value of carrier frequency
  • Operates on 1ms blocks of data
    • Corresponds to the length of a complete PRN code
  • Carrier frequency estimation
  • Generate local carrier
  • Adjust frequency until highest correlation is obtained


1 2 3 4 5 6 7 8

  • Correct value for code phase and carrier frequency provides a peak correlation
carrier tracking

PRN code







NCO carrier


Carrier Tracking
  • Enhance the accuracy of the carrier frequency obtained by acquisition
  • Generate local carrier signal
  • Measure the phase error between incoming carrier and local carrier signal
  • Adjust frequency until phase and frequency becomes stable
gps signal
GPS signal



1 data bit






and data

gps signal1
GPS signal


and data

PRN code



gps navigation message
GPS Navigation Message
  • The GPS navigation message consists of time-stamped data bits marking the time of transmission of each data bit frame
    • A data (bit) frame is transmitted every 30 seconds and is comprised of 1500 bits, subdivided into 5 300-bit subframes
      • Subframe 1 – Clock correction (6 seconds)
      • Subframes 2 and 3 – Ephemeris data for short segments of a satellite’s orbit
      • Subframe 4 – Ionospheric corrections (GPS-UTC time offset)
      • Subframe 5 – Almanac information
    • An entire navigation message (25 data frames made up of 125 subframes) is sent over a 12.5 minute period
important tasks of a gps receiver
Important tasks of a GPS receiver
  • Prepare received signals for signal processing
  • Find satellites visible to the receiver
  • For each satellite
    • Find coarse values for C/A code phase and carrier frequency
    • Find fine values for C/A code phase and carrier frequency
    • Keep track of the C/A code phase and carrier frequency as they change over time
    • Obtain navigation data bits
    • Decode navigation data bits
    • Calculate satellite position
    • Calculate pseudorange
  • Calculate position
surveying with gps
Surveying with GPS
  • Terminology
    • Code range: less complex, unambiguous signal…lower level of accuracy
    • Carrier range: more complex, ambiguous signal…higher level of accuracy
    • Real-time processing: position results must be available in the field immediately
    • Post-processing: positional data are processed later
surveying with gps1
Surveying with GPS
  • Terminology continued
    • Point positioning: a single receiver measures pseudoranges
    • Differential positioning: an improved point positioning technique where corrections are applied to pseudoranges
    • Relative positioning: two receivers are used, and simultaneously receive signals from the same satellites
    • In general…point = navigation; relative = surveying, carrier phase; differential = code phase
surveying with gps2
Surveying with GPS
  • Terminology continued
    • Static point positioning: derivation of point positions without correction; 10 m accuracy
    • Static relative positioning (static surveying, carrier): most accurate; surveying technique; determination of the vector between two stationary receivers; cms. accuracy
    • Kinematic relative positioning: two receivers perform observations simultaneously; one is stationary and one is moving
surveying with gps observation techniques
Surveying with GPS – Observation Techniques
  • Point Positioning
    • Standard Positioning Service is standard for civilian users
    • Precise Positioning Service for military
  • Differential GPS: Two or more receivers are used…one as a stationary “base”, and the other as a mobile “rover”
    • Position correction; and pseudorange correction
differential gps
Differential GPS
  • Real-Time
    • Wide Area Augmentation System (WAAS)
    • Originated for commercial air flights
  • Post-Processing
    • National Oceanic and Atmospheric Administration (NOAA) National Geodetic Survey (NGS) Continuously Operating Reference Station (CORS) network
real time dgps the waas network
Real-Time DGPS: The WAAS Network
  • Wide Area Augmentation System –
    • Wide area ground reference stations (WRS) have been linked to form a U.S. WAAS network.
      • Signals from GPS satellites are received by these precisely surveyed ground reference stations and any errors in the signals are identified.
    • Each station in the network relays the data to one of two wide area master stations (WMS) where correction information for specific geographical areas is computed.
    • A correction message is prepared and uplinked to a geostationary communications satellite (GEO) via a ground uplink station (GUS).
    • This message is broadcast on the same frequency as GPS (L1, 1575.42 MHz) to GPS/WAAS receivers within the broadcast coverage area
base station data where does it come from
Base Station Data: Where Does it Come From?
  • In many cases, base station data in the United States is obtained from the National Oceanic and Atmospheric Administration (NOAA) National Geodetic Survey (NGS)
  • USNGS administers a program called CORS – Continuously Operating Reference Stations
  • Data from a network of base stations across the US is available…including customized data sets
surveying with gps relative positioning
Surveying with GPS – Relative Positioning
  • “…the highest accuracies are achieved in the relative positioning mode with observed carrier phases.”
    • Processing of baseline vectors
    • Static relative positioning
    • Kinematic relative positioning
    • Pseudokinematic relative positioning
surveying with gps planning a gps survey
Surveying with GPS – Planning a GPS Survey
  • The Federal Geodetic Control Subcommittee (FGCS) has classified GPS surveys based on the levels of accuracy necessary
    • A & B – very high accuracy geodetic control
    • 1st, 2nd , 3rd – surveying, engineering, topographic mapping
      • The higher the accuracy requirements, the more planning required
planning a gps survey
Planning a GPS Survey
  • GPS Survey Planning Parameters:
    • Site characteristics (obstructions, cover, etc.)
    • Satellite configurations (number, constellation dispersion, data quality)
    • Number and type of receivers
  • Primitives
    • Where, When, How Long, Quality
planning a gps survey1
Planning a GPS Survey
  • When – determination of the optimum daily observation period(s)
    • The period when the maximum number of satellites can be observed simultaneously
    • The period when the most advantageous constellation of SV azimuth/elevation combinations is “in view”
    • Use of Plan modules available on receivers and/or lab software
what have we covered
What have We Covered
  • Context of the GPS
  • Structure of the GPS
  • Reference Systems
    • Earth-fixed, Space-fixed, Geodetic
    • Time systems
  • Satellite orbits
    • Specification and characteristics
    • Keplerian motion; perturbed motion
  • Characteristics of Trimble GeoXH and GeoXT GPS receivers
  • GPS Satellite Signals
    • Code phase; pseudoranges
    • Carrier phase; ambiguity
what have we covered1
What have We Covered
  • Combination of Code and Carrier phases (smoothing)
  • GPS Navigation message explanation
  • Explanation of PathFinder Office and TerraSync softwares
  • Hands-on use of PathFinder Office and TerraSync softwares
  • Data Dictionary expanation/development
  • Field Data Collection
  • High Accuracy (survey-grade) GPS
what you should have obtained
What You Should Have Obtained
  • Project experience
    • Needs assessment
    • Database design
    • Data development
  • Final Project documents (portfolio)
  • References
  • Other?




cm cm cm 10-8 .001" .001" .001" IERS Tech.

. . . . . . . Note #, page

RATES T1 T2 T3 D R1 R2 R3

cm/y cm/y cm/y 10-8/y .001"/y .001"/y .001"/y


ITRF93 0.6 -0.5 -1.5 0.04 -0.39 0.80 -0.96 88.0

RATES -0.29 0.04 0.08 0.00 -0.11 -0.19 0.05 18 82

ITRF92 0.8 0.2 -0.8 -0.08 0.0 0.0 0.0 88.0 18 80

ITRF91 2.0 1.6 -1.4 0.06 0.0 0.0 0.0 88.0 15 44

ITRF90 1.8 1.2 -3.0 0.09 0.0 0.0 0.0 88.0 12 32

ITRF89 2.3 3.6 -6.8 0.43 0.0 0.0 0.0 88.0 9 29

ITRF88 1.8 0.0 -9.2 0.74 0.1 0.0 0.0 88.0 6 34


World Geodetic System 1984 (WGS 84)

  • The original WGS 84 reference frame established in 1987 was realized through a set of Navy Navigation Satellite System (NNSS) or TRANSIT (Doppler) station coordinates
  • Significant improvements in the realization of the WGS 84 reference frame have been achieved through the use of the NAVSTAR Global Positioning System (GPS).
  • Currently WGS 84 is realized by the coordinates assigned to the GPS tracking stations used in the calculation of precise GPS orbits at NIMA (former DMA).
  • NIMA currently utilizes the five globally dispersed Air Force operational GPS tracking stations augmented by seven tracking stations operated by NIMA. The coordinates of these tracking stations have been determined to an absolute accuracy of ±5 cm (1s).

World Geodetic System 1984 (WGS 84)

Using GPS data from the Air Force and NIMA permanent GPS tracking stations along with data from a number of selected core stations from the International GPS Service for Geodynamics (IGS), NIMA estimated refined coordinates for the permanent Air Force and DMA stations. In this geodetic solution, a subset of selected IGS station coordinates was held fixed to their IERS Terrestrial Reference Frame (ITRF) coordinates.


World Geodetic System 1984 (WGS 84)

  • Within the past years, the coordinates for the NIMA GPS reference stations have been refined two times, once in 1994, and again in 1996. The two sets of self-consistent GPS-realized coordinates (Terrestrial Reference Frames) derived to date have been designated:
    • WGS 84 (G730 or 1994)
    • WGS 84 (G873 OR 1997) , where the ’G’ indicates these coordinates were obtained through GPS techniques and the number following the ’G’ indicates the GPS week number when these coordinates were implemented in the NIMA precise GPS ephemeris estimation process.
  • These reference frame enhancements are negligible (less than 30 centimeters) in the context of mapping, charting and enroute navigation. Therefore, users should consider the WGS 84 reference frame unchanged for applications involving mapping, charting and enroute navigation.

Differences between WGS 84 (G873) Coordinates and WGS 84 (G730), compared at 1994.0

Station Location NIMA Station Number D East (cm) D North (cm) D Ellipsoid Height (cm)

Air Force Stations

Colorado Springs 85128 0.1 1.3 3.3

Ascension 85129 2.0 4.0 -1.1

Diego Garcia(<2 Mar 97) 85130 -3.3 -8.5 5.2

Kwajalein 85131 4.7 0.3 4.1

Hawaii 85132 0.6 2.6 2.7

NIMA Stations

Australia 85402 -6.2 -2.7 7.5

Argentina 85403 -1.0 4.1 6.7

England 85404 8.8 7.1 1.1

Bahrain 85405 -4.3 -4.8 -8.1

Ecuador 85406 -2.0 2.5 10.7

US Naval Observatory 85407 39.1 7.8 -3.7

China 85409 31.0 -8.1 -1.5

*Coordinates are at the antenna electrical center.


World Geodetic System 1984 (WGS 84)

  • The WGS 84 (G730) reference frame was shown to be in agreement, after the adjustment of a best fitting 7-parameter transformation, with the ITRF92 at a level approaching 10 cm.
  • While similar comparisons of WGS 84 (G873) and ITRF94 reveal systematic differences no larger than 2 cm (thus WGS 84 and ITRF94 (epoch 1997.0) practically coincide).
  • In summary, the refinements which have been made to WGS 84 have reduced the uncertainty in the coordinates of the reference frame, the uncertainty of the gravitational model and the uncertainty of the geoid undulations. They have not changed WGS 84. As a result, the refinements are most important to the users requiring increased accuracies over capabilities provided by the previous editions of WGS 84.

World Geodetic System 1984 (WGS 84)

  • The global geocentric reference frame and collection of models known as the World Geodetic System 1984 (WGS 84) has evolved significantly since its creation in the mid-1980s primarily due to use of GPS.
  • The WGS 84 continues to provide a single, common, accessible 3-dimensional coordinate system for geospatial data collected from a broad spectrum of sources.
  • Some of this geospatial data exhibits a high degree of ’metric’ fidelity and requires a global reference frame which is free of any significant distortions or biases. For this reason, a series of improvements to WGS 84 were developed in the past several years which served to refine the original version.

Other commonly used spatial reference systems

    • North American Datum 1983 (NAD83)
    • State Plane Coordinate System (SPCS) based on NAD83
    • Universal Transverse Mercator (UTM)

North American Datum (NAD)

NAD27 established in 1927

  • defined by ellipsoid that best fit the North American continent, fixed at Meades Ranch in Kansas
  • over the years errors and distortions reaching several meters were revealed

In 1970’s and 1980’s NGS carried out massive readjustment of the horizontal datum, and redefined the ellipsoid

The results is NAD83 (1986)

  • based on earth-centered ellipsoid that best fits the globe and is more compatible with GPS surveying
  • in 1990’s state-based networks readjustment and densification, accuracy improvement with GPS (HARN and CORS networks)

NAD 83 Defining Parameters

Parameter Notation Magnitude

Semi-major Axis a 6378137.0 meters

Reciprocal of Flattening 1/f 298.2572221

Datum point – none

Longitude origin – Greenwich meridian

Azimuth orientation – from north

Best fitting – worldwide

X,Y,Z (Lat, Lon, h) based on the definition of GRS80 ellipsoid


State Plane Coordinate System

  • Based on Lambert and Transverse Mercator projections
  • Developed in 1930’s and redefined in 1980’s and 90’s
  • NAD ellipsoid was projected to the conical (Lambert) and cylindrical (Transverse Mercator) flat surfaces
  • Allowed the entire USA to be mapped on a set of flat surfaces with no more than one foot distortion in every 10,000 feet (maximum scale distortion 1 in 10,000)
  • Coordinates used are called easting and northing; derived from NAD latitude, longitude and ellipsoidal parameters

State Plane Coordinate System

  • The scale of the Lambert projection varies from north to south, thus, it is used in areas mostly extended in the east-west direction
  • Conversely, the Transverse Mercator projection varies in scale in the east-west direction, making it most suitable for areas extending north and south
  • Both projections retain the shape of the mapped surface
  • Each state is usually covered by more than one zone, which have their own origins – thus, passing the zone boundary would cause the coordinate jump!

Universal Transverse Mercator, UTM

  • Developed by the Department of Defense for military purpose
  • It is a global coordinate system
  • Has 60 north-south zones numbered from west to east beginning at the 180th meridian
  • The coordinate origin for each zone is at its central meridian and the equator

Universal Transverse Mercator

  • UTM zone numbers designate 6-degree longitudinal strips extending from 80 degrees south latitude to 84 degrees north latitude
  • UTM zone characters designate 8-degree zones extending north and south from the equator
  • There are special UTM zones between 0 degrees and 36 degrees longitude above 72 degrees latitude, and a special zone 32 between 56 degrees and 64 degrees north latitude

UTM Zones

  • Each zone has a central meridia. Zone 14, for example, has a central meridial of 99 degrees west longitude. The zone extends from 96 to 102 degrees west longitude
  • Easting are measured from the central meridian, with a 500 km false easting to insure positive coordinates
  • Northing are measured from the equator, with a 10,000 km false northing for positions south of the equator

Vertical Datum Definition 1/2

  • Horizontal control networks provide positional information (latitude and longitude) with reference to a mathematical surface called sphere or spheroid (ellipsoid)
  • By contrast, vertical control networks provide elevation with reference to a surface of constant gravitational potential, called geoid (approximately mean see level)
    • this type of elevation information is called orthometric height (height above the geoid or mean sea level) determined by spirit leveling (including gravity measurements and reduction formulas).
  • Height information referenced to the ellipsoidal surface is called ellipsoidal height. This kind of height information is provided by GPS

Height Systems Used in the USA

  • Orthometric
  • Normal (orthometric normal)
  • Dynamic
  • Ellipsoidal

Variety of height systems (datums) used requires careful definition of differences and transformation among the systems


Vertical Datum Definition 2/2

  • Vertical datum is defined by the surface of reference – geoid or ellipsoid
  • An access to the vertical datum is provided by a vertical control network (similar to the network of reference points furnishing the access to the horizontal datums)
  • Vertical control network is defined as an interconnected system of bench marks
  • Why do we need vertical control network?
    • to reduce amount of leveling required for surveying job
    • to provide backup for destroyed bench marks
    • to assist in monitoring local changes
    • to provide a common framework

The height reference that is mostly used in surveying job is orthometric

  • Orthometric height is also commonly provided on topographic maps
  • Thus, even though ellipsoidal heights are much simpler to determine (eg. GPS) we still need to determine orthometric heights

Normal to the ellipsoid


Normal to the geoid (plumb line or vertical)







  • - angle between the normal to the ellipsoid and the vertical direction (normal

to the geoid), so-called deflection of the vertical

H – orthometric height

h – ellipsoidal height h = H + N

N – geoid undulation (computed from geoid model provided by NGS)


Orthometric vs Ellipsoidal Height

(Orthometric height)

(computed from a geoid model)


So, how do we determine orthometric height?

  • By spirit leveling
  • And gravity observations along the leveling path, or
  • Recently -- GPS combined with geoid models (easy!!!) but not as accurate as spirit leveling + gravity observations

H = h-N

But why do we need gravity observations with spirit leveling?

Because the sum of the measured height differences along the leveling path between points A and B is not equal to the difference in orthometric height between points A and B



Level Surfaces and Plumb Lines 1/2

Equipotential surfaces are not parallel to each other


Level Surfaces and Plumb Lines 2/2

  • The level surfaces are, so to speak, horizontal everywhere, they share the geodetic importance of the plumb line, because they are normal to it
  • Plumb lines (line of forces, vertical lines) are curved
  • Orthometricheights are measured along the curved plumb lines
  • Equipotential surfaces are rather complicated mathematically and they are not parallel to each other
  • Consequently:
    • Orthometric heights are not constant on the equipotential surface !
    • Thus, points on the same level surface would have different orthometric height !

Spirit leveling

Height differences between the consecutive locations of backward and forward rods

correspond to the local separation between the level surfaces through the bottom of the

rods, measured along the plumb line direction


Orthometric Height vs. Spirit Leveling









dhi H

C1, C2, C3, C4 – geopotential numbers corresponding to level (equipotential) surfaces

dh1, dh2, dh3, dh4 – height difference between the level surfaces (determined by spirit leveling, path-dependent); their sum is not equal to H !

Because equipotential surfaces are not parallel to each other


Geopotential Numbers 1/3

  • The difference in height, dh, measured during each set up of leveling can be converted to a difference in potential by multiplying dh by the mean value of gravity, gm, for the set up (along dh).

geopotential difference = gm*dh

  • Geopotential number C, or potential difference between the geoid level W0 and the geopotential surface WP through point P on the Earth surface (see Figure 2-8), is defined as

Where g is the gravity value along the leveling path. This formula is used to compute C when g is measured, and is independent on the path of integration!


Geopotential Numbers 2/3

Since the computation of C is not path-dependent, the geopotential number can be also expressed as

C = gm*H,

where H is the height above the geoid (mean sea level) and gm represents the mean value of gravity along H (along the plumb line at point P on Figure 2-8; see “orthometric height vs. spirit leveling)

  • the last relationship justifies the units for C being kgal*meter; it is not used to determine C!
  • Finally:
    • Geopotential number is constant for the geopotential (level) surface
    • Consequently, geopotential numbers can be used to define height and are considered a natural measure for height

REMEMBER: Orthometric heights are not constant on the equipotential surface !


Observed difference in height depends on leveling route

  • Points on the same level surface have different orthometric heights

Local normal (plumb line direction) to equipotential (level) surfaces








Reference surface (geoid)


Orthometric height measured along the plumb line direction


No direct geometrical relation between the results of leveling and orthometric heights

H = H1-H2  dhup + dhdown  0


What then, if not orthometric height, is directly obtained by leveling?

  • If gravity is also measured, then geopotential numbers, C (defined by the integral formula shown earlier), result from leveling
  • Thus, leveling combined with gravity measurements furnishes potential difference, that is, physical quantities
  • Consequently, orthometric height are considered as quantities derived from potential differences
  • Thus, leveling without gravity measurements introduces error (for short lines might be neglected) to orthometric height

Geopotential Numbers 3/3

Let’s summarize:

  • The sum of leveled height differences between two pints, A and B, on the Earth surface will not equal to the difference in the orthometric heights HA and HB
  • The difference in height, dh, measured during each set up of leveling depends on the route taken, as level (equipotential) surfaces are not parallel to each other
  • Consequently, based on the leveling and gravity measurements
    • the geopotential numbers are initially estimated (using the integral formula introduced earlier), based on the leveling and gravity measurements along the leveling path
    • geopotential numbers can then be converted to heights (orthometric, normal or dynamic – see definitions below) if gravity value along the plumb line through surface point P is known

Height = C/gravity


Height Systems 1/5

  • In order to convert the results of leveling to orthometric heights we need gravity inside the earth (along the plumb line)
    • since we cannot measure it directly, as the reference surface lies within the Earth, beneath the point, we use special formulas to compute the mean value of gravity, along the plumb line, based on the surface gravity measured at point P
    • reduction formulas used to compute the mean gravity, gm, based on gravity measured at point P on the Earth surface lead to:
        • Orthometric height, (H = C/gm) or
  • The reduction formula used to compute mean gravity, based on normal gravity at point P on the Earth surface leads to:
        • Normal (also called normal orthometric) height, (H* = C/ m )

Where  is so-called normal gravity (model) corresponding to the gravity field of an ellipsoid of reference (Earth best fitting ellipsoid), and subscript “m” stands for “mean”


Height Systems 2/5

  • We can also define dynamic heights
    • use normal gravity, 45, defined on the ellipsoid at 45 degree latitude, (HD = C/ 45)
  • Note: term “normal gravity” always refers to the gravity defined for the reference ellipsoid, while “gravity” relates to geoid or Earth itself

Height Systems 3/5

Sometimes, instead of formulas provided above (involving C), it is convenient to use correction terms and apply them to the sum of leveled height differences:

  • Consequently, the measured elevation difference has to be corrected using so-called orthometric correction to obtain orthometric height (height above the geoid)

Max orthometric correction is about 15 cm per 1 km of measured height difference

  • Or, the measured elevation difference has to be corrected using so-called dynamic correction to obtain dynamic height (no geometric meaning and factual reference surface; defined mathematically)
  • Or, normal correction is used to derive normal heights
  • All corrections need gravity information along the leveling path (equivalent to computation of C based on gravity observations!)

Height Systems 4/5

  • Dynamic heights are constant for the level surface, and have no geometric meaning
  • Orthometric height
    • differs for points on the same level surface because the level surfaces are not parallel. This gives rise to the well-known paradoxes of “water flowing uphill”
    • measured along the curved plumb line with respect to geoid level
  • Normal height of point P on earth surfaceis a geometric height above the reference ellipsoid of the point Q on the plumb line of P such as normal gravity potential and Q is the same as actual gravity potential at P.
    • measured along the normal plumb line (“normal” refers to the line of force direction in the gravity field of the reference ellipsoid (model))
  • All above types of heights are derived from geopotential numbers

Height Systems 5/5

  • A disadvantage of orthometric and normal heights is that neither indicates the direction of flow of water. Only dynamic heights possess this property.
  • That is, two points with identical dynamic heights are on the same equipotential surface of the actual gravity field, and water will not flow from one to the other point.
  • Two points with identical orthometric heights lie on different equipotential surfaces and water will flow from one point to the other, even though they have the same orthometric height
  • The last statement holds for normal heights, although due to the smoothness of the normal gravity field, the effect is not as severe

Vertical Datums: NGVD 29 and NAVD 88

  • NGVD 29 – National Geodetic Vertical Datum of 1929
    • defined by heights of 26 tidal stations in US and Canada
    • uses normal orthometric height (based on normal gravity formula)
  • NAVD 88 – North American Vertical Datum of 1988
    • defined by one height (Father Point/Rimouski, Quebec, Canada)
    • 585,000 permanent bench marks
    • uses Helmert orthometric height (based on Helmert gravity formula)
    • removed systematic errors and blunders present in the earlier datum
    • orthometric height compatible with GPS-derived height using geoid model
    • improved set of heights on single vertical datum for North America

Vertical Datums: NGVD 29 and NAVD 88

  • Difference between NGVD 29 and NAVD 88
    • ranges between – 40 cm to 150 cm
    • in Alaska between 94 and 240 cm
    • in most stable areas the difference stays around 1 cm
    • accuracy of datum conversion is 1-2 cm, may exceed 2.5 cm
    • transformation procedures and software provided by NGS (

International Great Lake Datum (IGLD) 1985

  • IGLD 85
    • replaced earlier IGLD 1955
    • defined by one height (Father Point/Rimouski, Quebec, Canada)
    • uses dynamic height (based on normal gravity at 45 degrees latitude)
    • virtually identical to NAVD 88 but published in dynamic heights!

Vertical Datums

  • Use of proper vertical datum (reference surface) is very important
  • Never mix vertical datums as ellipsoid – geoid separation can reach 100 m!
  • Geoid undulation, N, is provided by models (high accuracy, few centimeters in the most recent model) developed by the National Geodetic Survey (NGS) and published on their web page

So, in order to derive the height above the see level (H) with GPS observations – determine the ellipsoidal height (h) with GPS and apply the geoid undulation (N) according to the formula H = h - N

space fixed reference
Space-fixed Reference
  • The Conventional Celestial Reference System
    • Based on a kinematical definition, making the axis directions defining the coordinate system fixed with respect to distant matter of the universe
    • A celestial reference frame defined by the precise coordinates of extragalactic objects (mostly quasars)
    • Based on IAU recommendations, the coordinate origin is to be at the barycenter of the solar system, and the axes should be fixed with respect to the quasars
    • Principal coordinate plane to be as close as possible to the mean earth equator at J2000.0
satellite orbits
Satellite Orbits
  • Implementation of GPS depends heavily on being able to quantify satellite orbits
  • Keplerian Motion – a satellite is supposed to move in a central force field
    • Equation of satellite motion is described by Newton’s second law of motion: where f is the attracting force; m is the mass of the satellite

The fundamental frequency of GPS signal

  • 10.23 MHz
  • two signals, L1 and L2, are coherently derived from the basic frequency by multiplying it by 154 and 120, respectively, yielding:
  • L1 = 1575.42 MHz (~ 19.05 cm)
  • L2 = 1227.60 MHz (~ 24.45 cm)
  • The adaptation of signals from two frequencies is a fundamental issue in the reduction of the errors due to the propagation media, mainly, ionospheric refraction and SA
gps signals
Two carrier frequencies (to remove ionospheric effects)

L1: 1575.42 MHz (154  10.23 MHz)

wavelength - 19.05 cm

L2: 1227.60 MHz (120  10.23 MHz)

wavelength - 24.45 cm

GPS Signals

New GPS Signal FOR Civilian Users

  • Planned for Block IIF satellites (2005)
    • L5: 1176.45 MHz (115  10.23 MHz)
    • wavelength – 25.5 cm
  • Signal L2 will remain a civilian signal as well

GPS Signals

  • Carrier L1 and L2
  • Codes superimposed on carrier
    • P-code (precise/protected code, under AS it’s replaced by a Y-code) on L1 and L2
    • C/A – code (clear/coarse acquisition) on L1
  • The fourth type of signal transmitted by GPS satellites is the broadcast message (navigation message) on L1 and L2 (identical)
gps signal structure
Code modulation (sequence of binary values: +1 or –1)

L1: P1 & C/A code, navigation message

L2: P2 code, navigation message

P-code frequency - 10.23 MHz (i. e., 10.23 million binary digits or chips per second)

P-code repetition rate: 266.4 days, 7-day long portion of the code are assigned to every satellite; codes are restarted every week at midnight from Saturday to Sunday.

P-code “wavelength” - 29.31 m

C/A-code frequency - 1.023 MHz (i.e., 1.023 million binary digits or chips per second; codes are repeated every millisecond)

C/A-code “wavelength” - 293.1 m

GPS Signal Structure

How do we get the numbers right?

  • Assuming 1.023 MHz frequency for C/A-code, and repetition rate of 1 millisecond:
    • 1,023,000 Hz * 10-3 sec = 1023 bits (or chips); this is the length of the C/A code
    • For 1023 chips in 1 millisecond we get separation between two chips equal to (roughly) 1 microsecond
    • 1 microsecond separation between the chips corresponds to ~300 m chip length (for 300,000 km/sec speed of light)
  • Check it out the same way for the P-code!!!

GPS Signal Structure

  • The epochs of both codes are synchronized
  • In civilian receivers, the short C/A code is acquired first to allow access to the P-code
  • Carrying two codes on L1 is achieved by phase quadrature
    • unmodulated L1 carrier is split off and shifted in phase by 90º, then mixed with C-code and then added to the
    • P-modulated signal – see Figure 7.8 below

GPS Message

  • Data File - carrier phase, pseudorange, and range rate (Doppler)
  • Navigation Message (broadcast ephemeris) - provides information about satellite orbits, time, clock errors and ionospheric model to remove the ionospheric delay (error) from the observations)
  • Provided in binary-receiver dependent format
  • Usually converted to RINEX - Receiver Independent Exchange format (ASCII file)

GPS Navigation Message

TLM = Telemetry Word HOW = Handover Word (contains Z-count)


TLM, telemetry word – contains a synchronization pattern which facilitates the access to the navigation data

  • HOW, handover word allows direct access to the P code; but first the C/A code must be acquired to allow for time synchronization; this allows an access to HOW from the navigation message, and then the P-code can be acquired
    • P-code can be accessed only after the C/A code-supported receiver time synchronization with GPS time through the Z-count
    • HOW contains so-called Z-count
  • Z-count is defined as integer number of 1.5-second periods since the beginning of the GPS week, and thus identifies the epoch of a data record in GPS time
    • If one knows the Z-count, one can acquire the P-code within the next six seconds

But we don’t know the actual P-code (under AS)

  • We already discussed how a GPS receiver measures the range (or pseudorange) to the satellite by measuring the time delay between the incoming signal and its replica generated by the receiver
  • Signal synchronization (correlation) provides the signal travel time measure
  • The PRN code (P-code) carried by the signal allows to achieve that (if its known; currently, civilians know only C/A code)
  • But how do we get an access to the precise code under AS policy, if the Y-code (replacing the P-code) is not known, and thus, the time synchronization scheme will not work?

GPS Navigation Message (RINEX)


DAT2RIN 1.00e The Boss 29JUN98 17:59:25 GMT PGM / RUN BY / DATE


.1118D-07 .0000D+00 -.5960D-07 .0000D+00 ION ALPHA

.9011D+05 .0000D+00 -.1966D+06 .0000D+00 ION BETA

-.142108547152D-13 -.372529029846D-08 61440 159 DELTA-UTC: A0,A1,T,W



3 97 10 10 18 0 0.0 .605774112046D-04 .352429196937D-11 .000000000000D+00

.760000000000D+02 .494687500000D+02 .448018661776D-08 .220198356145D+00

.264309346676D-05 .244920048863D-02 .842288136482D-05 .515366117668D+04

.496800000000D+06 .335276126862D-07 -.790250226717D+00 -.372529029846D-07

.951777921211D+00 .211531250000D+03 .259765541557D+01 -.819891294621D-08

.160720980388D-10 .100000000000D+01 .926000000000D+03 .000000000000D+00

.700000000000D+01 .000000000000D+00 .139698386192D-08 .588000000000D+03


6 97 10 10 15 59 44.0 -.358093529940D-06 .000000000000D+00 .000000000000D+00

.220000000000D+02 .526250000000D+02 .438268255632D-08 -.281081720890D+00



GPS Observation File Header (RINEX)


DAT2RIN 1.00e The Boss 29JUN98 17:59:19 GMT PGM / RUN BY / DATE


5137 TRIMBLE 4000SSI Nav 7.25 Sig 3. 7 REC # / TYPE / VERS

0 4000ST L1/L2 GEOD ANT # / TYPE

____0001 MARKER NAME


557180.9687 -4865886.9211 4072508.3413 APPROX POSITION XYZ

0.0000 0.0000 0.0000 ANTENNA: DELTA H/E/N




1997 10 10 15 13 5.000000 TIME OF FIRST OBS

1997 10 10 16 38 8.000000 TIME OF LAST OBS


3 1598 1603 1504 1504 PRN / # OF OBS

6 4051 4051 4051 4051 PRN / # OF OBS

9 4208 4212 4150 4150 PRN / # OF OBS

……………………… (rest of the SV is given here)………………………………… PRN / # OF OBS



GPS Observation File (RINEX)

97 10 10 15 13 6.000 0 5 6 10 17 23 26 0.000215178

-331628.90610 21627234.69600 -258412.19950 21627239.86440

-330564.59210 23839375.76600 -264155.63150 23839382.29440

-344922.28510 20838559.61800 -268770.84150 20838564.48140

-344734.12710 22476960.02400 -268624.54850 22476965.59140

-338016.17810 20319996.64100 -263389.71350 20320000.46240

97 10 10 15 13 7.000 0 5 6 10 17 23 26 0.000215197

-329205.73500 21627695.91400 -256524.01640 21627700.98840

-327788.16700 23839904.12500 -261992.18640 23839909.89140

-346924.68000 20838178.43000 -270331.14940 20838183.24640

-346674.25800 22476590.73400 -270136.33740 22476596.25440

-337719.08000 20320053.10100 -263158.20940 20320056.88740

97 10 10 15 13 8.000 0 5 6 10 17 23 26 0.000215216

-326782.19000 21628157.18700 -254635.54040 21628162.34340

-325011.83600 23840432.60100 -259828.81640 23840438.14440

-348926.80400 20837797.46000 -271891.24440 20837802.31240

-348614.34600 22476221.42900 -271648.09340 22476226.99540

-337421.42500 20320109.74100 -262926.27040 20320113.51540

………………………………………………………………………………. continues


RINEX 2 description:

  • Code Pseudorange
  • Carrier Phase Pseudorange
  • Doppler
  • Combinations of data
  • Biases and Noise terms
  • Doppler shift depends on radial velocity
    • More useful for determining velocities than for determining positions
  • To get positions, need to integrate Doppler shifts (phase differences)
data combinations
Data Combinations
  • Theoretically, data can be obtained from
    • Code ranges – RL1, RL2
    • Carrier phases – ΦL1,ΦL2
    • Doppler shifts – DL1, DL2
  • Combinations of these data could be used as well
data combinations1
Data Combinations
  • In general, linear combinations of phase will look like
    • φ = n1φ1 + n2φ2
    • Where n1 and n2 can be any integer
  • Noise level increases for combined data
    • Assuming noise levels are equal for both, the increase is by a factor of √2
data combinations2
Data Combinations
  • If n1 = n2 = 1, then
    • ΦL1+L2 = ΦL1 +ΦL2
      • Denoted narrow-lane
      • λL1+L2 = 10.7cm
  • If n1 = 1 and n2 = -1, then
    • ΦL1-L2 = ΦL1 – ΦL2
      • Denoted wide-lane
      • λL1-L2 = 86.2cm
  • Used for integer ambiguity resolution
data combinations3
Data Combinations
  • If n1 = 1 and n2 = –fL2/fL1, then
    • ΦL3 = ΦL1 –fL2/fL1ΦL2
    • Called L3 (sometimes denoted ionosphere-free)
  • Used to reduce ionospheric effects
what to do with errors
What to do with Errors?
  • There are essentially 4 options:
    • Ignore them
      • Works if the errors are small (negligible)
    • Model them
      • Need good models
      • Not all effects can be modeled
    • Solve for them
      • Increases complexity of solution
    • Make them go away
gps ephemeris errors
GPS Ephemeris Errors
  • 3 types of ephemerides
    • Almanac – very crude (~100m), used only for planning purposes
    • Broadcast – reasonably accurate (~1m), used for real-time work
    • Precise – very accurate (~10cm), used for high precision work
      • Available after the fact
selective availability sa
Selective Availability (SA)
  • Way to degrade the navigation accuracy of the code pseudorange
  • Comprised of two parts:
    • Dithering the satellite clock (δ-process)
    • Manipulating the ephemerides (ε-process)
selective availability
Selective Availability
  • Dithering the satellite clock
    • Changing the fundamental frequency
    • Changes over the course of minutes
    • Can be eliminated by differencing between receivers
  • Manipulating the ephemerides
    • Truncating the navigational information
    • Changes over the course of hours
clock errors
Clock Errors
  • Both satellites and receivers will have clock errors
    • There’s no such thing as a perfect clock
  • Any error in a clock will propagate directly into a positioning error
    • Remember distance = velocity*time
  • Satellite clock errors can be reduced by applying the corrections contained in the broadcast
ionospheric delay
Ionospheric Delay
  • Caused by the electrically charged upper atmosphere, which is a dispersive medium
    • Ionosphere extends from 40 to 1100 km
    • Effects carrier phase and code ranges differently
    • Effect on the phase and group velocity
      • nph = 1 + c2/f2 …
      • ngr = 1 – c2/f2
    • Note that this will effect frequencies differently
      • Higher frequency is affected less
ionospheric delay1
Ionospheric Delay
  • Measured range given by s = ∫n ds
    • n is the refractive index
    • ds is the path that the signal takes
  • The path delay is given by
    • Δphiono = –(40.3/f2) ∫Ne ds0 = –40.3/f2 TEC
    • Δgriono = (40.3/f2) ∫Ne ds0 = 40.3/f2 TEC
      • Where TEC = ∫Ne ds0 is the total electron content
ionospheric delay2
Ionospheric Delay
  • Still need to know TEC
  • Can either
    • Measure using observations
    • Estimate using models
  • Note that with data on 2 frequencies, estimates of the unknowns can be made
tropospheric delay
Tropospheric Delay
  • Caused by the neutral atmosphere, which is a nondispersive medium (as far as GPS is concerned)
    • Troposphere extends up to 40 km
    • Effects carrier phase and code ranges the same
  • Typically separate the effect into
    • Dry component
    • Wet component
  • ΔTrop = 10-6∫NdTrop ds + 10-6∫NwTrop ds
    • Where N is the refractivity
    • ds is the path length
tropospheric delay1
Tropospheric Delay
  • Dry component contributes 90% of the error
    • Easily modeled
  • Wet component contributes 10% of the error
    • Difficult to model because you need to know the amount of water vapor along the entire path
tropospheric delay2
Tropospheric Delay
  • There are many models which estimate the wet component of the tropospheric delay
    • Hopfield Model
    • Modified Hopfield Model
    • Saastamoinen Model
    • Lanyi Model
    • NMF (Niell)
    • Many, many more
special relativistic considerations
Special Relativistic Considerations
  • Time dilation
    • Moving clock runs slow
  • Lorentz contraction
    • Moving object seems contracted
  • Second order Doppler effect
    • Frequency is modified like time
  • Mass relation
general relativistic considerations
General Relativistic Considerations
  • Perturbations in the satellite orbit
  • Curvature of the path of the signal
    • Longer than expected in Euclidian space
  • Effects on the satellite clock
    • Clocks run fast further out of the potential well
  • Effects on the receiver clock (Sagnac effect)
phase center errors
Phase Center Errors
  • Phase center is the ‘point’ from which the GPS location is measured
  • Difficult to measure precisely
  • Changes with different factors:
    • Elevation
    • Azimuth
    • Frequency
  • Either model the error or reduce the effect of the error by always orienting antenna the same direction
receiver noise
Receiver Noise
  • All electronic devices will have a certain amount of noise
  • Because of the characteristics of the noise modeling is not an option
  • The best that can be done is average the data to reduce the effects of the noise
multipath errors
Multipath Errors
  • GPS assumes that the signal travels directly from the satellite to the receiver
  • Multipath results from signal reflecting off of surface before entering the receiver
    • Adds additional (erroneous) path length to the signal
  • Difficult to remove; best to avoid
multipath illustration
Multipath Illustration


geometric factors
Geometric Factors
  • The strength of figure of the satellites is taken into consideration by the dilution of precision (DOP) factor
    • Depends on number of satellites
    • Depends on location of satellites
geometric factors1
Geometric Factors


geometric factors2
Geometric Factors
  • Different kinds of DOPs
    • HDOP (horizontal)
    • VDOP (vertical)
    • PDOP (position) (3-D component)
    • TDOP (time)
    • GDOP (geometric) (PDOP and TDOP)
user equivalent range error uere
User Equivalent Range Error(UERE)
  • Crude estimate of the expected error
  • Consists of contributions from
    • Measurement noise
    • Satellite biases
    • Wave propagation errors
  • Transmitted through the Navigation message
  • Combined with DOP information
gps signals1
GPS signals
  • Navigation data
  • Pseudo-random noise sequences
  • Carrier wave
navigation data
Navigation data
  • Satellite orbit information (ephemerides)
  • Satellite clock information
  • Satellite health and accuracy
  • Satellite orbit information (almanac)
  • Bit-rate of 50bps
  • Repeated every 12.5 minutes
pseudo random noise sequences
Pseudo-random noise sequences
  • Spreading sequences (C/A)
  • Length of 1023 chips
  • Chipping rate of 1.023Mcps
  • 1 sequence lasts 1ms
  • 32 sequences to GPS satellites
  • Satellite identification
  • Separate signals from different satellites
carrier wave
Carrier wave
  • Signal transmission
  • Two frequencies: L1=1575.42MHz L2=1227.60MHz
  • C/A code on L1
  • Bipolar phase-shift keying (BPSK) modulation
receiver overview
Receiver overview
  • Prepare received signals for signal processing
























receiver overview1
Receiver overview
  • Find satellites visible to the receiver
    • Find coarse values for C/A code phase and carrier frequency for each satellite
























receiver overview2
Receiver overview
  • Find fine value for C/A code phase
  • Find fine value for carrier frequency
  • Keep track of the C/A code phase and carrier frequency as they change over time

Bit syn-chronization


nav. data

Code tracking




satellite position



Receiver channel

receiver overview3
Receiver overview
  • Obtain navigation data bits

Bit syn-chronization


nav. data

Code tracking




satellite position



Receiver channel

receiver overview4
Receiver overview
  • Decode navigation data bits

Bit syn-chronization


nav. data

Code tracking




satellite position



Receiver channel

receiver overview5
Receiver overview
  • Calculate satellite position

Bit syn-chronization


nav. data

Code tracking




satellite position



Receiver channel

receiver overview6
Receiver overview
  • Calculate pseudorange

Bit syn-chronization


nav. data

Code tracking




satellite position



Receiver channel

receiver overview7
Receiver overview
  • Calculate position
























implemented parts
Implemented parts

Prepare received signals for signal processing


Code tracking

Carrier tracking

Bit synchronization

Decode navigation messages

Calculate satellite positions

Calculate pseudoranges

Calculate receiver position

signal conditioning
Signal conditioning
  • Purpose of signal conditioning
    • Remove possible disturbing signals by filtering
    • Amplify signal to an acceptable amplitude
    • Down-sample signal to an intermediate frequency













receiver PRN code start position at time of full correlation

is time of arrival of the SV PRN at receiver

the time of arrival is a measure of range to SV

offset by amount to which receiver clock is offset from GPS time

…the time of arrival is pseudo-range


position of receiver is where pseudo-ranges from set of SVs intersect

• position determined from multiple pseudo-range measurements

from a single measurement epoch (i.e. time)

• psuedo-range measurements used together with SV position

estimates based on precise orbital elements

(ephemeris data) sent by each SV

GPS navigation data


navigation message


each SV sends amount to which GPS time is offset from

UTC (universal time) time…

correction used by receiver to set UTC to within 100 nanoseconds




·Based on the basic physical relationship:

distance = velocity * time

·Observations (pseudo-ranges) from 4 satellites provide 3 dimensional position (3 positional and 1 time unknown)

·Coordinate system realized by the satellite orbits (ephemerides) and by the coordinates and physical locations of the control and tracking stations



The Geocentric Cartesian Coordinate System


Satellite P

Greenwich Meridian










AP = √(XP-XA)2 + (YP-YA)2 + (ZP-ZA)2


Geometric Dilution of Precision

- Measures the effect of geometry on the precision of the observations

- Multiply GDOP by the Std Error to get actual uncertainty


Position Dilution of Precision (PDOP)

- This is positional part of GDOP


Real Time Kinematic (RTK)

Differential corrections are broadcast via radio

Base station over free point

Base station over known point

“Site Calibration/Local Transformation”



  • Service available commercially (e.g. Omnistar)
  • Sub-meter accuracies possible when used in combination with L1
  • User needs only one receiver

GPS satellites




Differential Base



Footprint of Communication

Satellite coverage



Eccentric Points




Useful when Canopy prevents direct occupation of point or when Communication Satellite is blocked


A: Geodetic (carrier phase with resolved ambiguities), real-time/post-processed

B: Carrier smoothed C/A Code Phase, post-processed

C: Real-time (RTCM SC104), post-processed C/A Code

D: Real time P-Code (Precise Positioning Service [PPS])

E: Real time C/A-Code (Standard Positioning Service [SPS])





100 m

civilian (SPS)




(prior to 05/02/00)


20 m

civilian (SPS) – post 05/02/00


10 m

military (PPS)

5 m

1 m

0.5 m













Selective Availability switched off – see