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Introduction to GPS “… it isn’t hard to operate a GPS receiver – matter of fact, most of them are so user- friendly you don’t need to know the first thing about GPS to make them work; that is, until they don’t. Getting coordinates from a GPS receiver is usually a matter of pushing buttons, but knowing what those coordinates are, and more importantly, what they aren’t, is more difficult.” Jan Van Sickle

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Use of Satellites in Surveying Started as early as Sputnik (1957) Continued with other satellites – Measuring positions of satellites against background stars on photographs – Laser ranging – Used Doppler effect to determine velocity vector

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TRANSIT Satellite Navy Navigation Satellite System (NNSS) started in 1960s Used the Doppler shift of the signal to determine velocity vector Six satellites in low (1100 km) circular, polar orbits One satellite every 90 minutes, need 2 passes – Susceptible to atmospheric drag and gravitational perturbations – Poor quality orbital parameters Produces poor positions (by modern standards)

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Brief History of GPS Initial work in 1970s – Counselman, Shapiro, etc. (MIT) First used for practical purposes in 1980s – Civilian use ahead of military use Initial operational capability (IOC) July ‘93 Full operational capability (FOC) 17 July 1995

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GPS Overview Consists of ~24 satellites 4 satellites in 6 orbital planes – Planes inclined 55° 20,000 km orbits – Periods of 11h 58m Each satellite carries multiple atomic clocks

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GPS Segments User Segment – Military and civilian users Space Segment – 24 satellite constellation Control Segment – Worldwide network of stations

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Space Segment Block I Block II Block IIA (A – advanced) Block IIR (R – replenishment) Block IIF (F – Follow on) Block III – See http://www.spaceandtech.com/spacedata/constellations/navstar- gps-block1_conspecs.shtml

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GPS Block IIR Satellite

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Control Segment Worldwide network of stations – Master Control Station – Colorado Springs, CO – Monitoring Stations – Ascension Island, Colorado Springs, Diego Garcia, Hawaii, Kwajalein Other stations run by National Imagery and Mapping Agency (NIMA) – Ground Control Stations – Ascension, Diego Garcia, Kwajalein

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Control Segment

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Data Flow Master Control Station USNO Monitor Station USNO AMC Satellite Signal Timing Links Time Timing data Control Data Satellite Signal

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Basic Idea Broadcast signal has time embedded in it Need to determine distance from satellite to receiver One way uses distance = velocity * time – If time between when the signal is sent and when it is received is known, then distance from satellite is known Using multiple distances, location can be determined (similar to trilateration)

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Overview of GPS

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GPS Signal Frequency Fundamental Frequency 10.23MHz (f 0 ) 2 Carrier Frequencies – L1 (1575.42 MHz) (154 f 0 ) – L2 (1227.60 MHz) (120 f 0 ) 3 Codes – Coarse Acquisition (C/A) 1.023 MHz – Precise (P) 10.23 MHz – Encrypted (Y) Spread Spectrum – Harder to jam

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Amplitude Modulation

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Frequency Modulation

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Phase Modulation

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Codes Stream of binary digits known as bits or chips – Sometimes called pseudorandom noise (PRN) codes Code state +1 and –1 C/A code on L1 P code on L1 and L2 Phase modulated

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C/A Code 1023 binary digits Repeats every millisecond Each satellite assigned a unique C/A-code – Enables identification of satellite Available to all users Sometimes referred to as Standard Positioning Service (SPS) Used to be degraded by Selective Availability (SA)

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P Code 10 times faster than C/A code Split into 38 segments – 32 are assigned to GPS satellites – Satellites often identified by which part of the message they are broadcasting PRN number Sometimes referred to as Precise Positioning Service (PPS) When encrypted, called Y code – Known as antispoofing (AS)

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Future Signal C/A code on L2 2 additional military codes on L1 and L2 3 rd civil signal on L5 (1176.45 MHz) – Better accuracy under noisy and multipath conditions – Should improve real-time kinematic (RTK) surveys

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Time Systems Each satellite has multiple atomic clocks – Used for time and frequency on satellite GPS uses GPS Time – Atomic time started 6 January 1980 – Not adjusted for leap seconds – Used for time tagging GPS signals Coordinated Universal Time (UTC) – Atomic time adjusted for leap seconds to be within ±0.9 s of UT1 (Earth rotation time)

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Pseudorange Measurements Can use either C/A- or P-code Determine time from transmission of signal to when the signal is received Distance = time*speed of light Since the position of the satellite is assumed to be known, a new position on the ground can be determined from multiple measurements

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Carrier-phase Measurements The range is the sum of the number of full cycles (measured in wavelengths) plus a fractional cycle – ρ = N*λ + n* λ The fraction of a cycle can be measured very accurately Determining the total number of full cycles (N) is not trivial – Initial cycle ambiguity – Once determined, can be tracked unless …

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Cycle Slips Discontinuity or jump in phase measurements – Changes by an integer number – Caused by signal loss Obstructions Radio interference Ionospheric disturbance Receiver dynamics Receiver malfunction

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How to Fix Cycle Slips? Slips need to be detected and fixed Triple differences can aid in cycle slips – Will only affect one of the series Should stand out Once detected, it can be fixed

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GPS Errors and Biases Satellite Errors – Potentially different for each satellite Transmission Errors – Depends on path of signal Receiver Errors – Potentially different for each receiver

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Linear Combination Errors and biases, which cannot be modeled, degrade the data Receivers that are ‘close enough’ have very similar errors and biases Data can be combined in ways to mitigate the effects of errors and biases

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Linear Combination Combine data from two receivers to one satellite – Should have same satellite and atmospheric errors – Differences should cancel these effects out

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Linear Combination Combine data from one receiver to two satellites – Should have same receiver and atmospheric errors – Differences should cancel these effects out

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Linear Combination Combine data from two receivers to two satellites – Should have same receiver, satellite and atmospheric errors – Differences should cancel out

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Linear Combination Can also combine the L1 and L2 data to eliminate the effects of the ionosphere – Ionosphere-free combination L1 and L2 phases can also be combined to form the wide-lane observable – Long wavelength – Useful in resolving integer ambiguity

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Reference Systems

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Two Reference Frames Satellites operate in an inertial reference frame – Best way to handle the laws of physics Receivers operate in a terrestrial reference frame – Sometimes called an Earth-centered, Earth-fixed (ECEF) frame – Best way to determine positions

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Inertial Frame (Historically) X axis through the vernal equinox Y axis is 90° to the ‘east’ Z axis through the Earth’s angular momentum axis X-Y plane is the celestial equator Z axis is through the celestial North Pole

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Inertial Frame From http://celestrak.com/columns/v02n01/

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Inertial Frame Defined by the positions of distant radio sources called quasars Realization from observations provided by Very Long Baseline Interferometry (VLBI) – e.g. International Celestial Reference Frame Right-handed, Cartesian coordinate system

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Terrestrial Frame (Historically) X axis through the Greenwich meridian Y axis is 90° to the east Z axis through the Earth’s angular momentum axis X-Y plane is the equator Z axis is through the North Pole

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Terrestrial Frame From http://www.nottingham.ac.uk/iessg/coord1.htm

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Terrestrial Frame Defined by the positions of reference points Realization from observations provided by VLBI, SLR, and GPS – e.g. International Terrestrial Reference Frame – e.g. World Geodetic System (WGS)-84 Right-handed, Cartesian coordinate system

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Terrestrial Frame Can transform from non-Cartesian (geodetic) coordinates to Cartesian coordinates – X = (N+h) cosφ cosλ – Y = (N+h) cosφ sinλ – Z = [ N(1-e 2 )+h] sin φ Where N = a/sqrt(1-e 2 sin 2 φ) h = ellipsoid height φ = latitude λ = longitude

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Transformation between Frames Transformation is accomplished through rotation by Earth orientation parameters (EOPs) – Polar Motion (W) – Earth rotation (T) – Precession/nutation (P)(N) x cts = (W)(T)(N)(P)x cis

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Datums Based on a reference ellipsoid – Semimajor axis (a) and semiminor axis (b) or semimajor axis (a) and flattening (f) Needs to have a well defined center (origin) Needs to have a well defined direction or axes (orientation)

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Datums Can be done with 8 parameters – 2 define the ellipsoid – 3 define the origin of the ellipsoid – 3 define the orientation of the ellipsoid

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Datums North American Datum 1927 (NAD27) – Clarke ellipsoid of 1866 North American Vertical Datum 1929 (NAVD29) North American Datum 1983 (NAD83) – GRS 1980 ellipsoid North American Vertical Datum 1988 (NAVD88) Even the last two have minimal input from GPS

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Vertical Measurements Vertical measurements from GPS are relative to the ellipsoid (ellipsoid height) – Not from the geoid or topography To translate to other surfaces (either reference or real) requires additional information – Orthometric or geoid heights

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Vertical Surfaces From http://www.butterworth.uk.com/geodesy.html

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HARN High Accuracy Reference Network (HARN) Created by states, with federal assistance (NGS) Predominantly based on GPS observations – Very accurate

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Plane Coordinate Systems Used over ‘local’ areas State Plane Coordinate (SPC) systems – Results of projection onto surface Lambert conic projection Mercator (cylindrical) projection

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Time Systems Earth rotation time – Solar/sidereal Dynamical – Barycenter/terrestrial Atomic (off by integer seconds) – Coordinated Universal Time (UTC) – International Atomic Time (TAI) – GPS Time

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Calendar Julian Date (JD) are days from noon (UT) January 4713 BC – JD = INT[365.25y] + INT[30.6001(m+1)] + D + UT/24 + 1720981.5 y = Y-1 and m = M+12 if M ≤ 2 y = Y and m = M if M > 2 Modified Julian Date – MJD = JD – 2400000.5 – http://tycho.usno.navy.mil/mjd.html Calculator - http://aa.usno.navy.mil/data/docs/JulianDate.html

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Satellite Orbits

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Kepler Orbital Parameters (Kepler Elements) Ω – right ascension of ascending node i – inclination of orbital plane ω – argument of perigee a – semimajor axis of orbital ellipse e – numerical eccentricity of ellipse T 0 – epoch of perigee passage

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Kepler Elements From http://www.stk.com/resources/help/Data/ DemoScenarios/Training/kepler/satorbits.htm

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Perturbation of Orbits Mathematically, treat the problem as small corrections to the idealized motion Can use mathematical tricks to simplify the problem – Assume the corrections are sufficiently ‘small’ – Use Taylor’s Theorem

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Disturbing Accelerations Gravitational – Nonsphericity of the Earth – Tidal attraction (direct and indirect) Nongravitational – Solar radiation pressure – Relativistic effects – Solar wind – Magnetic field – Out-gassing

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Nonsphericity of the Earth The Earth’s potential can be approximated using spherical harmonics Disturbing Potential can be given as R = V – V 0

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Tidal Effect (direct) Celestial body will attract the satellite The effect will be a function of the angle between the celestial body, the Earth, and the satellite Only a few bodies need to be considered – Sun – Moon – Venus Acceleration is ~10 -6 m/s 2

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Tidal Effect (indirect) Celestial body will deform the Earth – Both ocean tides and solid earth tides Deformation of the Earth will perturb the orbit of the satellite Acceleration is ~10 -9 m/s 2

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Solar Radiation Pressure Sunlight impinging on a surface imparts momentum Two components – Principal component away from the Sun Modeled – Component along satellite y-axis (y-bias) Solved for Eclipse ‘season’ causes additional problems Acceleration is ~10 -7 m/s 2

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Relativistic Effect Caused by the Earth’s gravity field Creates a perturbing acceleration Acceleration is ~10 -10 m/s 2

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Other Solar Wind – Sun emits a wind which interacts with objects in the solar system Magnetic Field – Interaction of the Earth’s magnetic field with a (metallic) satellite Out-gassing – Gasses from satellite evaporate – Act similar to a jet

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Orbit Dissemination Best orbital determinations come from a global network with a ‘good’ geometric distribution – Want ~30 stations if possible Military network – Monitoring Stations Civilian – International GPS Service (IGS)

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Types of Orbits Almanac – Poor quality (~100m) – Used well into the future Broadcast – Good quality (1-2m with SA off) – Used in real-time work Precise – Excellent quality (5-10cm) – Used in the most precise work

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Satellite Signal

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Fundamental Relationships f = 2π/P = c/λ f = dφ/dt Doppler shift f r = f t ± (v/c)*f t Wheref r – received frequency f t – transmitted frequency

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Phase Modulation

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Summary of Carriers and Codes 2 carrier waves 2 codes (+1 and –1) Combined, they look like – L1(t) = a 1 P(t)D(t)cos(f 1 t) + a 1 C/A(t)D(t)sin(f 1 t) Note the phase shift between the P-code and C/A- code – L2(t) = a 2 P(t)D(t)cos(f 2 t)

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C/A Code Produced by 2 10-bit feedback shift registers Frequency is 1.023 MHz Repetition rate of 1ms The code length is 1023 chips Time interval between 2 chips is 1μs – 300 m chip length

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P Code Produced by 2 shift registers The code length is 2.3547*10 14 bits Corresponding time span is 266.4 days Chip length is 30 m To protect against deliberate misinformation, combined with the encrypting W-code to produce Y-code – Only accessible if you know how to decode (i.e. military applications)

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Navigation Message Contains information about each satellite – Clocks, orbits, health, corrections Subframes contain – Telemetry word (TLM) – Hand-over word (HOW) – Clock Corrections – Broadcast ephemeris – Almanac data

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Signal Processing Different inputs (codes, NAV message, carriers) get combined Combined signal is broadcast by satellite Receiver picks up broadcast and must decompose the signal to recover – Code – Navigation message – Carrier

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Receivers Must contain – Signal reception (antenna) Omnidirectional Signals measured from phase center – Signal processing Microprocessor controls system Control device provides communications Storage device

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Radio Frequency Signal Need to discriminate between satellites – Use unique codes – Use unique Doppler shifts Modern receivers use a separate channel for each satellite (continuous tracking) Receivers also need to be able to generate frequency to create their own signals – Usually uses internal oscillator

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How to Determine Time? PRN code generated on satellite Identical code created in receiver If the time on the satellite were synchronized to the receiver, problem solved – Unfortunately, not the case Trick is to match up the code to find time Use autocorrelation

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Autocorrelation

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Autocorrelation

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Additional Techniques Squaring technique Cross correlation technique Code correlation plus squaring technique Z-tracking technique

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Code Squaring Used to eliminate code information – Results consist only of carrier wave Multiply the modulated carrier by itself (square the signal) Code signal (which consists of +1 and – 1) becomes 1 throughout – (+1) 2 = 1 – (-1) 2 = 1

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Phase Modulation

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Observables

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Data Code Pseudorange Carrier Phase Doppler Combinations of data Biases and Noise terms

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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 = t r – t s = [t r (GPS)-δ r ] – [t s (GPS) – δ s ] Pseudorange given by R = c Δt = ρ + cΔδ – Pseudo because of cΔδ (where Δδ = δ s – δ r ) factor

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Carrier Phase Based on the number of cycles (wavlengths) between satellite and receiver Phase data will include errors in both the satellite and receiver as well as an initial integer number, N

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Doppler 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)

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Data Combinations Theoretically, data can be obtained from – Code ranges – R L1, R L2 – Carrier phases – Φ L1, Φ L2 – Doppler shifts – D L1, D L2 Combinations of these data could be used as well

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Data Combinations In general, linear combinations of phase will look like – φ = n 1 φ 1 + n 2 φ 2 – Where n 1 and n 2 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

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Data Combinations If n 1 = n 2 = 1, then – Φ L1+L2 = Φ L1 + Φ L2 Denoted narrow-lane λ L1+L2 = 10.7cm If n 1 = 1 and n 2 = -1, then – Φ L1-L2 = Φ L1 – Φ L2 Denoted wide-lane λ L1-L2 = 86.2cm Used for integer ambiguity resolution

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Data Combinations If n 1 = 1 and n 2 = –f L2 /f L1, then – Φ L3 = Φ L1 – f L2 /f L1 Φ L2 – Called L3 (sometimes denoted ionosphere- free) Used to reduce ionospheric effects

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Combinations of Phase and Code Historically smoothed the code pseudorange using carrier phase Several different algorithms Don’t see as many applications today

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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

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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

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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)

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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

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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

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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 n ph = 1 + c 2 /f 2 … n gr = 1 – c 2 /f 2 – Note that this will effect frequencies differently Higher frequency is affected less

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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 – Δ ph iono = –(40.3/f 2 ) ∫N e ds 0 = –40.3/f 2 TEC – Δ gr iono = (40.3/f 2 ) ∫N e ds 0 = 40.3/f 2 TEC Where TEC = ∫N e ds 0 is the total electron content

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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

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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 Δ Trop = 10 -6 ∫N d Trop ds + 10 -6 ∫N w Trop ds – Where N is the refractivity – ds is the path length

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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

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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

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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

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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)

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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

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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

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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

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Multipath Illustration From http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap6/6212.htm

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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

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Geometric Factors From http://www.romdas.com/surveys/sur-gps.htm

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Geometric Factors Different kinds of DOPs – HDOP (horizontal) – VDOP (vertical) – PDOP (position) (3-D component) – TDOP (time) – GDOP (geometric) (PDOP and TDOP)

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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

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Surveying with GPS

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General Thoughts on Survey Accuracy Project size Density of control Physical restrictions Number of receivers Adjustment capability Station and reference azimuth mark visibility Cost Observation time

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More Specific Thoughts Code range vs. carrier phase Real-time processing vs. postprocessing Point positioning vs. relative positioning Static vs. kinematic

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Observation Techniques Point Positioning Differential GPS Relative Positioning

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Point Positioning Determines the coordinates of the receiver If using a single receiver, this is the only reasonable option Standard Positioning Service (SPS) uses C/A code – ~10 m accuracy Precise Positioning Service (PPS) uses both codes – ~1 m accuracy

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Differential GPS Uses (at least) two receivers – One located at a known point – One used to determine position of unknown point Typically uses pseudorange data Known position used to compute corrections At least four common satellites must be observed

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Differential GPS Correction transmitted to other receiver – Need to have a (radio) data link Data usually transmitted using the Radio Technical Commission for Maritime Service, Special Committee 104 (RTCM) format Initial position combined with correction to create a refined position

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Relative Positioning Uses (at least) two receivers – One located at a known point – One used to determine position of unknown point Typically uses carrier phase Determine the vector between known point and unknown point

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Relative Positioning Static – Receivers remain stationary Rapid Static – Receivers remain stationary for short times – Need good receivers (dual frequency)

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Relative Positioning Kinematic – Receiver is continually moving – Must maintain lock on 4 satellites at all times Semi-kinematic (stop-and-go) – Receiver makes brief stops Pseudokinematic – Receiver makes stops but must reoccupy after significant (~1 hour) time

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Field Equipment Typical equipment includes (but not limited to) – Receiver – Battery – Meteorological sensor – Tripod – Tribrach – Communication device

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Survey Planning Decide the extent of the planning Study a map of the area Point selection Satellite coverage – DOP estimates Session length Field reconnaissance

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Survey Planning Monumentation Organizational Design – Personnel – Vehicles – Equipment – Sites

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Organizational Design Number of sessions – n = (s-o)/(r-o) s – number of sites r – number of receivers o – overlapping sites – n = ms/r m – number of times site to be occupied

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Organizational Design Radial survey – One receiver placed at fixed site – Other receivers placed at locations – Measure lines from fixed site to other locations Network survey – Closed geometric figures

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Surveying Procedure Preobservation Observation Postobservation Ties to control monument

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Preobservation Antenna setup – Avoid multipath – Center antenna over point – Know antenna phase center – Know your H.I. Receiver calibration – One antenna, two receivers

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Preobservation Initialization – Input parameters to receiver – Phase ambiguity resolution e.g. on-the-fly (OTF), antenna swap, etc.

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Observation Communication can be crucial if observations need to be coordinated Receivers are automated Need good DOPs Potentially need to track same satellites Can observe through rain but not lightening

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Survey Procedure Postobservations – Document! Prepare site occupation sheet Ties to the control monuments – Usually need to connect the survey to control

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Data Processing Transfer the data to computer Process the data – Use ‘canned’ software – Two strategies for static surveys Vector-by-vector (single baseline) –Easier to detect bad baselines Mulitpoint solutions –Not as common

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Vector Processing (directly from the book) 1. Generation of orbit files. 2. Computation of the best fit value for point positions from code pseudorange. 3. Creation of undifferenced phase data from receiver carrier phase readings and satellite orbit data. Time tags may also be corrected. 4. Creation of differenced phase data and of computation of their correlations.

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Vector Processing (directly from the book) 5. Computation of an estimate of the vector using triple-difference processing. This method is insensitive to cycle slips but provides least accurate results. 6. Computation of the double-difference solution solving for vector and (floating point or real) values of phase ambiguities. 7. Estimation of integer values for the phase ambiguities computed in the previous step, and decision whether to continue with fixed ambiguities.

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Vector Processing (directly from the book) 8. Computation of the fixed bias solution based upon best ambiguity estimates computed in the previous step 9. Computation of several other fixed bias solutions using integer values differing slightly (e.g. by 1) from selected values 10. Computation of the ratio of statistical fit between chosen fixed solution and the next best solution. This ratio should be at least two to three indicating that the chosen solution is at least two to three times better than the next most likely solution.

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Troubleshooting Easiest to see with single baseline vectors Check standard error estimates Check ratio Check rms Check ambiguities

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Network Adjustment Check loop closures Perform minimally constrained least-squares solution – Bad lines must be removed first – Check computed coordinates with previous Points with large shifts could be problematic Check residuals (both normalized and unnormalized) Scale errors by appropriate factor

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And Finally … Transform coordinates into appropriate coordinate system Produce final report – Formats will differ depending on employer – See book for an example of things to consider

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GPS Standard Formats

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Formats Each receiver stores data in its own (proprietary) binary format – Saves space Combining data from different receivers could potentially be problematic Need standard formats that are supported by different equipment

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Formats RINEX NGS-SP3 RTCM SC-104 NMEA 0183

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RINEX Receiver Independent Exchange (RINEX) ASCII file – Easily readable (even by people) – Less compact than binary Has been different versions – Current version is 2.10 – Version 2.20 proposed to deal with low earth orbit (LEO) satellites

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RINEX Six different RINEX files 1. Observation data file 2. Navigation message file 3. Meteorological file 4. GLONASS navigation message file 5. Geostationary satellites data file 6. Satellite and receiver clock file

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RINEX Naming convention is ssssdddf.yyt where – ssss is the site designation – ddd is the day of year of the first record – f is the file sequence number – yy is the two digit year – t is the file type O – observation N – navigation M – meteorological G – GLONASS H – geostationary

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RINEX Observation files – Header Information on observing session – Data Divided into epochs

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RINEX Navigation file – Header – Data Clock parameters Broadcast orbit Meteorological file – Header – Data Temperature Barometric Pressure Relative Humidity

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NGS-SP3 National Geodetic Survey – Standard Product #3 ASCII file Facilitates exchanging precise satellite ephemerides

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NGS-SP3 Header – Information on observing session (date, number of satellites, Data – Divided into epochs – Each satellite on a separate line Satellite orbits, clock corrections

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RTCM SC–104 Radio Technical Commission for Maritime Services, Special Committee 104 Original format used for transmitting information for real-time DGPS – Differential corrections Current version 2.2

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RTCM SC–104 64 message types – DGPS corrections – GPS information – RTK corrections – GLONASS corrections

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NMEA 0183 National Marine Electronics Association ASCII file Current version 3.0 Used to transmit GPS information from the receiver to hardware that uses the positioning as input – Real-time marine navigation

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Data Processing

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Data Handling Downloading – Need to move data from receiver to computer Data Management – Need structure to handle large amounts of data – Separating by projects is often used Data Exchange – Original data usually binary – May want data in other formats Most receivers now convert to Receiver Independent Exchange (RINEX) format

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Cycle Slips When a receiver is turned on, there is an initial integer number of wavelengths (N j ) for every satellite j when measuring carrier phase When a receiver loses lock on a particular satellite, there is a new initial integer number of wavelengths (N j* ) for every satellite j – This event is called a cycle slip – Note that N j ≠ N j* Unfortunately, the receiver/software assumes that N j is a constant unless told otherwise – Produces a sudden apparent jump in position

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Cycle Slips Generally caused by one of four things – Obstructions Caused by trees, buildings, bridges, mountains, etc. Most frequent problem – Low signal-to-noise (SNR) ratio Caused by ionospheric conditions, multipath, high receiver dynamics, low satellite elevations – Failure in receiver software Infrequent – Malfunctioning satellite oscillators Rare

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Cycle Slips http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap7/735.htm

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Cycle Slips Need to determine the instant at which the slip occurs – Accomplished by comparing observations at successive epochs – Often done using triple differences ‘Repairs’ consist of correcting all subsequent observations for the jump – Note that the jump must be an integer

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Ambiguity Resolution Assuming that tracking is continuous, there is no time dependence to equations – Φ = λ -1 ρ + fΔδ + N – λ -1 Δ Iono – Need to determine integer ambiguity N Once accomplished, ambiguity is said to be resolved or fixed Note that ambiguity resolution is not always a possibility

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Ambiguity Resolution For instance, look at double differences – λΦ = ρ AB jk (t) + λN + noise – Effect of ionosphere, troposphere are neglected Any errors from these terms will contaminate the parameter estimation – The ‘best’ estimates (think least-squares) for N may not be an integer even though they should be

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Ambiguity Resolution Satellite geometry is an important consideration – More satellites with better geometry will provide better DOPs – Better DOPs will improve ambiguity resolution Length of observation critical to ambiguity resolution – Want to track the satellite across the sky

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Ambiguity Resolution Multipath can make ambiguity resolution more difficult – It contaminates observations which makes parameter estimation more difficult

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Ambiguity Resolution Three steps need to followed – Determine the ‘search space’ – Identify the correct integers – Validation of integer set

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Ambiguity Resolution Determine the ‘search space’ – Which integers could possibly be correct? Remember that the problem is multi-dimensional Every satellite will have an integer ambiguity – Since the solution will be pulled from the search space, you need to be conservative to ensure that the correct integers will be selected – However, the bigger the search space, the longer it will take to find the integers – In static positioning, can be determined approximately from float solution

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Ambiguity Resolution Identify the correct integers – Done statistically – Minimizing sum of squared residuals – Assume that the integers that best fit the observations are most likely to be correct – Also assumes that the integers are normally distributed Not always true Most frequent cause of resolution failure in long baselines

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Ambiguity Resolution Validation of integer set – How correct are the integers selected? – Success rate depends on Observation equations Precision of observables Method of estimation – Are the integers chosen significantly better than the other possibilities Look at ratio of the sum of squared residuals Want the ratio to be three or greater

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Ambiguity Resolution Approaches Single frequency phase data Dual frequency phase data Combining dual frequency carrier phase and code data Combining triple frequency carrier phase and code data – Only after modernization

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Search Techniques If processing double-differences by least-squares, the initial estimates of ambiguities are real (floating point) numbers – Called a float solution Produces ‘best estimate’ of ambiguities

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Search Techniques However, the results won’t be correct because the numbers won’t be integers They will be close if – Stations are close together – Observation span is long If the two results are close, the resulting differences in position should be close Otherwise, ambiguity resolution is more important

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Search Techniques For the static case, the search space can be created from the float ambiguity solution and statistics – Take the float solution estimate and use the standard deviations to indicate how big a window to use – Typically use 3σ windows The number of possibilities increases quickly with the uncertainty and number of satellites

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Search Techniques Every ambiguity combination is checked – Ambiguities are fixed to a set of integers inside the search space – Measurement residuals are computed for observations – Residual sum of squares is computed The smallest residual sum of squares ‘wins’ Note that this number will be bigger than the residual computed by least-squares

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Search Techniques The candidate solution needs to be validated Often use the ratio of the residual sum of squares between the best two integer solutions Ratio should be greater than 3 If not, the candidate may not be the best solution – May be safer to stick with the float solution

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Search Techniques If the observations are made in kinematic mode, a float solution won’t work to provide an initial estimate of the ambiguities – At every epoch, there is a new position Typically use ‘on-the-fly’ ambiguity resolution

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Search Technique Can use code solution to estimate position – Need a good receiver – The search space will be larger than for static case because of the increased uncertainties Use wide-lane to get a better estimate of the position – Smaller search space Use improved position for final ambiguity resolution

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Search Technique On-the-fly methods include – Ambiguity function method – Least-squares ambiguity search technique – Fast ambiguity resolution approach – Fast ambiguity search filter – Least-squares ambiguity decorrelation adjustment method – Ambiguity determination with special constraints

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Least-Squares Adjustment Ax = ℓ where – A – design matrix (m x 4) – x – vector of unknowns (4 x 1) – ℓ – vector of observations (m x 1) – m – number of observations In addition, let – σ 0 2 – a priori variance – Σ – covariance matrix

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Least-Squares Adjustment Q ℓ is called the cofactor matrix – It is a covariance-like quantity – Q ℓ = σ 0 -2 Σ The weight matrix is given by – P = Q ℓ -1

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Least-Squares Adjustment To get a consistent solution, noise is added – ℓ + n = Ax A unique solution can be found with – n T Pn = minimum – A T PAx = A T Pℓ – x = (A T PA) -1 A T Pℓ – Q x = (A T PA) -1 (from covariance propagation)

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Kalman Filtering A way of combining different observations which are related to each other Takes into account the uncertainties of the observations Optimal linear filter – Must assume a linear process – Optimal in many statistical senses

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Linearization Linearize equation using Taylor’s theorem Like many applications, only the first order terms need to be included – Higher order terms are small enough to be neglected

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Linearization Applying Taylor’s theorem to an arbitrary function of three variables, f(X i,Y i,Z i ), and keeping terms to first order gives Note that you need partial derivatives

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Linearization

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Linearization We now have a linear equation that relates the range to the unknown positions – In this case, the unknowns are actually the (usually small) corrections ΔX i ΔY i ΔZ i

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Point Positioning For this example, simplify the equation to not account for ionosphere, troposphere, etc.

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Point Positioning This assumes that the satellite clock error is known – Not a bad assumption because of the clock corrections in the navigation signal For every epoch, t, there are 4 unknowns Observations from 4 satellites are needed in order to solve the equations

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Point Positioning

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Assuming four satellites are being observed

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Point Positioning

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Other Observations Analogously, can set up equations for carrier phase – (or Doppler, or combinations, etc.) Can also set up equations for relative positioning

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Network Adjustment There are two methods of determining positions of a network – Single baseline solution – Multipoint solution

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Single Baseline Solution Baseline by baseline computation Need to compute for all possibilities The number of baselines is – n i (n i -1)/2 Where n i is the number of stations Only n i -1are independent (Why?) Redundant baselines are used – For additional adjustment – Misclosure checks

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Single Baseline Solution In the end, the vectors are subjected to a simultaneous adjustment Note that because of the way the problem was set up, the correlations of the simultaneously observed baselines are ignored – Not the correct way to handle the problem theoretically

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Multipoint Solution Handles all points at once – Correlations between baselines are accounted for

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Single Baseline vs. Multipoint (from text) Correlations not modeled correctly with the single baseline solution Computer program simpler for single baseline Computation time not an issue Cycle slips easier to detect and repair in multipoint solution Easier to isolate (and eliminate) bad measurements in single baseline Correlations with multipoint while better than single baseline still might not be perfect

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Dilution of Precision The dilution of precision (DOP) is a measure of the geometry of the satellites It changes with time – Number of satellites changes – Position of satellites changes

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Dilution of Precision

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The first three elements in each row are components of the unit vector pointing from the four satellites to the observing site i Solution exists as long as the design matrix (A) is non-singular – The determinant is not zero

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Dilution of Precision The determinant is proportional to the scalar triple product The scalar triple product is one way to compute the volume of a body defined by the three vectors

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Dilution of Precision The larger the volume, the better the geometry The better the geometry, the lower the value of DOP Therefore, want DOP to be inversely proportional to the volume

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Dilution of Precision DOP can be calculated from the inverse of the normal equation matrix – Q X = (A T A) -1 (if weight matrix is the identity) Q X is called the cofactor matrix – It is a covariance-like quantity

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Dilution of Precision Note that these are expressed in the equatorial system

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Dilution of Precision Similar quantities can be calculated for the topocentric local coordinate system – Axes along local north, east, and up The global cofactor matrix Q X needs to be transformed into the local cofactor matrix Q x – Use the law of covariance propagation

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Dilution of Precision

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The three dimensional error, whether computed in the equatorial coordinate system or the local coordinate system must be the same However – q XX ≠ q xx – q YY ≠ q yy

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Dilution of Precision Assuming σ is the measurement accuracy, positioning accuracy is given by – GDOP σ – geometric accuracy in position and time – PDOP σ – accuracy in position – TDOP σ – accuracy in time – HDOP σ – accuracy in the horizontal position – VDOP σ –accuracy in the vertical position

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GPS Integration

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Integration GPS determines positions – Can provide a lot of input in a short amount of time Many other systems can use positions as inputs – Either real-time or post-processed GPS and other technology make a good match

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GPS/GIS Geographic information system (GIS) – Acquires, stores, manipulates, analyzes, and displaying spatially oriented data – Data stored in layers GIS is a tool to study the geographic information – Coordinates can be provided by GPS

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GPS/GIS Industries that use this combination include – Utility – Forestry – Agriculture – Public safety – Vehicle fleet management

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GPS/LRF Laser range finder (LRF) – Uses laser to determine distance between finder and target – Needs to be tied to coordinate system – Works as long as there is a line of sight between finder and target

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GPS/LRF Set up GPS in an area with clear view of sky Use LRF to determine distances and azimuth from GPS to other objects – Think about using this in a wooded area – Capable of determining positions even in an area where the sky is not clear enough for GPS Needs some post-processing to combine the data

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GPS/Dead Reckoning Utilizes odometer sensor and gyroscopes – Computes relative distance and direction Determines distance with odometer Determines changes in direction with gyroscope Needs GPS to pin down positions in an absolute frame Used in automatic vehicle location

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GPS/Dead Reckoning Dead reckoning needs to continuous information GPS is subject to data outages – Overpasses, urban canyons, trees, etc. Odometer and gyroscopes subject to drift Combining GPS positions and dead reckoning information can provide better estimates of positioning and direction always – Uses Kalman filter to combine Not good for accurate applications

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GPS/INS Inertial Navigation System (INS) – Also inertial measurement unit (IMU) Similar to dead reckoning equipment Uses accelerometers and gyroscopes – Determines accelerations – Determines angular velocity

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GPS/INS GPS and INS (IMU) data combined – Combination done with a Kalman filter – Utilizes the best of both information GPS good for long-term stability of positions –Subject to data outages INS good for determining moment-by-moment changes –Tends to drift but should always provide data –Provides data at a very high rate

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GPS/INS Combined data provide excellent position and attitude information Equipment is more expensive than dead reckoning equipment Used for high-accuracy applications

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GPS/Pseudolite Pseudo-satellite – Ground-based device – Transmits a satellite-like signal Used to provide signal (information) to areas that can’t receive satellite signal – Urban canyons – mines

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GPS/Pseudolite Used to increase the number of signals and the geometry of the signal senders VDOP in particular can be improved Signal needs to be ‘just right’ to avoid the near-far problem Also suffers because of inaccurate clocks and potential multipath Used in mining, precise aircraft landing

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GPS/Cellular Instances where it would be beneficial to determine where a cell call originates – 911 emergencies (1/3 come from cell phones) FCC has made it mandatory to be able to locate 911 calls within 125m Can be done with time-difference of arrival (TDOA) and/or angle of arrival – Need GPS receivers at base stations

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GPS/Cellular Can also be done with GPS chipsets in handset – Need to insert chips into new phones – Signal will be weak inside of buildings Used in vehicle navigation

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GPS Applications

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Applications Fast growing especially since SA was turned off – That was the idea Stand-alone GPS users can obtain 10- 20m accuracy – Good enough for some kinds of navigation Can also use carrier phase or DGPS for higher accuracy

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Applications Global Regional Local

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Global Navigation Primary planned use when the system was conceived Both military and civilian applications In the future, all planes, boats, etc. will have GPS installed Used for – Route navigation – Safety (collision avoidance) – Automated vehicle navigation

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Global Geodetic Measurements GPS can provide coordinates in a global terrestrial reference frame – Perfect for making large-scale observations GPS has already made significant contributions to the study of – Plate tectonics/crustal deformation – Earth orientation parameters – Postglacial rebound/volcanic uplift – Sea-level monitoring

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Global Timing/Communcation Because time is an implicit part of the signal, GPS can provide a cheap and easy way to determine accurate time Most communication needs accurate timing/frequency information As communication needs increase, accurate time/frequency will provide the ability to pack more information into the same amount of bandwidth

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Regional Navigation U.S. Coast Guard has set up network to help approaching vessels reach the harbor safely – This will work in poor/no visibility scenarios Used in conjunction with GIS to provide regional information Can be used for vehicle fleet management

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Regional Surveying Monitoring fault lines can provide information on stresses and strains – Could lead to improved understanding of earthquakes Could possibly help in predicting earthquakes Most complete networks in California and Japan Can also monitor subsidence

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Local Navigation Will aid in aircraft landings Emergency vehicle management – Make sure that vehicles are going where they’re needed in the quickest possible way Can help in finding alternate routes Also can be used in farming, forestry, and mining

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Local Surveying Probably the most common application for people in this class GPS can provide coordinates to varying accuracies (depending on method of observing) Coordinates can be used in a variety of surveying related activities (cadastral, stakeout, etc.)

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Attitude Determination Theoretically possible to determine attitude of aircraft using GPS Could potentially be used for photo- control Not as accurate as using GPS/INS

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Satellite Positions GPS is now being used on-board satellites to determine satellite positions – TOPEX/Poseidon – SPOT – Even GPS itself

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Installation of Control Networks GPS provides three dimensional coordinates Excellent for setting high-accuracy networks – GPS has made significant contributions to the International Terrestrial Reference Frame (ITRF) – HARN based on GPS observations – Continuously Operating Reference Station (CORS) occupied by GPS receivers

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Other Applications Utility industry – Power poles, lines, mains, etc. – Often used in conjunction with GIS Forestry and Natural Resources – Need to know topography and tree locations Farming – Want to know exactly where crops, chemicals are in the field

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Other Applications Civil Engineering – Road construction, Earth moving, structural placement – Monitoring structural deformation Mining – Drilling blast holes precisely – Open pit mining equipment can be controlled using inputs provided by GPS

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Other Applications Seismic Surveying (both land and marine) – Used for oil and gas exploration studies Need to know position of transmitted acoustic waves and receivers Airborne mapping – Need to determine position and attitude of plane Use GPS/INS combination

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Other Applications Seafloor Mapping – Hydrographic mapping requires that the position of the vessel is accurately known Vehicle Navigation – Automated techniques need the position of the vehicle to by known – Transit systems can use it to determine the positions of vehicles – Retail industry use it to determine truck fleet locations

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Future of GPS

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New Applications Intelligent Vehicle/Highway Systems (IVHS) Intelligent Transportation Systems Automated Construction Equipment Time Determination/Time Transfer Atmospheric Sensing Aircraft Navigation and Landing

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GPS Modernization New Block IIF scheduled to be launched in next few years (2007?) – Ability to transmit data between satellites – Autonomous navigation Navigation accuracy maintained for six months (????) Uplink jamming less of a concern One upload per spacecraft per month (??) Minimize ground tracking Improved navigation

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Augmented Signal Structure SA is now off and likely to stay off Additional L5 carrier frequency – Ability to correct for ionospheric effects when using carrier phase – Modulated by a new civil code (similar to P-code) – L2-L5 produces extra wide lane – L1-L5 can be used as ionosphere free Military Y-code replaced by split M-code

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GPS Augmentation Want to use GPS for aviation – Reliability needs to be extremely good – Want to augment GPS to provide additional reliability and improve results Local Area Augmentation Systems (LAAS) will use pseudolites – Should allow precision approach and landing Category II/III

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GPS Augmentation Can also use geostationary satellites – Will have broadcast capability – Transmit DGPS corrections and integrity messages Wide Area Augmentation System (WAAS) will use Inmarsats to augment GPS – Operational sometime

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GNSS Global Navigation Satellite System (GNSS) Integration of different satellite navigation systems – Already have capability of combining information from GPS and GLONASS – Also includes augmentation from other kinds of satellites (like Inmarsat) – Also include Galileo when launched

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GNSS/LORAN-C Long Range Radio Navigation (LORAN) – Used mostly for maritime navigation – Broadcast stations organized into ‘chains’ – Very similar to GPS cannot provide vertical component – Can be used to augment GPS

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Hardware In short, hardware will continue to get better, cheaper, smaller – Cost will drop if quantities increase in a way that everyone has (at least) one GPS receiver working in his/her life – Resolution of wave will improve (<0.1%) – More channels (for increased number of observables) More frequencies and more satellites

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Software In short, software will continue to get more sophisticated and run faster – Improved modeling or solution for unknown parameters – Better algorithms for solution – Faster computers will allow more to be done in the same amount of time

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GPS Products Data will continue to improve – Centimeter level orbits will be available – Centimeter level positioning will be possible in real time – Sub-centimeter positioning will be possible by post-processing

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Other Navigation Systems

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Other Systems GLONASS Beidou Galileo WAAS LAAS EGNOS MSAS

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GLONASS Global Navigation System developed by Russia Nominally consists of 21 satellites plus 3 spares 8 satellites arranged in 3 orbital planes with an inclination of 64.8º Orbits are approximately circular with a period of 11h 15m

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GLONASS Also transmits L1&L2 carriers, C/A & P codes – L1 is in 1602-1615.5 MHz band To be shifted to (1598.0625-1604.25 MHz) – L2 is in 1246-1256.5 MHz band To be shifted to (1242.9365-1247.75 MHz) – C/A code is 0.5Mps – P Code is 5.11 Mbps

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GLONASS Carrier frequency depends on the satellite – Each one is currently unique After shift, each pair of satellites will be assigned the same frequency – Pairs on opposite sides of the Earth (antipodal) Uses frequency channel rather than code to identify satellite

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GLONASS The system is not as robust as predicted Economic crisis has severely hurt the Russian space program – Fewer satellites in orbit than expected As little as 7 in May 2001 New class of satellites (GLONASS-M) should be launched soon

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GLONASS Can be used in conjunction with GPS to improve navigation/positioning Need to account for 2 differences in reference – Need to transform Earth Parameter System 1990 (PZ-90) to WGS 84 Can differ by up to 20 m – Need to relate Russian time scale to GPS time Can differ by 10s of μs

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Beidou Chinese regional satellite navigation system Consists of 2 satellites in geostationary orbits – Altitude of 36000 km Used in land and marine transportation Plans for next generation system

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Galileo Proposed and being planned by Europe It will be controlled by civilians Plans call for 30 medium Earth orbit satellites Distributed in 3 orbital planes – Altitude of 23000 km

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Galileo Will provide 2 levels of service – Basic (free-of-charge) – Chargeable service 3 phases of development – Definition phase (already completed) – Development and validation phase – Deployment phase Scheduled to begin in 2006/7 timeframe Service by 2008 (?)

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Galileo Because it is civilian operated, it will have advantages in the marketplace Already promising to provide a service that will meet legal standards – GPS can’t do this If the lawyers are happy, the business money is more likely into Galileo products

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WAAS Wide Area Augmentation System (WAAS) – Covers North America – South America could be covered later Utilizes GPS but augments it with additional satellite information – Use geostationary satellites International Maritime Satellite (Inmarsat) – Provides additional reliability and accuracy Used for aircraft navigation – Not necessarily for takeoff and landing

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LAAS Local Area Augmentation System (LAAS) Utilizes GPS but augments it with pseudolite information at critical locations – Typically around airports but could be used in other locations theoretically Used for aircraft takeoff and landing – Including category II/III

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EGNOS European Geostationary Navigation Overlay System (EGNOS) European version of WAAS – Covers all of Europe and North Africa – Could be extended to cover all of Africa and Middle East Will eventually be superceded by Galileo

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MSAS MTSAT Satellite-Based Augmentation System (MSAS) – Multi-functional Transport Satellite (MTSAT) Japanese version of WAAS – Covers parts of Asia and the Pacific

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Projections and coordinate systems

Projections and coordinate systems

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