Global Positioning Systems - GPS

GPS

• Why?• What is it?• How does it work?• Differential GPS• How can it help me?

GPS – Why??Where am I?

How do I get there? Where are you, and how do I get to

You?

WHO CARES???

Department of DefenseThe U.S. Department of Defense decided that the military had to have a super precise

form of worldwide positioning. And fortunately they had the kind of money ($12 billion!) it took to build something really good.

In the latter days of the arms race the targeting of ICBMs became such a fine art that they could be expected to land right on an enemy's missile silos. Such a direct hit would destroy the silo and any missile in it. The ability to take out your opponent's missiles had a profound effect on the balance of power.

But you could only expect to hit a silo if you knew exactly where you were launching from. That's not hard if your missiles are on land, as most of them were in the Soviet Union. But most of the U.S. nuclear arsenal was at sea on subs. To maintain the balance of power the U.S. had to come up with a way to allow those subs to surface and fix their exact position in a matter of minutes anywhere in the world Hello GPS!

What is GPS?Other Satellite Constellations• GPS: United States• Glonass: Russian• Beidou: China• Galileo: Europe

What is GPS?“A Worldwide Radio-Navigation System”

• 24 Satellites-Constellation– Name: NAVSTAR

Manufacturer: Rockwell International Altitude: 10,900 nautical miles (12,550 miles) Weight: 1900 lbs (in orbit)Size: 17 ft with solar panels extended Orbital Period: 12 hours Orbital Plane: 55 degrees to equatorial planePlanned Lifespan: Block IIR – 7.5 years; Block IIF - 12.5 years Current constellation: 12 Block IIR, 7 Block IIR-M, & 12 Block II-F production satellites Future satellites: GPS III/IIIF

• Ground Base Stations– These stations monitor the GPS satellites, checking both their operational health and their

exact position in space. The master ground station transmits corrections for the satellite's ephemeris constants and clock offsets back to the satellites themselves. The satellites can then incorporate these updates in the signals they send to GPS receivers.

– There are currently sixteen monitoring stations.

*1 nautical mile is approximately 1.15078 miles (6076.12 ft)-1 min

of arc of the earth’s surface

GPS Satellites have onboard atomic clocks with an accuracy of 1 nanosecond (1 billionth of a second)

• 24 Satellites• 4 satellites in 6 orbital planes

inclined at 55o

• 20,200 km above the Earth

Space Segment

12 hour orbits Same satellite in view for 4-5

hours Designed to last 7.5 or 12.5

years Different Classifications

Block 1, 2, 2A, 2R & 2F

Equator55o

Tracking Facilities

- 1 Master Control Station – Schriever AFB, Colorado- 1 Alternate Master Control Station – Vandenburg AFB, California- 11 Command and Control Antennas- 16 Monitoring Sites

How GPS WorksHow GPS works can basically be described in 5 logical steps:

1. The basis of GPS is “triangulation" from satellites. The word "triangulation" is used very loosely here because it's a word most people can understand, but purists would not call what GPS does "triangulation" because no angles are involved. It's really "trilateration."

2. To "triangulate," a GPS receiver measures distance using the travel time of radio signals.

3. To measure travel time, GPS needs very accurate timing which it achieves with some tricks.

4. Along with distance, you need to know exactly where the satellites are in space. High orbits and careful monitoring are the secret.

5. Finally you must correct for any delays the signal experiences as it travels through the atmosphere.

How GPS WorksHow GPS works can basically be described in 5 logical steps:

1. The basis of GPS is “triangulation" from satellites. The word "triangulation" is used very loosely here because it's a word most people can understand, but purists would not call what GPS does "triangulation" because no angles are involved. It's really "trilateration."

2. To use trilateration , a GPS receiver uses the travel time of radio signals Trilateration: methods involve the determination of absolute or relative locations of

points by measurement of distances (not angles), using the geometry of spheres or triangles.

GPS: measure the ranges (distances) to satellites not to control points. Ranging: the process of determining how far your receiver is from each satellite.

• The satellites are like “Orbiting Control Stations”

• Ranges (distances) are measured to each satellites using time dependent codes

• Typically GPS receivers use inexpensive clocks. They are much less accurate than the clocks on board the satellites

• A radio wave travels at the speed of light• (Distance = Velocity x Time)

• Consider an error in the receiver clock• 1/10 second error = 30,000 Km error• 1/1,000,000 second error = 300 m error

Outline Principle : Position

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Accurate Clocks Necessary

• Whole System Depends on the Accurate Measure of Signal Time of Travel

• Calculation Depends on Highly Accurate Clocks

• Satellites Have Atomic Clocks• Accurate but very expensive ($100,000)• SVs have up to four atomic clocks

• Ground Receivers Just Need Consistent Clocks (Quartz Clocks)

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Atomic Clocks

• Most accurate method for time-keeping ever developed

• Nanosecond accuracy: 0.000000001 sec

• If satellite and receiver out of sync by 1/100th of a second, distance measurement off by 1860 miles.

How GPS WorksTo measure travel time, GPS needs very accurate timing which it achieves with some tricks.

Finding the exact time is essential. Distance is a function of the speed of light, electromagnetic signals of

stable frequency and elapsed time. Satellite marks the moment the signals depart, the receiver marks the

moment they arrive. The difference in sync of the “receiver time” minus the “satellite time”

is equal to the travel time…kinda The GPS signal travel time for a satellite directly overhead is about

0.06 sec. GPS signals provide a receiver with information to measure the range

and the position of the satellite (moving 4 km /sec).

How GPS WorksTo measure travel time, GPS needs very accurate timing which it achieves with some tricks.

GPS signals carry information for the receiver to solve it’s position A GPS signal must communicate to its receiver

What time it is on the satellite The instantaneous position of a moving satellite Atmospheric corrections Satellite identification system and location of other satellites (Ephemeris Data) This information is sent from the Ground Monitoring Stations

How GPS WorksGetting Timing Sync for Accurate Ranging

• To determine a good range to the satellite we cannot only use the difference between the clocks in the satellite and the gps receiver.

– Atomic Clock vs. Quartz Clock

• GPS: One-way, two clocks in a satellite and a receiver need to perfectly synchronized (impossible; one microsecond discrepancy – 300 m error)

How GPS WorksAligning the Pseudo-Random Code

• The Pseudo Random Code is a fundamental part of GPS. Physically it's just a very complicated digital code, or in other words, a complicated sequence of "on" and "off" pulses as shown below.

• The signal is so complicated that it almost looks like random electrical noise. Hence the name "Pseudo-Random."

• There are several good reasons for that complexity: – receiver doesn't accidentally sync up to some other signal. – all the satellites can use the same frequency without jamming each other. And it makes it more

difficult for a hostile force to jam the system. – the Pseudo Random Code gives the DoD a way to control access to the system.

Aligning the Psuedo-Random Code for Range

D = V (∆T)

• Pseudoranges (Code)• Each satellite sends a unique signal

which repeats itself approximately every millisecond

• Receiver compares self generated signal with received signal

• From the time difference (dT), a range observation can be determined

• Receiver clock needs to be synchronized with the satellite clock ∆T

Received Codefrom Satellite

GeneratedCode fromReceiver

Range Determination from Code Observation

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R = c ∆T + λN

Phase Observations

• Wavelength of the signal is 19 cm on L1 and 24 cm on L2

• Receiver compares self-generated phase with received phase

• Number of wavelengths is not known at the time the receiver is switched on (carrier phase ambiguity)

• As long as you track the satellite, the change in distance can be observed (the carrier phase ambiguity remains constant)

∆T

Received Satellite Phase

GeneratedPhase fromReceiver

Range Determination from Phase Observation

Xll

Vl

GPS Principle : Range

Xll

Vl

Xll

Vl

Xll

Vl

Range = Time Taken x Speed of Light

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Trilateration

One satellite determines a locationanywhere on a sphere of radius R1.

Two satellites give a circle of points at the intersection of the spheres of radii R1 and R2.

The third satellites gives an intersection of a sphere of radius R3 with the circle to establish two possible points in space. One point is usually easily discarded.

R1

R2

R3

P

We are somewhere on a sphere of radius, R1

R1

GPS Principle : Point Positioning

R2

2 spheres intersect as a circle

R3

3 spheres intersect at a point (Latitude, Longitude and Height)

4 ranges to resolve for Latitude, Longitude, Height & TimeIt is similar in principle to a resection problem

Point Positioning

GPS Signals• Carriers

– L1 and L2 (L1C, L2C, L5)• The L1 carrier is 1575.42 MHz and carries both the status message and a

pseudo-random code for timing.• The L2 carrier is 1227.60 MHz and is used for the more precise military

pseudo-random code

• Pseudo-Random Codes– (C/A) Coarse Acquisition Code

• Basis for civilian GPS use

– P (Precise) Code• Modulates both the L1 and L2 carriers at a 10MHz rate• When encrypted by military it becomes the Y code• High precision work

• Navigation Message• Low frequency signal added to the L1 codes that gives information about the

satellite's orbits, their clock corrections and other system status.

Quick Review

1. Distance to a satellite is determined by measuring how long a radio signal takes to reach us from that satellite.

2. To make the measurement, assume that both the satellite and our receiver are generating the same pseudo-random codes at exactly the same time.

3. By comparing how late the satellite's pseudo-random code appears compared to our receiver's code, determine how long it took to reach us.

4. Multiply that travel time by the speed of light and you've got distance. ..But there is more!!

Solving for a Position and Determination of a Timing Correction

• Remember that both the satellite and the receiver need to be able to precisely synchronize their pseudo-random codes to make the system work. Code Phase GPS vs. Carrier Phase GPS

• The secret to achieving perfect timing is making extra measurements and syncing them all up at the same time…Much like a big resection

• If our receiver's clocks were perfect, then all our satellite ranges would intersect at a single point (which is our position). But with imperfect clocks, a fourth measurement, done as a cross-check, will NOT intersect with the first three.

• So the receiver's computer says "Uh-oh! there is a discrepancy in my measurements. I must not be perfectly synced with universal time.“

• Since any offset from universal time will affect all of our measurements, the receiver looks for a single correction factor that it can subtract from all its timing measurements that would cause them all to intersect at a single point.

Solving for a Position and Determination of a Timing Correction

• That correction brings the receiver's clock back into sync with universal time, and bingo! - you've got atomic accuracy time right in the palm of your hand.

• Once it has that correction, the receiver applies to all the rest of its measurements and now we've got precise positioning.

• One consequence of this principle is that any decent GPS receiver will need to have at least four channels so that it can make the four measurements simultaneously.

• With the pseudo-random code as a rock solid timing sync pulse, and this extra measurement trick to get us perfectly synced to universal time, we have got everything we need to measure our distance to a satellite in space.

• ***But for the triangulation to work we not only need to know distance, we also need to know exactly where the satellites are.***

Satellite Position for Accurate Geodetic Positioning

• The satellite’s orbit (ephemeris) and position is updated by the Ground Control Stations– DoD monitors and checks each satellite’s exact altitude, position, and speed

– These errors are called ephemeris errors and are a product of the gravitional pull from the moon, sun, and from the pressure of solar radiation on satellites

– Once the DoD has measured a satellite's exact position, they relay that information back up to the satellite itself. The satellite then includes this new corrected position information in the timing signals it's broadcasting.

– So a GPS signal is more than just pseudo-random code for timing purposes. It also contains a navigation message with ephemeris information as well.

Another Review

1. To use the satellites as references for range measurementswe need to know exactly where they are.

2. GPS satellites are so high up their orbits are very predictable. 3. Minor variations in their orbits are measured by the

Department of Defense. 4. The error information is sent to the satellites, to be

transmitted along with the timing signals.

The Error Budget

Errors in Satellite Measurements

Summary of GPS Error SourcesTypical Error in Meters(per satellites)

Satellite ClocksOrbit ErrorsIonosphereTroposphereReceiver NoiseMultipath

1.52.55.00.50.30.6

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IONOSPHERICDELAY

TOTALATMOSPHERICDELAY

TROPOSPHERICDELAY

HYDROSTATICDELAY

WETDELAY

GPS Signal Delays Caused by the Atmosphere

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Atmospheric Corrections

• System Does Not Operate in a Vacuum

• Ionosphere• Band of charged particles surround earth

• Troposphere• Weather

• Solar Activity (Mostly sun spots)

• Alters Calculated Position by Delaying Signal from Satellites

•The reception of the GPS signal via multiple paths than from a direct line of sight (reflection of the GPS signal)

• Reflected signals at the frequencies used for L1 and L2 tend to be weaker and more diffuse than the directly received signals

• Different circular polarization - Left hand polarization (multipath signal) Vs.

right hand polarization(direct signal)

Multipath Errors

Multipath Errors

Antenna design and Multipath– Ground Plane (a metal sheet)

- Eliminates signals from low elevation angles

Antenna design and Multipath• Choke ring design

- can reduce antenna gain at low elevations

• 15° cutoff or mask angle

Differential and Relative GPS Positioning

Base: GPS Receiver occupying a known position (HARN or CORS)

•Error is eliminated by the use of a correction factor

•Rover: GPS Receiver used to set new positions

Two Types:

Static: NOT MOVING

Real-Time Kinematic: MOVING

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WAAS Satellites provide on-the-fly differential correctorsfor stand-alone receivers improving accuracy to +/- 2 m.

WAAS = FAA’s Wide Area Augmentation System

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Differential GPS (DGPS)For Survey Grade Accuracy

• Requires two Receivers• Base receiver on a known point• Rover receiver surveys desired points

• Infinite number of rover receivers can use the same base station

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Differential GPS

X23y23z23

x19y19z19

x14y14z14

x21y21z21

Measured: x y z

Corrections appliedafter survey

True: x y zMeasured: x y z

______________Delta: x y z

Delta: x y z_________

True: x y z

• It is possible to determine the position of Rover ‘B’ in relation to Reference ‘A’ provided

• Coordinates of ‘A’ are known• GPS observations are

simultaneous

Differential Positioning eliminates errors in the

satellite and receiver clocks

minimizes atmospheric delays

Accuracy 5 mm - 5 m

BA

Differential GPS

?

• If using Code only, accuracy is in the range of 30 - 50 cm

• This is typically referred to as DGPS

BA

Differential Code / Carrier Phase

• If using Phase or Code & Phase,accuracy is in the order of 5 - 10 mm + 1ppm

Mask Angle (Elevation, Cut-Off Angle)

15 ° 15 °

A description of purely geometrical contribution to the uncertainty in a position fix

It is an indicator as to the geometrical strength of the satellites being tracked at the time of measurement

GDOP (Geometrical) Includes Lat, Lon, Height & Time

PDOP (Positional) Includes Lat, Lon & Height

HDOP (Horizontal) Includes Lat & Lon

VDOP (Vertical) Includes Height only

Good GDOP

Dilution of Precision (DOP) - 1/2

Summary of GPS Positioning

Point Positioning :10 - 20 m (1 epoch solution)

Differential Code :30 - 50 cm (P Code)1 - 5 m (CA Code)

Differential Phase :5 mm + 1 ppm

3 mm + 0.5 ppm (using Choke-Ring Antenna)

Differential GPS Correction

Real-Time Kinematic Positioning

Geoid• “The equipotential surface of the Earth’s gravity field which best

fits, in the least squares sense, (global) mean sea level.”*

• Geoid surface is neither visible or directly measureable.

• Geoid is mathematically related to and modeled from gravity data.

• A geoid height is the ellipsoidal height from an ellipsoidal datum to a geoid.

• Hence, geoid height models are directly tied to the geoid and ellipsoid that define them (i.e., geoid height models are notinterchangeable).

*Definition from the Geodetic Glossary, September 1986

Daniel R. Roman, National Geodetic Survey, National Oceanic and Atmospheric Administration

H

H = Orthometric Height (NAVD 88)

H = h - N

TOPOGRAPHIC SURFACE

h = Ellipsoidal Height (NAD 83)N = Geoid Height (GEOID 03)

h

Ellipsoid(NAD 83)

N

Geoid(NAVD 88)

Geoid Height(GEOID03)

A B

Geoid

GeoidDESIGNATION - LEV MAINTPID - DE9009STATE/COUNTY- IL/CHAMPAIGNUSGS QUAD - THOMASBORO (1975)

*CURRENT SURVEY CONTROL___________________________________________________________________* NAD 83(2007)- 40 11 15.08650(N) 088 14 18.02923(W) ADJUSTED * NAVD 88 - 222.6 (meters) 730. (feet) GPS OBS

ELLIP HEIGHT- 190.397 (meters) (02/10/07) ADJUSTEDGEOID HEIGHT- -32.12 (meters) GEOID03___________________________________________________________________

SUPERSEDED SURVEY CONTROL

ELLIP H (12/06/04) 190.415 (m) ELLIP H (12/18/02) 190.411 (m)

Occupational Planning

Continuously Operating Reference Stations

• The CORS system enables positioning accuracies that approach a few centimeters relative to the National Spatial Reference System, both horizontally and vertically.

• Surveyors, GIS/LIS professionals, and engineers can apply CORS data to position points at which GPS data have been collected.

• The National Geodetic Survey (NGS) coordinates two CORS networks:– the National CORS network and – the Cooperative CORS network.

Regional CORS Network

http://www.tdot.state.tn.us/Chief_Engineer/assistant_engineer_design/design/tdotgnss.html

1200+ Installed and Operated by various Federal-State-local Agencies

NOAA/National Geodetic SurveyNOAA/OAR Global Systems DivisionU.S. Coast Guard - DGPS/NDGPSCorps of Engineers - DGPSFAA - WAAS/LAAS State DOTs County and CityAcademiaPrivate Companies

National CORS Network

CORS Tower

NGS PROVIDES

• Horizontal and Vertical NSRS Connections• NAD 83 and ITRF00 Coordinates• Network Data Collection - Hourly & Daily• Daily 3D Network Integrity Adjustment• Public Data Distribution - Internet• 13 Year On-Line Data Holding

National CORS Network

In Summary• 4 satellites needed for accurate timing• Once timing is achieved an accurate position can be

calculated• A GPS solution without a correction is an

Autonomous Solution with a varying accuracy of +/-3m.

• To obtain a correction we apply a technique called differential positioning.– This involves two gps recievers (at a minimum)

• One base, one rover for RTK, Static can have many base stations

In Summary

• Differential Positioning can be done Static or in Real Time Kinematic (RTK)

• Static yields much higher accuracies and should be used for control networks

• RTK is still accurate, but not for traversable control. This method is best used for general topo, and construction surveying, but not control.

In Summary

• In Differential Positioning one GPS unit will occupy a known point or station. This is your base. The rover will occupy the point that you wish to know the position. The base will transmit the correction to the rover in a rtk setup either by radio, or by internet (CORS).

• In a static setup data for the CORS base stations are downloaded after the occupation and used to post process the rover’s position.

In Summary

• STATIC– Not moving– Higher accuracies– Used for control work– Base can be either another gps unit occupying a higher

order control point or a CORS.– This solution is post processed using office software after

the occupation– Typical occupation times can be 10 min + 2 min/mile of

baseline

In Summary

• RTK – Real Time Kinematic– On the move– Lower accuracy, but still survey grade, +/- .06’– Used for general survey and construction surveying– Base can be another gps unit transmitting a correction by

radio, or a CORS with a correction available over the internet.

– VRS (virtual reference station) is a multiple CORS correction factor that is available over the internet. This is used on where very long base lines are encountered using a CORS network correction factor.