Geographic, GPS,And Datum Fundamentals

A brief review of revolutionary ideas

and technologies

GPS

Description:

The Global Positioning System* (GPS) is based on observations of signals transmitted from satellites

Source:http://www.garmin.com/aboutGPS/

*Owned and operated by the Department of Defense

Beacon Receiver - Most CommonChoice for High Resolution Surveying

CORS –ContinuousOperationReferenceStation

PAPT—University of PittsburghCORS Station.Check us on the web athttp://www.ngs.noaa.gov

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Lines of EqualLatitude

Lines ofEqual Longitude

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Geographic Coordinates

Origin atGreenwichObservatoryandEquator

Old School:

Determining an unknown position.

Benchmarks represented highly accurate known reference positions!

Brass disk Chisel marks Rock piles Buried monuments

Now replaced, and being relocated with respect to, NGS CORS GPS Reference Stations.

Continuously Operating Reference Stations

PAPT: The Univ. of Pittsburgh CORS NGS Reference Station

NGS CORS Stations

NGS CORS Stations

Specifying an unknown Position

Measure unknown position with respect to known features.

Involved triangulation of known features to determine an unknown point.

National networks established.

Datum, Survey Network

Historically:Triangulation NetworkAstronomical observationInitial, intermittent, and

ending baselinesMultiple, redundant angle

measurements

Why these technologies?1. Easy to measure angles2. Difficult to measure

distance accurately3. Time consuming to

measure point position accurately

Survey Network, 1900

(from Schwartz, 1989)

Space based measurements

The advent of the Earth orbiting satellites starting in 1955, and the development of radio astronomy (Jansky, 1932) started to bring about a revolution in geodetic accuracy.

Activity started after WWII using technology developed during the war and in response to cold war.

New methods removed the need for line-of-sight

GPS Original Design

Started development in the late 1960s as NAVY/USAF project to replace Doppler positioning system

Aim: Real-time positioning to < 10 meters, capable of being used on fast moving vehicles.

Limit civilian (“non-authorized”) users to 100 meter positioning.

GPS Design

Innovations:Use multiple satellites (originally 21, now ~28)All satellites transmit at same frequencySignals encoded with unique “bi-phase,

quadrature code” generated by pseudo-random sequence.

Dual frequency band transmission:L1 ~1.5 GHz, L2 ~1.25 GHz

The Macrometer V1000 -- the first GPS receiver owned by NOAA!!

The GPS Pathfinder – puts a whole new spin on WHEN and

WHERE!!

GPS

Description:

The Global Positioning System* (GPS) is based on observations of signals transmitted from satellites

*Owned and operated by the Department of Defense

Source: http://msl.jpl.nasa.gov/QuickLooks/gps1QL.html

Measurements

Measurements: Time difference between signal transmission

from satellite and its arrival at ground station (called “pseudo-range”, precise to 0.1–10 m)

Carrier phase difference between transmitter and receiver (precise to a few millimeters)

All measurements relative to “clocks” in ground receiver and satellites (potentially poses problems).

Positioning

For pseudo-range to be used for “point-positioning” we need: Knowledge of errors in satellite clocks Knowledge of positions of satellites

This information is transmitted by satellite in “broadcast ephemeris”.

“Differential” positioning (DGPS) eliminates need for accurate satellite clock knowledge by differencing the satellite between GPS receivers (needs multiple ground receivers). Not discussed in this talk, but used in Geology and Planetary Science for ultra precise

measurements (less than 1 mm relative horizontal uncertainty).

Satellite constellation

Since multiple satellites need to be seen at same time (four or more):Many satellites (original 21 but now 28)High altitude so that large portion of Earth can

be seen (20,000 km altitude —MEO)

The Global Positioning System (GPS) was designed for military applications. Its primary purpose was to allow soldiers to keep track of their position and to assist in guiding weapons to their targets. The satellites were built by Rockwell International and were launched by the U.S. Air Force. The entire system is funded by the U.S. government and controlled by the U.S. Department of Defense. The total cost for implementing the system was over $12 billion.

A GPS satellite. The GPS constellation of satellites consists of at least 24 satellites – 21 primary satellites and 3 orbiting spares. They orbit the earth at an altitude of 17,500 KM (10,900 miles) at a speed of 1.9 miles per second between 60°N and 60°S latitude. Each satellite weighs 1900 lbs and is 17 feet (5.81 meters) wide with solar panels extended. The satellites orbit the earth twice a day. This guarantees that signals from six of the satellites can be received from any point on earth at almost any time.

Global Positioning SystemIts official name is NAVSTAR-GPS. Although NAVSTAR-GPS is not an acronym, a few backronyms have been created for it. The GPS satellite constellation is managed by the United States Air Force 50th Space Wing.

Similar satellite navigation systems include the Russian GLONASS (incomplete as of 2008), the upcoming European Galileo positioning system, the proposed COMPASS navigation system of China, and IRNSS of India.

From: http://en.wikipedia.org/wiki/GPS

SiRF Star III based GPS receiver with integrated antenna. M10214 from Antenova, a UK company.

THE

GLOBAL POSITIONING SYSTEM

PARTNERSHIP COUNCIL

2008 05 18 Partnership Council Welcome Slides

BRIGADIER GENERAL JOHN E. HYTEN

COLONEL DAVID W. MADDEN

Brig Gen John E. Hyten is the Director of Requirements, Headquarters Air Force Space Command, Peterson Air Force Base, CO. As Director, he is responsible for ensuring future space and missile systems meet the operational needs of our joint forces into the 21st century.

Colonel David W. Madden is Commander, Global Positioning Systems Wing (GPSW), Space and Missile Systems Center, LA AFB, CA. He is responsible for the multi-service, multi-national Systems Wing which conducts development, acquisition, fielding and sustainment of all GPS space segment, satellite command and control (ground) segment, and GPS military user equipment.

Hosting Organizations – Senior Representative

2008 05 18 Partnership Council Welcome Slides

Dr. Bradford W. Parkinson

Dr. Bradford Parkinson (then USAF Colonel) was the original Program Director for Navstar GPS during the programs first six critical years (1972-1978). He and his team championed the effort to define the GPS system, sell the concept, develop the system architecture and perform the first test for DoD. Their first attempt for program approval failed in August 1973. It was packaged as the Air Force’s 621B system. It was determined that a more broadly based program, embracing the views and requirements of all US military services be developed. In response, Dr. Parkinson assembled about a dozen members of the JPO, on the fifth floor of the Pentagon. He directed the development of a new design that employed the best of all available concepts and technology. The result was a synthesis of the Air Force and Navy’s prior systems: Air Force’s 621B, Navy’s Timation, and Navy/Applied Physics Lab’s Transit program, as well as new ideas. The GPS design of today is essentially unchanged from the concept approved in December 1973. Dr. Parkinson’s continual focus on the future has assured his place in the history of navigation.

2008 05 18 Partnership Council Welcome Slides

Dr. A.J. Van Dierendonck

Dr. A.J. Van Dierendonck, as an employee of AVAND Systems Engineering (his own company), has performed as a Consultant or Contract Engineer to eight major aerospace companies, all involved with the GPS program since 1977. He performed systems engineering tasks on GPS Monitor Station receivers, Position Reference System receivers, the GPSPAC Spaceborne Navigation Set, the X-set, the Y-set and the M-set. In addition, Dr. Van Dierendonck consulted on a significant portion of a FAA contract for an assessment of GPS applied to Civil Aviation Navigation requirements and on the development of a GPS user receiver simulation to be used in conjunction with their Inertial Navigation Systems simulations. Prior to March 1977, Dr. Van Dierendonck was the GPS Technical Manager at General Dynamics Electronics Division, responsible for the Phase I GPS Control Segment system designs requirements, system interfaces and algorithm development. The GPS program is indebted to Dr. A.J. Van Dierendonck for his tireless efforts.

2008 05 18 Partnership Council Welcome Slides

Dr. James J. Spilker, Jr.

For over thirty years, Dr. Spilker has made repeated and lasting

contributions to the technical, architectural and programmatic

definition of GPS. In the 1970’s, he was a key creator of, and

advocate for, the navigation signal structure now used by millions

of civil and military users around the world. In the 1980’s, he

founded and led Stanford Telecom as it developed a wide range of

electronic products and services for diverse customers. In the

1990’s he continued to be a strong advocate to the National

leadership for modernization of the GPS system. His leadership

has made GPS the success it is today.

2008 05 18 Partnership Council Welcome Slides

Mr. Gaylord B. Green

Colonel (ret) Green has made significant contributions in the civil, military, and scientific development and use of GPS. In the early 1970’s, he served an integral role in the development of GPS Block I satellites. In the 1980’s, he led the Guidance and Control Division of the Ballistic Missile Office where he integrated GPS receivers on two flights of Minuteman ICBMs. His government service culminated in his return to the JPO as the System Program Director. Upon entering the commercial sector in the late 1980’s, he continued to support GPS as President of the Institute of Navigation and President of Navastro Company, Inc., where he oversaw the application of high-precision GPS-based orbit determination to test Einstein’s General Theory of Relativity. Mr. Green’s distinguished service has contributed immeasurability to the success of GPS.

2008 05 18 Partnership Council Welcome Slides

Mr. Thomas A. Stansell, Jr.

Mr. Thomas A. Stansell, Jr. has made repeated and lasting contributions to the technical, architectural and programmatic definition as well as regulatory protection of GPS over the past twenty years. In the 1980’s, he was a key creator of, and advocate for, all-digital GPS receiver technology now use by million of civil and military users around the world. In the 1990’s, he brought forward the concept of the GPS L5 data-less channel, which has now been fully developed. In the 2000s, he led the technical development of GPS L2C signal and improved the antijam performance of M-Code. He has been a continuing advocate to the National leadership for GPS modernization, as well as fighting for regulatory protection of modernized civil and military signals. Mr. Stansell has been recognized repeatedly for his contributions. He has been a Technical and a General Chair for two GPS ION Conferences and is a Fellow of ION. He won the ION Capt P.V.H. Weems award in 1995 and the IEEE PLANS most prestigious honor, the Kershner award, in 2000. Mr. Stansell’s leadership has helped make GPS the success it is today.

2008 05 18 Partnership Council Welcome Slides

Mr. Charles (Charlie) Cahn

Dr. Charles Cahn was one of the primary architects of both the 621B program that preceded GPS and of the current GPS navigation signals. Dr. Cahn pioneered many advanced GPS receiver concepts during and after GPS Phases I and II, including novel signal tracking concepts to improve acquisition an “all digital” receiver architecture, and more recently, notch filtering, specialized interference cancellation, and other high antijam techniques. He also has advanced the state of the art of GPS multipath mitigation techniques. In recent years, Dr. Cahn has been a major contributor to GPS Signal modernization. He initially proposed Manchester modulation for what became the BOC (10, 5) M-Code, influenced Selection of convolutional coding for M-Code data, invented the M-Code Frequency Hopping acquisition method, provided the analysis which justified splitting all modernized GPS Signals into data and data-less components, including L5, L2C, and M-Code, and developed a code generator not based on Gold codes, which will be used for L2C. Dr. Cahn’s ongoing contributions span more than 30 years and continue unabated today

2008 05 18 Partnership Council Welcome Slides

30th Anniversary of 1st GPS Launch,22 Feb 78

Navstar 1 launched at Vandenberg AFB, 22 February 1978

Block I’s launched from 22 February 1978 - 9 October 1985

Block I contract (F04701-74-C-0527) signed August 1974 1st satellite launch (Navstar 1) was 42 months later 1st four satellites were launched within a year--all in 1978

Rockwell International made a special "first day of issue" card for each Block I launch Vandenberg AFB Post Office stamped them with the date of the launch.

Color scan of the memento on next slide

Inside GNSS recapped the 30th anniversary of 1st GPS launch at: insidegnss.com/node/522

2008 05 18 Partnership Council Welcome Slides

Block I

“First Day of Issue” Card

Vandenberg AFBPost Office

February 22, 1978

2008 05 18 Partnership Council Welcome Slides

The 3 segments of GPS

Current constellation

• Relative sizes correct (inertial space view)

• “Fuzzy” lines not due to orbit perturbations, but due to satellites being in 6-planes at 55o inclination.

Ground Track Paths followed by satellite along surface of Earth.

GPS Relativity Related Corrections Gravitational redshift (blueshift) predicted from General Relativity

Orbital altitude 20,183 km Clock runs fast by 45.7 s per day

Time dilation predicted from Special Relativity Satellite velocity 3.874 km/s Clock runs slow by 7.1 s per day

Net secular effect (satellite clock runs fast) Clock runs fast by 38.6 s per day

Residual periodic effect Orbital eccentricity 0.02 Amplitude of periodic effect 46 ns

Sagnac effect (rotation related) Maximum value 133 ns for a stationary receiver on the geoid

GPS (Summary)Net secular relativistic effect is 38.6 s per

dayNominal clock rate is 10.23 MHzSatellite clocks are offset by – 4.464733 parts in

1010 to compensate effectResulting (proper) frequency in orbit is

10229999.9954326 HzObserved average rate of satellite clock is same

as clock on the geoid

Residual periodic effectMaximum amplitude 46 nsCorrection applied in receiver

Sagnac effectMaximum value 133 nsCorrection applied in receiver

Pseudo-range accuracy

Original intent was to position using pseudo-range: Accuracy better than planned.

C/A code (open to all users) 10 cm-10 meters. Used by most hikers and low cost GPS units to determine position.

P(Y) code (restricted access since 1992) 5 cm-5 meters

Example of FM Station 97.1 with 440 A note

Determining an unknown location today.

Use GPS

Range = speed of light x travel timeRange = c(t1 – t2)

(c =299,792,458 meters per second)

GPS(code receivers)

Step 1: using satellite ranging

GPS is based on satellite ranging, i.e. distance from satellites …satellites are precise reference points

…we determine our distance from them

we will assume for now that we know exactly where satellite isand how far away from it we are…

if we are lost and we knowthat we are 11,000 miles

from satellite A…we are somewhere on a sphere

whose middle is satellite Aand diameter is 11,000 miles

if we also know that we are12,000 miles from satellite B

…we can narrow down wherewe must be…

only place in universe is oncircle where two spheres intersect

if we also know that we are13,000 miles from satellite C

…our situation improvesimmensely…

only place in universe is ateither of two points where

three spheres intersect

three can be enough to determine position… one of the two points generally is not possible (far off in space)

two can be enough if you know your elevation …why?

one of the spheres can be replaced with Earth… …center of Earth is “satellite position”

generally four are best and necessary….why this is a little later

this is basic principle behind GPS……using satellites for triangulation

step 2: measuring distance from satellite

because GPS based on knowing distance from satellite …we need to have a method for determing how far

away the satellites are

use velocity x time = distance

GPS system works by timing how long it takes a radio signal to reach the receiver from a satellite…

…distance is calculated from that time…radio waves travel at speed of light: 180,000 miles per second

problem: need to know when GPS satellite started sending its radio message

requires very good clocks that measure short times……electromagnetic waves move very quickly

use atomic clocks

came into being during World War II; nothing to do with GPS -physicists wanted to test Einstein’s ideas about gravity and time • previous clocks relied on pendulums • early atomic clocks looked at vibrations of quartz crystal

…keep time to < 1/1000th second per day ..not accurate enough to assess affect of gravity on time …Einstein predicted that clock on Mt. Everest

would run 30 millionths of a second faster than clock at sea level

…needed to look at oscillations of atoms

principle behind atomic clocks…

atoms absorb or emit electomagnetic energy in discrete amounts that correspond to differences in energy between different configurations of the atomswhen atom goes from one energy state to lower one, it emits an electromagnetic wave of characteristic frequency …known as “resonant frequency”

these resonant frequencies are identical for every atom of a given type:

cesium 133 atoms: 9,192,631,770 cycles/second

cesium can be used to create extraordinarily precise clock

(advances also led to using hydrogen and rubidium)

GPS clocks are cesium clocks

now that we have precise clocks……how do we know when the signals left the satellite?

this is where the designers of GPS were clever……synchronize satellite and receiver so

they are generating same code at same time

analogy: 2 people separated by some distance both start yelling

one, two, three…at same time person 2 hears “one” shouted by person 1 when

person 2 says “three” …if you both said one at same time,

the distance away person 2 is from person 1 is time difference between “one” and “three”

times the velocity of the sound

let us examine GPS satellite signals more closely…

SVs transmit two microwave carrier (carry information) signalsL1 (1575.42 MHz): carries navigation message; SPS code

(SPS: standard positioning servic)L2 (1227.60 MHz): measures ionospheric delay

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 SPSP-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.

3 binary codes shift L1 and/or L2 carrier phases

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

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

receiver PRN code start position at time of full correlation is time of arrival of the SV PRN at receiverthe 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 datafrom

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

GPS

With three satellites we have three observations and four unknowns (our X, Y, Z, and clock bias). We must either assume we know Z (e.g. at sea level or from map), or track extra satellite. Generally we track extra satellites.

We need at least three satellites for 2-D, four satellites for 3-D positioning.

Determine Position by Combining Pseudo RangeMeasurements

Onesatellite: Unknown location is somewhere on a sphere

GPS

Two satellites: circle of intersection

GPS

Three satellites: two points

Four or moresatellites: one point

RMS versus Time Carrier-Phase (North)

0.2 0.3 0.3 0.4 0.5

5.2

13.6

0.02.0

4.06.08.0

10.012.0

14.016.0

24 Hrs 12 Hrs 8 Hrs 6 Hrs 4 Hrs 2 Hrs 1 Hr

Observation Session Length

rms

(cm

)

RMS versus TimeCarrier-Phase (East)

0.2 0.3 0.3 0.4 0.7

8.3

15.4

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3.0

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9.0

12.0

15.0

18.0

24 Hrs 12 Hrs 8 Hrs 6 Hrs 4 Hrs 2 Hrs 1 Hr

Observation Session Length

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(cm

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RMS versus Time Carrier-Phase (Up)

0.8 1.1 1.3 1.5 1.9

12.5

30.8

0.03.06.09.0

12.015.018.021.024.027.030.033.0

24 Hrs 12 Hrs 8 Hrs 6 Hrs 4 Hrs 2 Hrs 1 Hr

Observation Session Length

rms

(cm

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Our Range MeasurementsAren’t Perfect

Standalone Positioning: Since May 1, 2000

C/A Code on L1No Selective

Availability

6-11 m

NOTE: The Time Difference shown here represents a complex 1-dimensional model of the velocity of electromagnetic radiation from the satellite to the receiver. The velocity of electromagnetic radiation, or light, varies with physical parameters.

Standalone Positioning: By 2011

C/A Code on L1C/A Code on L2New Code on L5

1-3 m

Better resistance to interference

GPS

Positional Uncertainty• Errors in range

measurements and satellite location introduce

errors• Creates a range of

uncertainty around the GPS receiver

position

finally… step 4: knowing where a satellite is in space

• Air Force injected satellites into known orbits• orbits known in advance and programmed into receivers• satellites constantly monitored by DoD …identify errors (ephemeris errors) in orbits …usually minor• corrections relayed back to satellite “data message” about their “health”

sites have co-located: • VLBI (very long baseline interferometry); • lunar laser-ranging (from instrument left by Apollo astronauts)

…primarily for length of day considerations • satellite laser-ranging

step 5: identifying errors

ionosphere: electrically charged particles 80-120 miles up;affects speed of electromagnetic energy…amount of affect depends on frequency …look at differences in L1 and L2 (need “dual-frequency” receivers to correct)

tropospheric water vapor: affects all frequencies; difficult to correct

multipath: reflected signals from surfaces near receiver

noise: combined effect of PRN noise and receiver noise

bias: SV clock errors; ephemeris errorsselective availability: SA; error introduced by DoD;

turned off May, 2000

blunders: human error in control segment user mistakes (e.g. incorrect geodetic datum)

…more on this in a minute receiver errors

geometric dilution of precision (GDOP): errors from range vector differences between receiver and SVs (pictures coming…)

IONOSPHERICDELAY

TOTALATMOSPHERICDELAY

TROPOSPHERICDELAY

HYDROSTATICDELAY

WETDELAY

GPS Signal Delays Caused by the Atmosphere

TEC

IPWV

On July 2nd, a summer lightning storm rolled in beneath a curtain of Northern Lights over Manitoba, Canada. "This is only the second time I've seen a scene like this," says veteran aurora photographer Chris Gray, who used a D100 Nikon camera set at f2.8 and ISO 1000 to capture this 30-second exposure.

http://www.spaceweather.com/

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August 1987 -Ionospheric refraction and Multipath Effects in GPS Carrier Phase ObservationsYola Georgiadou and Alfred Kleusberg IUGG XIX General Assembly Meeting, Vancouver, Canada

ø ø

Figure 1Multipath Description

d ø/dt ~ 2 rad/12 hr.h

Signal Multipath

PDOP – Position Dilution of Precision

Figure of merit that describes thequality of satellite geometry

Varies from 1 (best) to infinity

PDOP - Measure of Satellite Geometry

Low PDOPs Are GOOD!!!!!

Ideal (one overhead and three all at 120° intervals)

geometric dilution of precision (GDOP)

SVs occupy a small volume in the sky

SVs occupy a large volume in the sky

when measuring must have good GDOP and good visibility…may not always be possible

Causes of Range Uncertainty

Ionospheric effects 3 meterAtmospheric effects 0.5 meterSatellite/system errors 2 metersReceiver errors 0.5 meterMultipath depends

Total Range Error 6 metersTOTAL Positional Error 10 meters

According to the theory of relativity, due to their constant movement and height relative to the Earth-centered inertial reference frame, the clocks on the satellites are affected by their speed (special relativity) as well as their gravitational potential (general relativity). For the GPS satellites, general relativity predicts that the atomic clocks at GPS orbital altitudes will tick more rapidly, by about 45.9 microseconds (μs) per day, because they are in a weaker gravitational field than atomic clocks on Earth's surface. Special relativity predicts that atomic clocks moving at GPS orbital speeds will tick more slowly than stationary ground clocks by about 7.2 μs per day. When combined, the discrepancy is about 38 microseconds per day; a difference of 4.465 parts in 1010.[43]. To account for this, the frequency standard onboard each satellite is given a rate offset prior to launch, making it run slightly slower than the desired frequency on Earth; specifically, at 10.22999999543 MHz instead of 10.23 MHz.[44] Since the atomic clocks on board the GPS satellites are precisely tuned, it makes the system a practical engineering application of the scientific theory of relativity in a real-world environment.

Relativity is important in GPS

http://en.wikipedia.org/wiki/GPS

Non-Differential GPS(Autonomous or Stand-alone)

X23

y23

z23

x19

y19

z19

x14

y14

z14

x21

y21

z21

d21

d14d19d23

Measured: x y z

Differential GPS

X23

y23

z23

x19

y19

z19

x14

y14

z14

x21

y21

z21

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

Real-Time Differential GPS

X23

y23

z23

x19

y19

z19

x14

y14

z14

x21

y21

z21

Measured: x y z

Corrections appliedduring the survey

True: x y zMeasured: x y z

______________Delta: x y z

Delta: x y z_________

True: x y z

Selective Availability

It is possible to correct for Selective Availability (as well as other inherent signal errors).

However, SA has not been employed for many years. If it was, there would be media attention since it would affect car GPS systems and many others.

This process is called Differential Correction Here’s how it works…

Differential Correction There are already established base stations

established around the U.S. Surveyors have determined the precise location

of these base stations already. Each base station has a GPS receiver, which

collects incoming (scrambled) signals. The true (surveyed) location is then compared to

the GPS coordinates. The correction values are then sent to other

GPS receivers in the field.

Differential Correction

Exact known coordinates differ significantly from GPS coordinates at this location = exact amount of error!

GPS receiver in the fieldcollecting points, routes, etc.

Differential Correction Signal

Base station w/ GPS receiver at known location:

WAAS

• The Wide Area Augmentation System (WAAS) is a differential GPS system that is being constructed to support GPS accuracy in aircraft.

• WAAS also provides additional accuracy “on the ground”

• The GPS receivers that we are using are WAAS compatible

WAAS

Note: Not all GPS receivers are WAAS compatible. The GARMIN GPSMAP76Cx is WAAS compatible

WAAS Satellites

Historically, some areas have had trouble acquiring the WAAS satellites because only two.

A new WAAS satellite will be launched in the Fall 2006 (October…)

Better coverage for Mid-Atlantic and higher accuracy levels

Other Tricks of the Trade:Averaging

Averaging: A GPS receiver can collect points continuously for 15-30 seconds. The receiver can then average all these locations together

This only works when you are standing still!!

GPS Collected Points

GPS Averaged Position

“True” location

Orange County Real-Time Network

RTK Web Service for Orange County’s Geomatics/Land Information Division of the County's Public Facilities and Resource Department (PFRD).

Wireless radio telemetry for the 1 Hz real time data stream from 12 SCIGN/CORS sites.

Capture data on server. QC data and transfer via TCP/IP to CSRC/SOPAC in real-time (1 sec latency).

Testing Leica’s CRNet and Trimble’s VRS software.Y. Bock, CORS Users Forum, April 19, 2002

GPS Antennas (for precise positioning)

• Rings are called choke-rings (used to suppress multi-path)

Nearly all antennas are patch antennas (conducting patch mounted in insulating ceramic).

Portable GPS Receivers ($100 - $1,000)

GPS:

Source:http://www.trimble.com/geoexplorer3.html

Users with a device that records data transmitted by each satellite and processes this data to obtain three dimensional coordinates

Satellite Status

Shown:

Sky position of GPS satellite

Signal Strength of each satellite

Battery Life

Hiking and Driving with a GPS

Heading - direction of travel, Bearing - direction to a waypoint

Using a compass, compass rose on GPS ( motion is required for accurate heading indication

Navigation towards trail heads and trail crossings Horizontal accuracy - 100 ft or less. GPS is not a substitute for having accurate maps,

compass and the ten essentials on every trip. Common sense is always useful. Know the Map Projection and Earth Shape Model or

Datum being used by your GPS device

Map Projections

A map projection is used to portray all or part of the Earth on a flat surface.

Every flat map misrepresents the surface of the Earth in some way. No map truly representing the surface of the entire Earth.

However, a map or parts of a map can show one or more—but never all—of the following: True directions. True distances. True areas. True shapes.

What are the coordinates displayed on a GPS unit?

e.g. The earth's surface is complex and curved - how to make a flat map?

MAP PROJECTIONS

Definition: A systematic rendering of points from the earth to points on a flat sheet (Think of it as passing rays of light from some point through the globe and onto the map surface)

Check : http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html

Two Common Projection Types

1)Universal Transverse Mercator (also termed UTM)

2) Lambert Conformal Conic(also termed State Plane System)

TangentL ine

Remember that any map or parts of a map can show one or more—but never all—of the following: True directions. True distances. True areas. True shapes.

Gerardus Mercator (1512-1594). Frontispiece to Mercator's Atlas sive Cosmographicae, 1585-1595. Courtesy of the Library of Congress, Rare Book Division,

Map ProjectionsA map projection is used to portray all or part of the round Earth on a flat surface. This cannot be done without some distortion.Every projection has its own set of advantages and disadvantages. There is no "best" projection. The mapmaker must select the one best suited to the needs, reducing distortion of the most important features.Mapmakers and mathematicians have devised almost limitless ways to project the image of the globe onto paper. Scientists at the U. S. Geological Survey have designed projections for their specific needs—such as the Space Oblique Mercator, which allows mapping from satellites with little or no distortion.These slides gives the key properties, characteristics, and preferred uses of several historically important projections and of those frequently used by mapmakers today.

Which ones best suit your needs?

Every flat map misrepresents the surface of the Earth in some way. No map can rival a globe in truly representing the surface of the entire Earth. However, a map or parts of a map can show one or more—but never all—of the following: True directions. True distances. True areas. True shapes.For example, the basic Mercator projection is unique; it yields the only map on which a straight line drawn anywhere within its bounds shows a particular type of direction, but distances and areas are grossly distorted near the map's polar regions.On an equidistant map, distances are true only along particular lines such as those radiating from a single point selected as the center of the projection. Shapes are more or less distorted on every equal-area map. Sizes of areas are distorted on conformal maps even though shapes of small areas are shown correctly. The degree and kinds of distortion vary with the projection used in making a map of a particular area. Some projections are suited for mapping large areas that are mainly north-south in extent, others for large areas that are mainly east-west in extent, and still others for large areas that are oblique to the Equator.The scale of a map on any projection is always important and often crucial to the map's usefulness for a given purpose. For example, the almost grotesque distortion that is obvious at high latitudes on a small-scale Mercator map of the world disappears almost completely on a properly oriented large-scale Transverse Mercator map of a small area in the same high latitudes. A large-scale (1:24,000) 7.5-minute USGS Topographic Map based on the Transverse Mercator projection is nearly correct in every respect. A basic knowledge of the properties of commonly used projections helps in selecting a map that comes closest to fulfilling a specific need.

The Globe

Directions—TrueDistances—TrueShapes—TrueAreas—TrueGreat circles—The shortest distance between any two points on the surface of the Earth can be found quickly and easily along a great circle.Disadvantages:Even the largest globe has a very small scale and shows relatively little detail. Costly to reproduce and update. Difficult to carry around. Bulky to store. On the globe:Parallels are parallel and spaced equally on meridians. Meridians and other arcs of great circles are straight lines (if looked at perpendicularly to the Earth's surface). Meridians converge toward the poles and diverge toward the Equator.Meridians are equally spaced on the parallels, but their distances apart decreases from the Equator to the poles. At the Equator, meridians are spaced the same as parllels. Meridians at 60° are half as far apart as parallels. Parallels and meridians cross at right angles. The area of the surface bounded by any two parallels and any two meridians (a given distance apart) is the same anywhere between the same two parallels.The scale factor at each point is the same in any direction.

Mercator

Used for navigation or maps of equatorial regions. Any straight line on the map is a rhumb line (line of constant direction). Directions along a rhumb line are true between any two points on map, but a rhumb line is usually not the shortest distance between points. (Sometimes used with Gnomonic map on which any straight line is on a great circle and shows shortest path between two points).Distances are true only along Equator, but are reasonably correct within 15° of Equator; special scales can be used to measure distances along other parallels. Two particular parallels can be made correct in scale instead of the Equator.Areas and shapes of large areas are distorted. Distortion increases away from Equator and is extreme in polar regions. Map, however, is conformal in that angles and shapes within any small area (such as that shown by USGS topographic map) is essentially true.The map is not perspective, equal area, or equidistant.Equator and other parallels are straight lines (spacing increases toward poles) and meet meridians (equally spaced straight lines) at right angles. Poles are not shown.Presented by Mercator in 1569.Cylindrical— Mathematically projected on a cylinder tangent to the Equator. (Cylinder may also be secant.)

Transverse Mercator

Used by USGS for many quadrangle maps at scales from 1:24,000 to 1:250,000; such maps can be joined at their edges only if they are in the same zone with one central meridian. Also used for mapping large areas that are mainly north-south in extent.Distances are true only along the central meridian selected by the mapmaker or else along two lines parallel to it, but all distances, directions, shapes, and areas are reasonably accurate within 15° of the central meridian. Distortion of distances, directions, and size of areas increases rapidly outside the 15° band. Because the map is conformal, however, shapes and angles within any small area (such as that shown by a USGS topographic map) are essentially true.Graticule spacing increases away from central meridian. Equator is straight. Other parallels are complex curves concave toward nearest pole.Central meridian and each meridian 90° from it are straight. Other meridians are complex curves concave toward central meridian.Presented by Lambert in 1772.Cylindrical—Mathematically projected on cylinder tangent to a meridian. (Cylinder may also be secant.)

Note: UTM refers to a specific group of Transverse Mercator Map projections. UTM by itself is not a map projection.

Universal Transverse Mercator

Universal Transverse Mercator

UTM north to south subzones

Universal Transverse Mercator

Universal Transverse Mercator

Pennsylvania

Lambert Conformal Conic

Used by USGS for many 7.5- and 15-minute topographic maps and for the State Base Map series. Also used to show a country or region that is mainly east-west in extent.One of the most widely used map projections in the United States today. Looks like the Albers Equal Area Conic, but graticule spacings differ.Retains conformality. Distances true only along standard parallels; reasonably accurate elsewhere in limited regions. Directions reasonably accurate. Distortion of shapes and areas minimal at, but increases away from standard parallels. Shapes on large-scale maps of small areas essentially true.Map is conformal but not perspective, equal area, or equidistant.For USGS Base Map series for the 48 conterminous States, standard parallels are 33°N and 45°N (maximum scale error for map of 48 States is 2 ½%). For USGS Topographic Map series (7.5- and 15-minute), standard parallels vary. For aeronautical charts of Alaska, they are 55°N and 65°N; for the National Atlas of Canada, they are 49°N and 77°N.Presented by Lambert in 1772.Conic—Mathematically projected on a cone conceptually secant at two standard parallels.

Note: State Plane Coodinate System refers to a specific group of Lambert Conformal Conic Map projections. State Plane System by itself is not a map projection.

State Plane Coordinate System

State Plane Coordinate System

Pennsylvania

USGS topographic maps have different map projection specific coordinates to compare with your GPS location:

Post-seismic

EstimatesAs more earthquakes are seen with GPS, deformations after earthquakes are clearer

Here we show log dependence to the behavior.

WIDC (74 km from

epicenter)

Coseismic offset

removed

N 51.5±0.8 mmE 15.7±0.6 mmU 4.3±1.8 mm

Log amplitude

N 4.5 ± 0.3 mmE 0.7 ± 0.2 mmU 3.3 ± 0.7 mm

Deformation in the Los Angeles

BasinMeasurements of this type tell us how rapidly strain is accumulating

Strain will be released in earthquakes (often large).

Note 10 mm/yr scale

GPS Measured propagating

seismic waves

Data from 2002 Denali earthquake

Deformation in California

The position time series on the left shows the north position component of the SCIGN site at Pinemeadows (ROCH) changing by almost 200 mm over a 10-year interval. Each point represents a 24-hour solution of GPS data sampled at a 30 s sampling rate. The filtered time series (minus regional common-mode signature) is modeled by three linear trends discontinuous at Landers and Hector Mine earthquakes, three coseismic offsets (Joshua Tree, Landers, Hector Mine earthquakes), two postseismic decays (Landers and Hector Mine), an annual term, and one equipment-change offset. The weighted rms is only 1.2 mm.

Tectonic Motion in Southern California

Southern California is the location of the plate boundary between the North America and Pacific plates. The map shows the motion of the SCIGN sites with respect to the North America, including a total motion of about 45 mm/yr across a region about 200 km wide with numerous geologic faults. Determining the architecture of faulting and distribution of strain is critical for earthquake studies.

Subsidence in California

#

NEW ORLEANS

GeysersUplift

Sacramento

Santa Clara

Caldera ValleyUplift

Los Banos-Kettleman City

Tulare-Wasco

Arvin-Maricopa

Lancaster

Long Beach

San Jacinto

ImperialValley

Cascades

California is also “blessed” with large areas of vertical motion due to fluid extraction (water, oil), and volcanic deformation.

Y. Bock, CORS Users Forum, April 19, 2002

California also relies on other technologies to monitor crustal motion, but these also depend in some way on CORS. In this example, large areas in the Los Angeles and Orange Counties becomes inflated in April which is consistent with water table measurements and the end of the rainy season. The spatial pattern of the amplitude of the annual signal (solid yellow contours in mm) derived from SCIGN sites is consistent with the shape of the interferometric SAR fringes (black/white image). Each fringe represents about 28 mm of motion in the line of sight to the satellite.Reference: Watson et al., Journal of Geophysical Research, in press, 2002.

Vertical motion in Southern California

CONCLUSIONS

GPS is probably the most successful dual-use (civilian and military) system developed by the United States

GPS allows accurate navigation and location.

Maps, compass and the ten essentials should be included with every GPS unit when hiking.

DATUMS

Kindly made availble for student use and prepared entirely by

John Hamilton, CEO Terrasurv Inc.

COORDINATE

One of an ordered set of N numbers which designates the location of a point in a space of N dimensions

In surveying and mapping, 1≤N≤3A coordinate is AN ESTIMATE OF THE

POSITION of a pointAs more data is collected, the position is

refined, coordinate changes

DATUM

“Any quantity or set of such quantities that may serve as a reference or basis for calculation of other quantities”

Geodetic Datum-”A set of constants specifying the coordinate system used for geodetic control, i.e., for calculating coordinates of points on the Earth”

ACRONYMS US

Defining a Datum

5 parameter-horizontal location (2), azimuth, and size of ellipsoid (2)Used for older datums before geocentric

datums were possible8 parameter-spatial location (3), spatial

orientation (3), and size of ellipsoid (2)Used for modern datums

Other possibilities

Early Horizontal Datums

New England Datum – based on astronomic position of PRINCIPIO in Maryland (1879)

Position transferred to MEADES RANCH (Kansas), later renamed US Standard Datum in 1901 and North American Datum (NAD) in 1913

Horizontal Control-1900

Horizontal Control-1927

NAD 1927

NAD 1927 – readjustment of all data accumulated up to that time

Used MEADES RANCH in Kansas as origin (astronomic position)

Non-geocentricBest fit to CONUS

Horizontal Control-1985

NAD 1983 (1986)

NAD 1983 1986readjustment by NGS of all NSRS data geocentric, GRS 1980 ellipsoid, same

parameters as WGS 1984 (very slight difference)

contained small (up to 1 m) distortionsfixed to the North American continent

HARN

NAD 1983 199Xbased on High Accuracy Reference Network

(HARN) surveysdifferent states have different year suffixes,

but basically the sameimprovement on NAD 1983 1986, with space

based technologiesNot a different datum than NAD 1983 1986,

but a different realization

NEW ADJUSTMENT

NAD 1983 (NSRS)February 2007 completionGPS observations onlyHold CORS fixed

Accurate to a couple of cmChanges in existing coordinates up to 10 cm,

usually less than 5 cmSame parameters as NAD 1983, more

accurate realization

ITRF XX

International Terrestrial Reference Frame, where XX is the epoch of the system, for example ITRF 96

most accurate system in useworldwide, not fixed to any continental

plateNAD 1983 coordinates have velocity

component in ITRF

ITRF

Slightly different ellipsoid, basically same as GRS 1980

Updated every few years, latest is ITRF 2000, ITRF 2004 is due out soon

Plate Tectonics are accounted forNo single fixed pointAll points have velocities

WGS 1984

Created by Defense Department (third in a series, replaced WGS 1972)

Intended to be the same as NAD 1983, used same ellipsoid

DIFFERENT REALIZATION“realized” by coordinates of GPS tracking

stationsNOT ACCESSIBLE to public users

WGS 1984

Periodically “redefined”Made to coincide with ITRF at a certain epochLatest is WGS 9184 (G1150)=ITRF 2000

2001.0Broadcast by GPS satellites in the

ephemerisWill change again due to plate tectonics

North American Datum of 1983 (NAD 83)

* Legal reference system in the United States

* National Geodetic Survey is responsible agency in U.S.

* First realized in 1986, revised for HARN,revised again for CORS

* Originally, NAD 83 was mostly a horizontal reference system

* Evolving to a 3-dimensional reference system, thanks to GPS

North American Datum of 1983 (NAD 83) (continued)

* Origin is located about 2 meters from Earth’s center

* Orientation of axes differs from current international standard

* Scale has been changed to agree with current international standard

* Discrepancies exist between HARN and CORS positional coordinates

World Geodetic System of 1984 (WGS 84)

* GPS broadcast orbits give satellite positions in WGS 84

* Department of Defense is responsible agency

* System originally agreed with NAD 83

* Revised to agree with International Terrestrial Reference Frame (ITRF)

* Supports stand-alone positioning

* Does not support high-precision differential positioning

SHANNON

SHANNON

NAD 1983 (1992) 40º21´33.39838" N/80º01´25.03102" W

NAD 1983 (1995) 40º21´33.39907" N/80º01´25.03264" W

NAD 1983 (1986) 40º21´33.40178" N/80º01´25.03959" W

NAD 1927 40º21´33.15538" N/80º01´25.85590" W

NAD 40º21´33.53" N/80º01´26.95" W

Inverses from HARN position

NAD 1983 19950.044 m (0.14 ft) 299º

NAD 1983 19860.228 m (0.75 ft) 297º

NAD 192720.86 m (68.44 ft) 249º

NAD45.46 m (149.15 ft) 275º

NAD 83, NAD 27, NAD

Vertical Datums

NGVD 1929 (previously called Mean Sea Level)

Fixed to the tide level at 29 stations across the US and Canada

Distortions present for various reasonsUsed in US from 1930’s until 1990Still used in many areas for legacy

reasons

Vertical Datums

NAVD 1988 Legislated in the Federal Register, Feds often try

to force states to use it More accurate, more consistent Difference in western PA between NGVD 1929

and NAVD 1988 is about ½ foot. Can convert using VERTCON or CORPSCON

Approximate, good for mapping, not accurate enough for survey purposes

Coordinate Systems

ECEF - Earth Centered Earth FixedLLH - Latitude, Longitude, HeightGrid - State Plane, UTM, localHeight Systems

GeoidEllipsoid

ECEF

three dimensional cartesian system

origin at center of mass

used by GPS system convert to/from LLH cartesian geometry independent of

ellipsoid

LLH

Latitude, Longitude, (Ellipsoidal) Height

convert to/from ECEF convert to/from grid

coordinates complicated formulas

for direct/inverse computations

depends on ellipsoid

Grid Coordinates

two dimensional - Y and X or N and Erelated to LLH, can convert back and fortheasy computationsmost systems distort distances vary in extentplane, Transverse Mercator, LambertUTM, State Plane, Local

State Plane

developed by the US Coast & Geodetic Survey (now NGS) to enable use of geodetic control by local surveyors

mathematically rigorousLambert or Transverse Mercator

Projectionsmaximum 100 ppm distance distortion transform to/from LLH

UTM

Universal Transverse Mercatordeveloped by US militaryworldwide, broken into sixty 6° zonesmaximum distance distortion 400 ppmMGRS - Military Grid Reference System transform to/from LLHeasy to program into GPS receiverUS National Grid – 1 meter resolution

Local Grid Systems

usually tangent system (plane) if origin is known, can transform to/from

LLHsimplified computationsvery common, but not recommended

City of Pittsburgh Origin

Geoid

level surface of the gravity field which best fits mean sea level

not a smooth mathematical surfaceaffected by gravity anomalies, such as

mountains reference surface for orthometric heights

Ellipsoid

mathematical surface which closely approximates the physical shape of the earth

generated by rotating an ellipsoid about its semiminor axis

defined by two axes, or by one axis and the flattening

geocentric or non-geocentric (“local”)

Relation between Ellipsoid and Geoid

N is the separation varies from point to point interpolated using geoid model

GEOID96 (North America), other regional models

OSU91 and other worldwide

Ellipsoid & Geoid

Geoid 2003

Fin

I hoped you enjoyed this overview of GPS, map projections and earth shape models.

GPS gear and maps should not be a replacement for common sense and careful navigation in remote regions.

Remember to always have available the 10 essentials when in remote regions regardless of your navigation system.

The 10 Essentials Map and compass (and know how to use them) Water (including filter or purification tablets) Emergency food First aid kit (including personal medication) Flashlight and/or headlamp (including spare bulb and batteries) Necessary clothing

rain/wind protection extra shoe laces

Pocket knife or multi-purpose tool Pencil and paper Large plastic trash bag (33-gallon) or emergency “space” blanket (to

serve as emergency rain protection, emergency shelter) Signaling device (whistle)

These should always be carried when hiking in remote regions.

Time dilation of muon lifetimeB. Rossi and D.B. Hall (1941); D.H. Frisch and J.H. Smith (1963)

Muons observed in 1 h at top of Mt. Washington (elev. 1910 m) and at sea level.Number observed at elev. 1910 m is 568. Number observed at sea level is 412.

Exponential law of decay with mean proper lifetime = 2.2 s

Muons selected with velocity 0.9952 c

Time of flight in laboratory frame = 6.4 s

Time of flight in muon rest frame = 0.63 s

Around the world atomic clock experiment(J.C. Hafele and R.E. Keating (1971)

Around the world atomic clock experiment(Flying clock – Reference clock)

predicted effect direction

East West

Gravitational potential (redshift) + 144 ns + 179 ns

Velocity (time dilation) 51 ns 47 ns

Sagnac effect 133 ns + 143 ns

Total 40 23 ns + 275 21 ns

Measured 59 10 ns + 273 7 ns

Gravitational redshift of an atomic clockC.O. Alley, et al. (1975)

Gravitational redshift 52.8 nsTime dilation 5.7 ns

Net effect 47.1 ns

TWTT Flight TestsTests conducted by Timing Solutions Corp., Zeta Associates, and AFRL

Flight clock data collected on a C-135E aircraft to demonstrate TWTT in background of an active communications channel

6 flights in November 2002 from WPAFB

Ku Band Satellite Terminal

Transceiver ModemMeas

ChassisFlight Clock

Flight Hardware

IF

IF

GPS Rx/INS

Transceiver

Ku Band GT

(2.4m)

Modem

Meas

Chassis

GroundClock

1 PPS 5 MHz

IFIF

Ground Hardware

Ku Band GT

(24 inch)

Transceiver ModemMeas

ChassisFlight Clock

Flight Hardware

IF

IF

GPS Rx/INS

Transceiver ModemMeas

ChassisFlight Clock

Flight Hardware

IF

IF

GPS Rx/INS

Transceiver

Ku Band GT

(2.4m)

Modem

Meas

Chassis

GroundClock

1 PPS 5 MHz

IFIF

Ground Hardware

Ku Band GT

(24 inch)

L-Band Antenna

General Relativity Test

This slide combines images found at: http://www.leapsecond.com

World’s Most Accurate Wristwatch

This slide combines images found at: http://www.leapsecond.com

Pack too light—throw in an Atomic Clock

This slide combines images found at: http://www.leapsecond.com