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• Position is usually given as geographic

coordinates, Latitude/Longitude

• Datums

–WGS84

– Many others usually available

• Projections

– UTM

– State Plane

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Latitude and Longitude

Defining a Location

units of measurement are Degrees

equator

Prime

Meridian

Degree is divided into 60 Minutes, Minute is divided into 60 Seconds

Authalic Sphere

•Cartographer realised that earth is not a

perfect Sphere and hence they visualised it

as a perfect sphere with Surface area same

as that of the real earth

•This authalic Sphere has a radius of 6371

km and hence circumference of 40,030.2

km.

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Earth As an Ellipsoid

•Newton (1670) proposed that the earth would be flattened

because of rotation. The polar flattening would be1/300 th of

the equatorial radius.

• Actual flattening is about 21.5km.

•The amount of the polar flattening as per (WGS [world geodetic

system] 84) is 1/ 298.257.

WGS 84 ellipsoida = 6,378,137m

b = 6,356,752.3m

equatorial diameter = 12,756.3km

polar diameter = 12,713.5km

equatorial circumference =

40,075.1km

surface area = 510,064,500km2

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a

b

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Graticule

•The imaginary network of parallels and meridians on the earth

and their projection onto a flat map is called graticule.

•The properties of the graticule are used to compute distance,

direction and area.

•Assume the earth to be spherical.

Definition of Ellipse

Area of an Ellipse

πab

a < b

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Eccentricity of an Ellipse is a measure of how close it is to Circular Shape

? Eccentricity of a Circle 0

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Geoidal Earth

•Geoid (“earth like”): Sea level equi-potential surface.

•Gravity is everywhere equal to its strength at mean

sea level.

•The surface is irregular, with difference of -104m at

the southern tip of India to a Maximum of 75 m near

Guinea.

• The direction of gravity everywhere is not directed

towards the centre of the earth.

Geoid surface computed from the GEM-T3 gravity model by

the NASA/Goddard Space Flight Centre. (Cited in Robinson, et al., 2002)

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GEOID Representation

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In the fields of chronology an epoch

means an instant in time chosen as the origin

of a particular era. The "epoch" then serves as

a reference point from which time is measured.

Time measurement units are counted from the

epoch so that the date and time of events can

be specified unambiguously.

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epoch date uses rationale for selectionJanuary 1, 0 MATLAB, Turbo DB and tdbengine

January 1, 1 Symbian, Microsoft .NET, REXX This epoch date is known as Rata Die

January 1, 1601 NTFS, COBOL, Win32/Win64

1601 was the first year of the 400-year

Gregorian calendar cycle at the time

Windows NT was made. [7]

December 31, 1840 MUMPS programming language

1841 was roughly the birthyear of the world's

oldest living person when the language was

designed.[8]

November 17, 1858VMS, United States Naval Observatory, other astronomy-

related computations

November 17, 1858 equals the Julian Day

2,400,000.[9]

December 30, 1899 Microsoft COM DATE

Technical internal value used by Microsoft

Excel; to simplify calculations by falsely

assuming 1900 to be a leap year.[10]

January 0, 1900 Microsoft Excel[10], Lotus 1-2-3

While logically January 0, 1900 is equivalent

to December 31, 1899, these systems do not

allow users to specify the latter date.

January 1, 1900 Network Time Protocol, IBM CICS, Mathematica, RISC OS

January 1, 1904Apple Inc.'s Mac OS through version 9, Palm OS, MP4,

Microsoft Excel (optionally)[10]

1904 is the first leap year of the twentieth

century.[11]

January 1, 1960 S-Plus, SAS

December 31, 1967 Pick OS

January 1, 1970

Unix time, used by UNIX, Linux, other UNIX-like systems, Mac

OS X, as well as Java, JavaScript, C and PHP Programming

languages

January 1, 1978 AmigaOS

January 1, 1980 MS DOS, OS/2, FAT16 and FAT32 filesystem

January 6, 1980 Qualcomm BREW, GPS

January 1, 1981 Acorn NetFS

January 1, 2001 Apple's Cocoa framework2001 is the year of the release of Mac OS X

10.0.

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? Time

• Time has been defined as the continuum in which events occur in

succession from the past to the present and on to the future.

•Time has been a major subject of religion, philosophy, and science, but

defining it in a non-controversial manner applicable to all fields of study has

consistently eluded the greatest scholars.

•Time is one of the seven fundamental physical quantities in the

International System of Units

Temporal measurement has occupied scientists and technologists, and

was a prime motivation in navigation and astronomy. Periodic events

and periodic motion have long served as standards for units of time.

Examples include the apparent motion of the sun across the sky, the

phases of the moon, the swing of a pendulum, and the beat of a heart.

Currently, the international unit of time, the second, is defined in terms of

radiation emitted by caesium atoms . Time is also of significant social

importance, having economic value ("time is money") as well as

personal value, due to an awareness of the limited time in each day and

in human life spans.

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The second is the duration of 9,192,631,770 periods of the radiation

corresponding to the transition between the two hyperfine levels of the ground

state of the caesium 133 atom.

At its 1997 meeting, the CIPM affirmed that this definition refers to a caesium

atom in its ground state at a temperature of 0 K.

Prior to 1967, the second was defined as:

the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12

hours ephemeris time.

The current definition of the second, coupled with the current definition of the

metre, is based on the special theory of relativity, which affirms our space-

time to be a Minkowski space.

International Atomic Time (TAI) is a statistical atomic time scale based on a

large number of clocks operating at standards laboratories around the world

that is maintained by the Bureau International des Poids et Mesures; its

unit interval is exactly one SI second at sea level. The origin of TAI is such that

UT1-TAI is approximately 0 (zero) on January 1, 1958. TAI is not adjusted for

leap seconds. It is recommended by the BIPM that systems which cannot

handle leapseconds use TAI instead.

Coordinated Universal Time (UTC) is defined by the CCIR (Consultative

Committee on International Committee) Recommendation 460-4 (1986). It

differs from TAI by the total number of leap seconds, so that UT1-UTC stays

smaller than 0.9s in absolute value. The decision to introduce a leap

second in UTC is the responsibility of the International Earth Rotation

Service (IERS). According to the CCIR Recommendation, first preference

is given to the opportunities at the end of December and June, and second

preference to those at the end of March and September. Since the system

was introduced in 1972, only dates in June and December have been

used. TAI is expressed in terms of UTC by the relation TAI = UTC + dAT,

where dAT is the total algebraic sum of leap seconds.

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The Global Positioning System (GPS) epoch is January 6, 1980 and is

synchronized to UTC. GPS Time is NOT adjusted for leap seconds.

BEFORE THE 2012 LEAP SECOND: GPS-UTC IS 15 (GPS IS AHEAD OF

UTC BY 15 SECONDS) AFTER THE 2012 LEAP SECOND: GPS-UTC WILL

BE 16 (GPS WILL BE AHEAD OF UTC BY 16 SECONDS)

As of 1 January 2008, and until the leap second of June 30 2012

TAI is ahead of UTC by 34 seconds.

TAI is ahead of GPS by 19 seconds.

GPS is ahead of UTC by 15 seconds.

After 30, June 2012,

TAI is ahead of UTC by 35 seconds.

TAI is ahead of GPS by 19 seconds.

GPS is ahead of UTC by 16 seconds.

•Definition:

• GPS time is synchronized with UTC (within ~1 microsecond), but does

not contain leap-seconds. GPS Time is currently ahead of UTC by ‘N’

seconds due to the leap-seconds that have been inserted into UTC. The

GPS epoch is identified as the number of seconds that have elapse since

the previous Saturday/Sunday midnight. GPS weeks start with week 0

on January 6, 1980.

• GPS satellites are equipped with atomic clocks and contribute to the

TAI* average. Parameters are uploaded to each GPS satellite to allow

the satellite to convert the reading of its atomic clock to GPS Time.

GPS Time

•TAI: International Atomic Time

( French Origin: Temps Atomique International )

UTC: Coordinated Universal Time ( CUT)

Temps Universel Coordonne ( TUC) French

Compromised as : UTC

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UT1: Time given by rotation of Earth. Noon is “mean” sun crossing meridian at Greenwich

UTC: UT Coordinated. Atomic time but with leap seconds to keep aligned with UT1

UT1-UTC must be measured

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� Definition:

� Terrestrial Time (TT) is a dynamic time scale based upon

the orbital motions of the Earth, Moon, and planets. It is

defined by clocks using SI seconds on the surface of the

Earth.

� Epoch is 00:00:00 January 1, 1977

� TT = TAI + 32.18 sec

(Note seconds in SI units is defined as the duration of 9,192,631,770 cycles of radiation of cesium 133)

Terrestrial Time (TT)

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-4

-2

0

2

4

6

8

1980 1985 1990 1995 2000 2005

Length-of-day (ms)

Year

Measured

Atmospheric Angular Momentum (converted to LOD)

-4

-2

0

2

4

6

8

1980 1985 1990 1995 2000 2005

Length-of-day (ms)

Year

Measured

Atmospheric Angular Momentum (converted to LOD)

LOD compared to Atmospheric Angular Momentum

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Integral of LOD is UT1 (or visa-versa)

If average LOD is 2 ms, then 1 second difference between UT1 and atomic time develops in 500 days

Leap second added to UTC at those times.

Jumps are leap seconds, last one before 2006 was 1999.

Historically had occurred at 12-18 month intervals

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1992.00 1994.00 1996.00 1998.00 2000.00 2002.00 2004.00 2006.00

UT1-UTC (s)

UT1-UTC (s)

Year

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1992.00 1994.00 1996.00 1998.00 2000.00 2002.00 2004.00 2006.00

UT1-UTC (s)

UT1-UTC (s)

Year

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Year Jun 30 Dec31

1972 +1 +1

1973 0 +1

1974 0 +1

1975 0 +1

1976 0 +1

1977 0 +1

1978 0 +1

1979 0 +1

1980 0 0

1981 +1 0

1982 +1 0

1983 +1 0

1984 0 0

1985 +1 0

1986 0 0

1987 0 +1

1988 0 0

1989 0 +1

1990 0 +1

1991 0 0

1992 +1 0

1993 +1 0

1994 +1 0

1995 0 +1

1996 0 0

1997 +1 0

1998 0 +1

1999 0 0

2000 0 0

2001 0 0

2002 0 0

2003 0 0

2004 0 0

2005 0 +1

2006 0 0

2007 0 0

2008 0 +1

2009 0 0

2010 0 0

2012 0 +1

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MODIFIED JULIAN DATE

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Overview of Satellite Transmissions

• All transmissions derive from a fundamental frequency of 10.23 Mhz

– L1 = 154 x 10.23 = 1575.42 Mhz

– L2 = 120 x 10.23 = 1227.60 Mhz

– L5 = 115 x 10.23 = 1176.45 MHz

• All codes initialized once per GPS week at midnight from Saturday to Sunday

– Chipping rate for C/A is 1.023 Mhz

– Chipping rate for P(Y) is 10.23 Mhz

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• L5 carrier (1176.45 MHz) =115x10.23(Safety Of Life Applications)

CARRIER WAVES

And C/A code

Schematic of GPS codes and carrier phase

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GPS Signal Characteristics

, L2

M-Code

• Satellites will transmit two distinct signals from two antennas: one for whole

Earth coverage, one in a spot beam.

• Modulation is binary offset carrier

• Occupies 24 MHz of bandwidth

• It uses a new MNAV navigational message, which is packetized instead of

framed, allowing for flexible data payloads

• There are four effective data channels; different data can be sent on each

frequency and on each antenna.

•I t can include FEC and error detection

• The spot beam is ~20 dB more powerful than the whole Earth coverage beam

• M-code signal at Earth's surface: –158 dBW for whole Earth antenna, –138 dBW

for spot beam antennas

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3rd civil signal on L5 (1176.45 MHz) =115x10.23Better accuracy under noisy and multipath conditions

Should improve real-time kinematic (RTK) surveys

Modulations

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Digital Modulation Methods

• Amplitude Modulation (AM) also known as amplitude-shift keying. This method requires changing the amplitude of the carrier phase between 0 and 1 to encode the digital signal.

• Frequency Modulation (FM) also known as frequency-shift keying. Must alter the frequency of the carrier to correspond to 0 or 1.

• Phase Modulation (PM) also known as phase-shift keying. At each phase shift, the bit is flipped from 0 to 1 or vice versa. This is the method used in GPS.

Modulation Schematics

AM

FM

PM

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Amplitude Modulation

Frequency Modulation

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Phase Modulation

VARIOUS CODES USED IN A GPS SIGNAL

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? Code• Stream of binary digits known as bits or chips

– Sometimes called pseudorandom noise (PRN) codes

• C/A code on L1

• P code on L1 and L2

• Phase modulated

• NEW (2008-09)

• C/A code on L2 (L2C)

• M Code ( Military Use )

• L5 (GPS IIF, 27 May 2009 on SVN49)

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)

Future Signal

• C/A code on L2 (L2C)

• 2 additional military codes on L1 and L2

• 3rd 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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Navigation Messages

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GPS Calendar and Almanac Data Utility

http://www.ngs.noaa.gov/CORS/Gpscal.html

http://www.navcen.uscg.gov/GPS/almanacs.htm

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Application and Importance of

L2C

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The L2C Initiative• 1996 – Presidential Decision Directive

– "encourage acceptance and integration of GPS into peaceful civil, commercial and scientific applications worldwide; and to encourage private sector investment in and use of U.S. GPS technologies and services."

– “committed the U.S. to discontinuing the use of SA by 2006 with an annual assessment”

• With S/A off, ionospheric error becomes significant

• 1998 – V.P. Gore announced L2 as 2nd civil signal• 1999 – V.P. Gore “for launch beginning in 2003”• 2001 – L2C was defined & presented to the public

– Two public meetings, ION paper, GPS World article,ICD-GPS-200 update, NAVCEN WEB posting

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user

position,

velocity, and time (PVT)

determination

The accuracy with which a user receiver can determine its position or velocity, or

synchronize to GPS system time, depends on a complicated interaction of various

factors. In general, GPS accuracy performance depends on the quality of the

pseudorange and carrier phase measurements as well as the broadcast navigation

data. In addition, the fidelity of the underlying physical model that relates these

parameters is relevant. For example, the accuracy to which the satellite clock offsets

relative to GPS system time are known to the user, or the accuracy to which satellite-

to-user propagation errors are compensated, are important. Relevant errors are

induced by the control, space, and user segments.

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What is the smallest possible unit of time?

Is time infinitely divisible, or is there a smallest possible unit of time measurement? Is space infinitely divisible, or is there a

smallest possible unit of spatial measurement? The following thought experiment suggests that neither space or time are

infinitely divisible.

Suppose I want to “demonstrate” the “value” of any very large number by counting down one number at a time to zero

and that I want to do this so that the count will not take longer than a typical working day, say 10 hours/600

minutes/36,000 seconds/3.6 x 104 seconds.

Lets start by taking a number that is around 3.6 x 1010. To count down from this number in the time set we need to count

106 numbers each second. This means that each number in the final column of our counting device needs to be displayed

for 10-6 second. During this period light will travel around 300m.

What if our number is a bit larger, say around 3.6 x 1020. To count down from this number in the time set we need to count

1016 numbers each second. This means that each number in the final column of our counting device needs to be displayed

for 10-16 second. During this period light will travel around 300nm. But 300nm is less than half the wavelength of visible

light – humans could never see that the number had changed from looking at the lowest digit.

Theoretically there is no limit to the size of number we could want to count down in our experiment. What if our number is

a bit larger, say around 3.6 x 1030. To count down from this number in the time set we need to count 1016 numbers each

second. This means that each number in the final column of our counting device needs to be displayed for 10-26 second.

During this period light will travel around 300 x 10-10nm. But 300 x 10-10nm is so small that it is probably not detectable by

anything a human could make. Just how small is the smallest measurable distance? Unfortunately when we get down to

the size of things like photons we are into quantum mechanics, with its consequential uncertainty of position and hence

size. The Proton Compton wavelength, however, is 10-6nm, so we are thinking here of something orders of magnitudes

smaller than a proton.

If we consider the Proton Compton wavelength (or any of the other Compton wavelengths, such as those for neutron and

the marginally smaller tau) as the smallest measurable thing there is, and compare this with the speed of light, 3 x 108m/s,

can we come up with a smallest possible measurable unit of time? There would seem to be no more than 3 x1023

measurable units within the space covered by light in a second. Doesn’t this imply that the shortest measurable time is 3 x

10-24s?