 V Madhava Rao, P Kesava Rao, R R Hermon
INTRODUCTION
The Global positioning system(GPS) is a satellite based navigation and surveying
system which determines the precise position and time, through radio signals from
the satellites, in realtime or in post processing mode. GPS has modernized the
diverse disciplines of science and technology together with Geographical Information
System (GIS).
The Navigation Satellite timing and ranging Global positioning system (NAVSTAR GPS)
developed by the U.S. Department of defense (DOD) to replace the TRANSIT Navy navigation
Satellite System (NNSS), is an all weather high accuracy radio navigation and positioning
system. The GPS comprises 27 satellites (out of which 24 satellites are operational)
in near circular orbits at above 20,200 km altitude, currently provides complete
coverage with signals from minimum 4 satellites available to the users at any place
on the Earth. The observer can determine the geometric position (latitude, longitude
and height), coordinates universal Time (UTC) and velocity vectors with higher accuracy,
by receiving those transmitted signals (figure 3.1). The uncertainties in the positions
of GPS satellite and timing signals, imposed due to security reasons by DOD and
other error sources are expected to limit accuracy of determination of absolute
position of observation station in real time mode to few meters with few minutes.
However, various modes of observations and data analysis available are developed.
They would yield accuracies better than few millimeters in relative position for
base lines up to 2000km with few hours of observations, at minimum cost. Highaccuracy,
point positioning has been an attractive research topic in the GPS community for
a number of years as quoted by Tomas Beran et al, (2005). However, use of lowcost
singlefrequency GPS receivers in similar applications is a challenge, reliant on
the mode of handling the ionosphere, multipath and other measurement error sources.
Practical applications of postprocessed, highaccuracy, singlefrequency point
positioning include a myriad of terrestrial and space borne applications, where
the size and cost of the GPS unit becomes an issue. With all the milieu literature
survey, the GPS datum conversion is currently discussed with its basic concepts
in the following sections.
1. OBJECTIVIES OF GPS:
The key performance objectives of the GPS system can be summarized as follows:
 High accuracy, realtime position, velocity, and time for military users on a variety
of platforms, some of which have high dynamics: e.g. high performance aircraft.
 Good accuracy for civil user is considered to be 100m or better in three dimensions.
 Worldwide, all weather operation, 24 hours a day.
 Resistance to intentional (jamming) or unintentional interference for all usersenhanced
resistance to jamming for military users.
 Capability for highly accurate geodetic survey to centimeter levels using radio
frequency carrier measurements and for highaccuracy time transfer to 100ns or better.
 Affordable, reliable user equipmentusers are not required to carry highaccuracy
clocks.
2. GPS SEGMENTS
The GPS basically is comprised of 3 segments. They are space segment, control segment
and user segment.
2.1. Space Segment The Space segment consists of a minimum of 24
operational satellites, as shown in figure 2, to provide optimal global coverage.
The satellites are arranged in six orbital planes, inclined at 55o to the equator.
They orbit at altitudes of about 20,150 kilo meters from earth’s surface and take
about 11 hours 58 minutes to orbit one time. Each satellite carries 4 atomic clocks
for transmitting signals (Pratap Misra et al., 2001).
2.2. Control Segment
It consists of 5 worldwide base  stations to monitor the performance of GPS satellites.
They track the exact position of satellites in space; check the system integrity,
behavior of satellite clocks, study atmospheric data and satellite almanac to ensure
their correct operation. The main base station called Master Control Station (MCS)
operates the system and provides command and control function. The corrected information,
which includes ephemeris constants and clock adjustments, is transmitted to the
satellite through the sband link. The satellites in turn use these updates in the
signal and send to GPS receivers. The Master Control Station is located at Colorado
and five monitor stations (MS) are located at Ascension Island (Atlantic ocean),
Diego Garcia (Indian ocean) and kwajalein Hawaii (both pacific Ocean) and Colorado
Springs (Hofmann et al., 1992).
2.3. User Segment
The user segment includes all the military and civilian users. With GPS receiver,
a user can receive the GPS signals and determine his position anywhere in the world.
All GPS receivers have an almanac programmed into their computer to notify the given
moment of each satellite. The user equipment consists of an antenna, a receiver,
a data processor with software and a control display unit. The GPS receiver measures
the pseudo range, phase and data using navigation signals from minimum 4 satellites
and computes the 3D position, velocity and system time (Figure 1). The position
is in geocentric coordinates in the basic reference coordinates system  World Geodetic
reference system1984 (WGS84), which are converted and displayed as geographic,
UTM, grid or any other type of coordinates. Corrections in delay due to ionospheric
and troposphere refraction clock errors, etc., are also computed and applied by
the user equipment/processing software.
2.4 POSITIONING USING GPS
The key concept of GPS is the measurement of the distance of receiver from a satellite
whose position is recognized. When the distance between satellite and receiver is
established to be 20,000 kilometers, the possible locations that the receiver could
be in the whole universe are narrowed down to the surface of a sphere that is centered
on this satellite and has a radius of 20,000 kilometers. This is shown in the figure
3.
The distance of the receiver from another reference satellite is now measured. Obviously
the receiver is supposed to be on the surface of sphere centered at the second satellite
and has a radius equal to the distance of the receiver from that satellite. The
receiver now is on the circle that is formed by the intersection of the two reference
satellites as shown in the figure 4.
The distance of the receiver is at present measured from a third satellite that
is orbiting in a different plane. If a sphere is constructed with center at this
satellite, having radius equal to this distance, the receiver is on the surface
of this sphere also. This intersects the aboveformed circle at two points. Finally
the position of receiver on earth is reduced to two points as shown in the figure
5.
However, habitually one of the two points is a ridiculous answer (either too far
from Earth or moving at an impossible velocity) and can be rejected without a measurement.
Thus the position of the receiver on earth is determined.
2.4.1 Measuring the Distance from the satellite
The determination of the position of a receiver on earth involves the measurement
of distances of the satellites from the receiver. The distance from the satellite
is measured by calculating the time taken for a signal to reach the receiver placed
on the earth from the satellite. The knowledge of basic kinematics guides us to
the result that the distance between the satellite and the receiver is the product
of the time taken by the signal to reach the receiver and the velocity of signal.
The signal transmitted by the satellite travels with the velocity of light.
2.4.2 Timing considerations
Since the velocity of the signal is very large, an error of even a fraction of a
second, results in an error of about 200 miles in position. Therefore, timing plays
a vital role in the Global Positioning System. Thus, there is a need for a clock
that can measure very minute intervals of time with great precision. Satellites
use atomic clocks that are accurate to nearly a hundredmillionth of a second. It
is not feasible to use clocks with such high precision in receivers. Hence, the
error in the measured distances occurs mainly due to inaccuracy of the clock in
the receiver.
2.4.3 Getting Perfect Timing
The error can be resolved by taking a fourth measurement. The key for eliminating
the error arises from the fact that all the measured times differ from the actual
values by the same factor. Due to the error in the measured distances, the spheres
constructed with the four satellites as the center do not intersect at a single
point. The measured distances are then altered by same amount until they all coincide
at a single point. This point gives the position of the receiver on the earth.
2.4.4 Point Positioning
GPS satellites are configured to provide the user with the capability of determining
his position expressed by latitude, longitude and elevation. The following factors
affect the accuracy of the position determined using a single receiver:
 Accuracy of each satellite’s position.
 Accuracy of pseudo range measurement
 Geometry.
2.5 FEATURES OF GPS SATELLITES
Some of the important features of the GPS satellites are
 Design life 5 years (with expendables stored for 7 years).
 On orbit weight 430kg.
 Endoflife power: 400 W.
 Power source: 5m2 solar arrays tracking the sun and 3 NiCd batteries for eclipse.
 3 axes established, earth pointing satellites.
 Navigation pay load: pseudo Random Noise (PRN) signal assembly, atomic frequency
standard cesium beam atomic clocks accurate to 1014 sec, processor and t band
antenna.
 Codes:
 Precision (p) code: generated at GPS clock frequency of 10.23 MHz (equivalent to
30m in range) interpolated to sub meter level. Repeats itself after 267 days. Resolution:
100 Nano seconds.
 Coarse Acquisition (C/A) code: Code sequence frequency 1.023 MHz (range 300m) interpolated
to few meters. Repeats itself every 1milli second resolution in 1 microsecond.
 PRN navigation signals on 2 frequencies :
 1575.42 MHz  L1 Band  Wavelength 19 cm.
 1227.6 MHz L2 Band wavelength 24 cm.
2.6 PRINCIPLE OF OPERATION
Each GPS satellite carries an atomic clock with stability better than 1 in 1014,
which is used to generate dual frequency PRN spread spectrum L band navigation signals.
These messages, continuously transmitted by satellites on P code and C/A code modulated
on L1 carrier frequency, contains information of satellite ephemarides and satellite
clock error. The Remote Monitor Stations located in U.S.A receive these messages
and transfer to Master Control Station which computes future information to be uploaded
and stored in satellite memory for further broadcast. The purpose of code is to
identify each satellite uniquely, to enable measurement of signal travel time and
to facilitate selective denial of use to unauthorized users. The user equipment
receives navigation messages from at least 4 satellites available above the horizon
at any place at any given time. The Correlation of received code with corresponding
code synthesized by receiver allows ground observer to measure transit time of signal
from satellite to the receiver from which, range to satellite can be computed. Simultaneous
reception of 4 navigation signals from 4 satellites containing information of time
of transmission of code to 10 nano second accuracy and satellite position, on the
basis of broadcast ephemeris enable the observer to form 4 pseudo range (actual
range + offset due to user’s clock bias) equations which can be solved to get the
parameters of the observers position in 3 dimensions, i.e. x, y and z in earth centered
Cartesian coordinates or equivalently other longitude, latitude and height above
ellipsoid and the receiver clock error. The receiver clock bias thus becomes the
fourth unknown to be estimated, in addition to three coordinates of the position
(Hoffmann et. al., 1992). Mathematically, user position is obtained by solving the
navigation equation 1 as
In equation (4.1), R_{k} is the measured satellite range, b is the receiver
clock bias at the instant of measurement and (x, y and z) is the user position on
the earth surface.
2.7 GPS RADIO FREQUENCY SPECTRUM
The choice of GPS frequencies is a tradeoff among ease of bandwidth allocation,
smaller ionospheric delay errors, lesser space loss and availability of bandwidth
for global transmission (Spilker, 1996).
The usage of GPS signals in Lband mete out acceptable received signal power with
reasonable satellite transmit power levels and earth coverage satellite antenna
patterns. And the C band path loss is approximately 10 dB higher, as the path loss
is proportional to f2 for an omni directional receive antenna and fixed transmit
antenna bandwidth and range. Therefore L band was selected and dual frequencies
permit ionospheric group delay measurements (Parkinson, 1996). In effect each GPS
satellite signal consists of three components (1) Carrier, (2) Ranging code and
(3) Navigation data code.
2.7.1 Carrier
The RF sinusoidal signals transmitted at L1 and L2 bands with each GPS satellite
signal contains carrier frequencies 1474.42 MHz and 1227.60 MHz respectively, which
are used by civilians and DOD authorized users respectively. The Satellites transmit
additional RF signals at frequencies referred to as L3 and L4. The L3 is associated
with the nuclear detonation detection system and L4 is reserved for other military
purposes (Pratap Misra, 2001). Subsequently another new civil code wider in bandwidth
than the current C/A code will be added at a new carrier frequency of 1176.45 MHz
at L5 (Mcneff, 2002).
2.7.2 Ranging Code
A unique sequence of 0s and 1’s are assigned to each satellite which allow the receiver
to determine the signal transit time instantaneously is called pseudo random noise
(PRN) sequences. PRN has distinctive properties, which allow all the satellites
to transmit at the same frequency without any mutual interference. The PRN sequence
is further divided into two codes, viz. course and acquisition (C/A) code for civilians
and precision (P) code for military users. Each C/A code is a unique sequence of
1023 bits, called chips, with chip rate of 1.023 MHz. A Pcode is a unique segment
of an extremely long (about 1014 chips) PRN sequence. The chipping rate is 10.23
MHz ten times that for a C/A code (Mcneff, 2002).
2.7.3 Navigation Data
A binary coded message has the data on the satellite health status, ephemeris (satellite
position and velocity), clock bias parameters and an almanac. It is transmitted
at 50 bits per second (bps) with bit duration of 20 milli seconds (Leick, 1990).
The signals L1 and L2 are coherently derived from a 10.23 MHz basic clock and are
given in equations 4.2 and4.3
L_{1}= 154*10.23 MHz = 1575.42 MHz.  equation (2)
L_{2}= 120*10.23 MHz = 1227.60 MHz. equation (3)
The dual carrier strategy serves two purposes:
 Incase L1 is lost or the receiver is being jammed on L1, then L2 serves as a backup.
 L1 and L2 collectively provide dual frequency compensation for signal delay due
to ionospheric refraction.
The power levels of L1 and L2 at the output of satellite transmitters and at the
input of receivers nearer to the earth are given in table  1 (Sharma,2005).
These three components of a signal are derived from standard atomic clock (10.23
MHz) aboard the satellite. The present structure of GPS is shown in figure 6.
2.7.4. Signal at L1
The L1 inphase component is modulated by a P (precise) code and data bits whereas
quadrature phase component is modulated by a C/A (Coarse/Acquisition) code and data
bits. P and C/A codes are +/1 ranging signals having chipping rates of 10.23 MHz
and 1.023MHz respectively, whereas navigation data bits are +/1 and have a frequency
of 50Hz. Therefore L1 satellite signal is expressed as in (Spilker, 1996) equation
4.
Where
I

is the satellite index

A_{p} and A_{c}

are the in phase and quadrature signal amplitudes respectively in (volt, volt),

D

is the navigation data bit.

ω_{1}

is the L1 center frequency (rad/sec) and

γ_{1}

is the small phase noise and oscillation drift component in radians.

2.7.5. Signal at L2
The L2 signal is biphase modulated by either a P or a C/A code as selected by the
ground command same data bits as in L1. Therefore the L2 satellite signal is given
in equation 5.
where
B_{p}

is the signal amplitude of L_{2},

ω_{2}

is the center frequency of L_{2} in (rad/sec) and

γ_{2}

is the phase noise.

The P code is replaced by the Y code when anti spoofing (AS) is activated. The
details of P, Y, C/A code and other signal characteristics are described in ICD
GPS200C (1991) and Spilker (1996). The carrier of GPS signal is modulated by a
PRN sequence spreading the signal within a wide band, suitable for spread spectrum
communication. The Spread spectrum communication allows Code Division Multiple Access
(CDMA), whereby each satellite transmits at the same frequency band and considerably
simplifies the receiver front end design. At the receiver, a replica of the PRN
sequence is generated and correlated with the incoming signals from all the satellites
to isolate and identify each satellite signal separately for generating range and
its measurements.
2.8 SPREAD SPECTRUM TECHNOLOGY
Spread spectrum signals in communications are used for the purpose of combating
the detrimental effects of interference due to jamming, interference arising from
other users of channel and self interference due to multipath propagation. The Spread
spectrum technology allows operating on common frequencies without interference
and also precise time transfer simultaneously. One of the principal reasons for
using spread spectrum is its inherent lack of delectability is greatly reduced to
spread a signal out over a narrow band of frequencies. The Thermal noise of the
system is described by the equation 6.
N=KTB Equation (6)
Where,
K= Boltzmann’s constant
T= Temperature in Kelvin.
B= bandwidth in hertz.
The information bandwidth is 50 Hz. Now Spread factor is defined using the equation
(7). Spreading factor is calculated as 1.023*106/50 that is 20460.
2.9 GPS DATA
GPS data consists of two parts. One is observation data and the other is navigation
data as in figure 7. The observation data is site specific. Mainly it consists of
pseudo range measurements.
2.9.1. Navigation data
The navigation message is superimposed on both the pcode and the C/A code with
a data rate of 50 bits/sec. It contains information on the ephemeredes of the satellites,
GPS time and clock behavior and system messages. The message format is a 1500 bit
frame made up of five subframes, each subframe being 300 bits long. Sub frames
4 and 5 will be sub communicated 25 times each, so that a complete data message
requires the transmission of 25 full frames. Each sub frame consists of 10 words
and each is of 30 bits long. It will therefore take 30 sec to receive one data page
and 12 ½ minutes to receive all 25 data pages. Subframes 1, 2 and 3 have identical
data on all 25 data pages. Telemetry (TLM) word and Hand over Word (HOW) both are
generated by the control segment. The frame will also contain eight data words generated
by the control segment. Each word contains the parity. The satellites calculate
parity for the Telemetry word and Hand over Word and the control segment calculates
the parity for all other words in each frame.
2.9.2. Navigation message content
The navigation message basically contains the following four sets of information.
 Time and satellite clock information.
 Correction data to compensate for signal delay
 Satellite orbit information
 Satellite health status
2.10. ACCURACIES WITH GPS AND COMPARISON WITH OTHER TECHNIQUES
GPS is the first positioning system to offer very high accuracy in the measurement
of base line lengths in relative mode, using the high precision geodetic instrumentation,
with many hours of observations and scientific data processing as
 0.14 mm in local surveys(10m100km base line lengths)
 410 mm in regional surveys( 1001000km base line lengths)
 12 cm in global surveys (100010,000km base line lengths)
The high accuracy standards make GPS suitable for various types of applications
as compared to the limited range of applications of other positioning system like
terrestrial surveying techniques, Inertial Navigation System (INS), Satellite Laser
Ranging (SLR) and Very Long Base Line Interferometry (VLBI).
2.11 COMPUTATION OF COORDINATES
From GPS observations, it is possible to obtain the Cartesian rectangular coordinates:
X Y and Z in an ECEF global reference system  geodetic latitude, longitude and
height or grid coordinates. Hence the transformation of coordinates from the global
system to the local system is essential.
2.12 GEODETIC COORDINATES TO MAP COORDINATES
The height deduced from GPS observations is the ellipsoidal height minus height
of the observation point above the reference ellipsoid. The geodetic height of a
point is the geoidal height minus height above the geoid, commonly termed as Mean
Sea Level (MSL) height. These two are related by the simple equation 8.
MSL Height (h) = Ellipsoidal Height (H)Geoidal Undulation (N).
 Equation (8).
The geoidal undulation (geoidellipsoid separation) is derived from astro geodetic
or gravimetric data, the accuracy of which is limited to few centimeters. World
gravity models are available for computing the value of Geoidal Undulation, N at
the observation station. Thus the Mean Sea Level heights computed from GPS data
will have the error in the value of Geoidal Undulation N, limiting its accuracy.
However, in differential GPS leveling the relative heights can be determined to
a much higher accuracy due to cancellation of a large part of this error. The estimated
precision of determination of heights using GPS is about 1.5 times the precision
of horizontal component.
2.14. APPLICATIONS OF GPS
GPS has the following numerous applications in many fields, ranging from the millimeter
level high precision geodesy to the several meter level navigational positioning
because of high accuracy, versatility, ease, economy of operation, and all weather
operation.
 Establishment of high precision zero order geodetic national survey control network
of GPS stations.
 Strengthening, densification and readjustment of existing primary control networks
using GPS stations.
 Connecting remote islands to mainland geodetic control networks.
 Determination of a precise geoid using GPS data
 Earth rotation and polar motion studies from GPS data.
 Estimating gravity anomalies using GPS.
 Marine geodesy: positioning of oceanic stations and buoys etc.
 Earthquake monitoring
2.15. STANDARD POSITIONING SERVICE (SPS) AND PRECISE POSITIONING SERVICE (PPS)
The accurate estimate of position, velocity and time can be provided by the GPS
to estimate with the position error 10 mvelocity error of 0.1 m/s and time error
of ions (all root mean square). These estimates are to be available to an unlimited
number of users all over the globe continuously and instantaneously. GPS should
also have a measure of resistance to jamming and interference. A policy was formulated
to offer two kinds of services: Standard Positioning Service (SPS) for peaceful
civil use and Precise Positioning Service (PPS) for the DOD authorized users.
2.15.1. Precise Positioning service (PPS)
The access to the full capability of the PPS system is restricted by cryptographic
techniques. The system transmits encrypted signals intended for DOD authorized users
equipped with the appropriate encryption keys. This feature is called AntiSpoofing
(AS).
2.15.2. Standard Positioning Service (SPS)
Each satellite transmits one signal for unrestricted user under Standard Positioning
Service. Standard Positioning Service signals were degraded throughout 1990’s by
introducing controlled errors to reduce precision. The DOD authorized users could
remove such errors. This feature called Selective Availability (SA) was deactivated
by presidential order on May 2000. The signal degradation was achieved by ‘dithering’
the satellite clock and timing marks on the ranging signals affecting the C/A, P[Y]
codes and carrier phase measurements equally.
With these basic concepts, the datum projections and its conversions are currently
discussed in the following sections.
2.16. GPS DATUM AND PROJECTIONS
Since the uneven and undulating physical surfaces of the earth is not suitable for
the mathematical computations of geodetic data reduction, coordinate reference and
map datum, a hypothetical, geometrical reference surface called ‘Geodetic Datum’
must be defined. Traditionally, two different data are used as reference surfaces
for the horizontal in the vertical coordinates: the horizontal datum, which is an
ellipsoid and the vertical datum which is geoid. The accuracy of the geodetic coordinates,
computations and mapping is directly affected by the suitability of the geodetic
datum used.
The Indian geodetic datum is the Everest ellipsoid, which is based upon the adjustment
of great trigonometrically triangulation network of India. The GPS yields the positions
of survey points on a global reference surface called World Geodetic system 84 (WGS
84). The geodetic datum is Geocentric (ECEFEarth centered earth fixed) and defined
to a high degree of accuracy by defence mapping agency, USA (DMA). The relationship
between WGS84 and the Indian map datum ought to be defined precisely to meet the
ever increasing accuracy requirements. The position of a satellite is determined
on the basis of the orbital parameters broadcast by each satellite as a part of
its navigation message. The Kepler’s three laws of motion and the six Keplerian
elements are used to characterize an ideal elliptical orbit needed for common reference
system.
2.16.1. Need for common reference system
Owing to the historical reasons each country has its own geodetic network and National
Geodetic reference frames are not identical with the Global WGS84 reference frame.
Because of the practical reasons, navigation facilities are surveyed and coordinated
with respect to the national reference frame. To represent these national coordinates
in global datum, certain transformation equations are to be developed in order to
achieve global compatibility. The distinctions between Global and local reference
frames are shown in figure 4.8 in which, the local reference frame is denoted by
(X1, Y1 and Z1) and global reference frame by (X, Y and Z). The difference in the
location of origin of reference frames have to be computed accurately for obtaining
precise datum transformation. Geodetic coordinates are also called geographic or
ellipsoidal coordinates which can be defined at a point p as follows:
Geodetic latitude (Φ)
The angle measured in the meridian plane through the point P between the equatorial
(xy) plane of the ellipsoid and the line perpendicular to the surface of the ellipsoid
at P (measured positive north from the equator, negative south).
Geodetic longitude (λ)
It is the angle measured in the equatorial plane between the reference meridian
and the meridian plane through p (measured positive east from the zero meridian).
Geodetic Height (h)
It is measured along normal to the ellipsoid through p. GPS measurements are based
on WGS 84 reference frame. As geographic information is exchanged both locally and
globally, position information is needed to be made available, both in terms of
a local and global datum. Hence there is need for datum conversion.
2.17. GEODETIC DATUM TRANSFORMATION
A geodetic datum transformation is a mathematical rule used to transform the surveyed
coordinates given in reference frame 1 into coordinates given in reference frame
2 as shown in figure 9. The mathematical rule is a function of the set of necessary
datum transformation parameters. Hence the result of the accuracy of any datum transformation
is not only dependent on the accuracy of the original data, but also on the accuracy
of the determination of the transformation parameters used.
2.18. WGS 84 SYSTEM
The World geodetic system – 1984 (WGS 84) coordinate system is a conventional terrestrial
system (CTS) as shown in figure 10. The origin and axes of the WGS 84 coordinate
system are defined as: Origin  Earth’s center of mass; Z – Axis  The direction
of the Conventional Terrestrial Pole (CTP) for polar motion, as defined by BIH on
the basis of the coordinates adopted for the BIH stations.
X  Axis – Intersection of the WGS 84 reference meridian plane and the plane of
the CTP’s equator, the reference meridian being the zero meridians defined by the
BIH on the basis of the coordinates adopted for the BIH stations. Y – axis  Completes
a righthanded, Earth Centered, Earth Fixed (ECEF) orthogonal coordinate system,
measured in the plane of the CTP equator, 90o East of the Xaxis. Earthfixed global
reference frame, including an earth model is defined by a set of primary and secondary
parameters.
The primary parameters are given in table 2. They define the shape of the earth
ellipsoid, its angular velocity and the earthmass, which is included in the ellipsoid
of reference. The secondary parameters define a detailed earth gravity field model
(EGM) of the degree and order n=m=180.
PARAMETER

NAME

WGS84

Semi major axis

A

6378137 m

Flattening

F

1/298.257223563

Angular velocity

Ω

7.292115*105rad s^{1}

Geocentric gravitational constant(mass of earth’s atmosphere included)

GM

398600.5 km^{3+s}2

Normalized 2nd degree zonal harmonic coefficient of the gravitational potential

C20

484.16685*10^{6}

2.18.1. Earth centered, earth Fixed (ECEF):
Earth centered, earthfixed, X, Y and Z, Cartesian coordinates (XYZ) define three
dimensional positions with respect to the center of mass of the reference ellipsoid.
 The zaxis points toward the North Pole.
 The Xaxis is defined by the intersection of the plane defined by the prime meridian
and the equatorial plane.
 The Yaxis completes a right handed orthogonal system by a plane 90o east of the
Xaxis and its intersection with the equator.
2.18.2. Universal Transverse Mercator (UTM)
All the GPS receivers can provide position information in terms of latitude, longitude,
and weight and usually in a variety of selectable geodetic datum. However, when
plotting the position information on maps, it can be advantageous to work with the
local or national grid coordinates on a particular map projection. The Universal
Transverse Mercator (UTM) is one of the most widely used two dimensional map projection
of any point defined on the globe and is a grid system (Langley, 1998). UTM was
established in 1936 by the International Union of Geodesy and Geophysics. In 1947,
the United States Army adopted the ellipsoidal transverse Mercator projection and
an associated grid system for designating rectangular coordinates on largescale
military maps covering up almost whole world
2.18.2.1. Transverse Mercator projection
A Transverse Mercator Projection is a Mercator projection, where the cylinder has
been rotated or transverse 90o. The ellipsoid and cylinder is tangent along a meridian.
By projecting the surface of the ellipsoid onto the cylinder as for the Mercator
projection, the Transverse Mercator Projection is developed on the surface of the
cylinder, which is then opened and flattened as shown in the figure 11. The central
meridian is the meridian where the cylinder touches the sphere. Theoretically the
central meridian is the line of zero distortion. By rotating the cylinder around
the poles, the central meridian (and area of least distortion) can be moved around
the earth.
2.18.2.2. Zone System
The globe is divided in to 60 zones, 6 degrees of longitude wide to reduce the distortion.
Zones are numbered eastward, 1 to 60, beginning at 180 degrees (W long). The system
is used from 84 degrees north to 80 degrees south as distortion at the poles is
too great with this projection. At the poles, an universal polar stereographic projection
(UPS) is used. Each zone is divided further into strips of 8 degrees latitude. Each
UTM zone’s central meridian lies midway between the two bounding meridians and its
scale is reduced to 0.9996 of true scale (Leick, 1990). This value keeps the scale
variation within a zone to less than about 1 part in 1,000. The lines of
true scales are approximately parallel to the central meridian and about 180 km
to either side of it. The UTM zone system is shown in figure (11). For more clarity
UTM zone 19 is depicted in figure (13).
2.18.2.3. UTM Coordinates
In UTM system, the coordinates are expressed in Eastings and Northings in contrast
to longitude and latitude in WGS84 system. The units of the coordinates are in
meters. Eastings (x) are displacements eastward. UTM easting coordinates are referenced
to the center line of the zone known as the central meridian. The central meridian
assigned an easting value of 500,000 meters east. Since this 500,000m value is arbitrarily
assigned, Eastings are sometimes referred to as “false Eastings” Northings (y) express
displacement northward. UTM northing coordinates are measured relative to the equator.
For locations north of the equator the equator is assigned the northing value of
0 meters north.
The central meridian is given an estimation of 500,000 m; the northing for the equator
varies depending on hemisphere. While calculating coordinates for locations in the
northern hemisphere, the equator has a northing of 0m. In the southern hemisphere,
the equator has a northing of 10,000,000m.
2.18.2.4. Universal Transverse Mercator coordinate system
The system identifies two forms of Oblique Mercator projection, differentiated only
by the point at which false grid coordinates are defined. If the false grid coordinates
are defined at the intersection of the initial line and the aposphere, the projection
is known as Hotline Oblique Mercator. If the false grid coordinates are defined
at the projection center the projection is known as Oblique Mercator. The initial
line central to the map is the area of given azimuth passes through a defined center
of the projection ( ). The point, where the projection of this line cuts the equator
on the aposphere is the origin of the (u, v) coordinate system. The uaxis is parallel
to the centerline and vaxis is perpendicular to this line as shown in the given
figure 14.
2.18.2.5. Advantages of UTM
 UTM provides a constant distance relationship anywhere on the map.
 In angular coordinate system like latitude and longitude the distance covered by
a degree of longitude differs while moving towards the pole and only equals to the
distance covered by a degree of latitude at the equator.
 Since land navigation is done in a very small part of the world at any one time
using largescale maps, the UTM system allows the coordinate numbering system to
be tied directly to a distance measuring system.
2.18.2.6. Disadvantages of UTM
 Full geo reference requires the zone number, easting and northing (unless the area
of the data base falls completely within a zone).
 Rectangular grid superimposed on zones defined by meridians cause axes on adjacent
zones to be skewed with respect to each other.
 No simple mathematical relationship exists between coordinates of one zone and an
adjacent zone.
2.18.2.7. Lambert conformal projections
Johann Heinrich Lambert (1972) developed the mathematics for conformal conic projection
with two standard parallels, and presented in 1972. Later Gauss fully described
it.
The salient features of the Lambert Conformal Conic Projection are:
 Conformal & Conical
 Parallels that are unequally spaced arcs of concentric circles and are more closely
spaced near the center of the map.
 Scale is true along two standard parallels, normally or along just one.
 Meridians are equally spaced radii of the same circles thereby cutting parallels
at right angles.
 Pole in same hemisphere as standard parallel is a point, other pole is at infinity.
 It is used for maps of countries and regions with predominant east west expanse.
 Coalfield companies use it in India extensively for geographical maps, IMW maps,
and grid in respect of topographical maps.
 It is used as state plane coordinate system (SPCS) in USA.
 It is used in china as basis for the coordinate system and all geodetic work.
2.18.2.8. Conformal Property
The property of map projections in which angles on the surface to be mapped are
preserved on the map, i.e. the corresponding angles on the map plane and the curved
surface are equal is called the conformal property. It implies that the “meridians
and parallels cut each other at right angles “everywhere, and at any point, scale
is the same in any direction so that there is no local distortion as shown in figure
15.
2.18.2.9. Standard Parallels
The projection can be with one standard parallels or two standard parallels. The
scale is true along the central parallel in one standard whereas it is true along
two parallels in the later case. It is always better to adopt projections with two
standard parallels to limit distortion in scale over areas. To design a projection,
limiting parallels and limiting meridians are prescribed which cover the entire
area to be projected. The standard parallels are then selected at 1/6th of the extent
in NS direction, i.e. latitudinal directions. Central meridian is chosen midway
between the limiting meridians.
Value of the central meridian is calculated mathematically. Intersection of central
parallel and central meridian is the origin of rectangular coordinate system, with
central meridian as yaxis and a line perpendicular to it as xaxis. The origin
assumes that value (0.0) called assumed origin popularly known as false origin.
We get a grid of NS and EW lines, in which NS lines are called Eastings and EW lines
are called Northings.
2.18.2.10. Advantages
There are many advantages of the system. Some of them are
 Simple and easy to understand.
 All cities, towns etc. can be referred to in meters. Easy to compute distances and
bearings.
 Takes care of scale error, and keeps it within control.
 All maps of state, from village to taluka, to district to state level maps including
cadastral, project, guide, tourist, topographical maps etc. be in this system.
2.19. INDIAN GEODETIC DATUM
It is necessary to specify the location of the origin of the coordinate system;
orientation of the coordinate system and the dimensions of the reference surface.
Everest spheroid (ellipsoid) is used as reference surface in INDIA to realize a
geodetic system. It was customary to define a geodetic datum by choosing an initial
point (origin) and specifying, the latitude and longitude of the initial point,
the azimuth of the line from this point and the (two) parameters of a reference
surface (ellipsoid) the components of deflection of vertical and geoidal undulation
at the initial point. Indian geodetic datum based on ‘Everest Spheroid’ was defined
piecemeal at various times. It is finally defined by the following:
Origin (Initial Point): Kalyanpur
Latitude of Origin:

24^{o}07’11”.26

Longitude of Origin:

77^{o}39’17”.57

Meridional deflection of vertical:

0”.29

Prime vertical deflection of Vertical:

2”.89

Semi Major axis of Everest Spheroid:

6,377,301 meters

Flattening of Everest Spheroid:

1/300.8017

Geoidal undulation:

0 meters

Azimuth to Surantal:

19^{o}27’06”.39

Indian Geodetic datum based on Everest Spheroid is a local geodetic datum, which
appropriately suits the Indian subcontinent to a certain extent. It is not a geocentric
ellipsoid, and its origin is far away from the geocentric. The geodetic coordinates
based on Everest spheroid differ considerably (in many cases even hundreds of meters)
as compared to WGS84 and other international ellipsoids. The parameters of the
Everest and WGS84, their differences and translation parameters are given in tables
3 and 4.

Everest

WGS84

Semi major axis (a)

6,377,301.243 m

6378137±2M

FLATTENING, F

1/300.8017

1/298.257223563

Table 3: Parameters of the Everest and WGS84
▲a(m)(WGS84Everest)

835.757

▲f*104(WGS84Everest)

0.28361368

Table 4: Translation parameters for WGS84 and Everest
Transformation Parameters (WGS84 Everest)

Remarks

▲x(m) ▲y(m) ▲z(m)

Based on 100 Doppler

217+15 823+6 299+12

stations

International ellipsoid 1924

International Everest

A=6378388

▲ (a) x104

F=1/297.0

1086.757 0.42554

Transformation parameters (InternationalEverest)

Remarks


Calculated by the author from the values of difference in deflection components
and Geoidal undulation.

▲x (m)

▲y (m)

▲z (m)

311.01

1032.74

160.56



Typical values of coordinates in Everest and International spheroids are given in
tables 5 and 6. This demonstrates that the coordinates between the two systems Everest
and international 1924 differ by nearly 50m in latitude and 100m in longitude and
10m in height. The difference shall vary from place to place. Similarly the coordinates
in Everest and WGS84 differ by even more than 100m in position and height.
The transformation parameters obtained between WGS84 and Everest depends upon 11
Doppler stations situated in neighboring countries. The transformation parameters
therefore, cannot be said to be reasonably accurate. Hence, unless reasonable accurate
transformation parameters are available, WGS84 coordinates obtained from point positioning
in GPS cannot be used for maps and data based on Everest Spheroid.
Table (5): The result of transformation of coordinates from Everest to International
in respect to two stations of Hyderabad 1924
Sno

Station

Coordinates in Everest Spheroid



Latitude

Longitude

δΦ

δλ

Δh in m

1

A

17^{o}31’36”900

78^{o}41’27”.457

0”.465

3”.314

+9.799

1

B

17^{o}32’03”.859

78^{o}23’09”.870

0”.474

3”.281

+10.302

Table (6): Coordinates in International Spheroid
Sno

Station

Coordinates in International Spheroid after transformation



Latitude

Longitude

1

A

17^{o}31’36”435

78^{o}41’24”.143

2

B

17^{o}32’03”.385

78^{o}23’06”.589

2.19.1 Procedure of Using GPS in I.G.S:
GPS is used in relative positioning static mode, using two single frequency or double
frequency precise GPS receivers; distances are found between points after post processing
using available software. The distances are used to compute positions of points
as in classical survey methods.
Slope distances are reduced to chord distances in space, and then reduced to chord
distance at ellipsoid or spheroid level (IGS). The cord distances are then converted
to spheroidal distance and used for computations.