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GLOBAL POSITIONING SYSTEM (GPS)

  • - 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 real-time 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. High-accuracy, 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 low-cost single-frequency 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 post-processed, high-accuracy, single-frequency 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:

    1. High accuracy, real-time position, velocity, and time for military users on a variety of platforms, some of which have high dynamics: e.g. high performance aircraft.
    2. Good accuracy for civil user is considered to be 100m or better in three dimensions.
    3. Worldwide, all weather operation, 24 hours a day.
    4. Resistance to intentional (jamming) or unintentional interference for all users-enhanced resistance to jamming for military users.
    5. Capability for highly accurate geodetic survey to centimeter levels using radio frequency carrier measurements and for high-accuracy time transfer to 100ns or better.
    6. Affordable, reliable user equipment-users are not required to carry high-accuracy 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 s-band 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 3-D position, velocity and system time (Figure 1). The position is in geocentric coordinates in the basic reference coordinates system - World Geodetic reference system-1984 (WGS-84), 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.

    Point_Positioning.jpg GPS_Satellite_Constellation.jpg 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.

    Surface_of_a_sphere.jpg

    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.

    intersecting_spheres.jpg

    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 above-formed circle at two points. Finally the position of receiver on earth is reduced to two points as shown in the figure 5.

    Three_satellites.jpg

    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 hundred-millionth 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:

    1. Accuracy of each satellite’s position.
    2. Accuracy of pseudo range measurement
    3. Geometry.
    2.5 FEATURES OF GPS SATELLITES

    Some of the important features of the GPS satellites are

    1. Design life 5 years (with expendables stored for 7 years).
    2. On orbit weight 430kg.
    3. End-of-life power: 400 W.
    4. Power source: 5m2 solar arrays tracking the sun and 3 Ni-Cd batteries for eclipse.
    5. 3 axes established, earth pointing satellites.
    6. Navigation pay load: pseudo Random Noise (PRN) signal assembly, atomic frequency standard- cesium beam atomic clocks accurate to 10-14 sec, processor and t band antenna.
    7. Codes:
      1. 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.
      2. 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.
    8. PRN navigation signals on 2 frequencies :
      1. 1575.42 MHz - L1 Band - Wavelength 19 cm.
      2. 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

    equation1.jpg

    In equation (4.1), Rk 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 trade-off 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 L-band 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 P-code 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

    L1= 154*10.23 MHz = 1575.42 MHz. ------------------ equation (2)

    L2= 120*10.23 MHz = 1227.60 MHz. -------------------equation (3)

    The dual carrier strategy serves two purposes:

    1. Incase L1 is lost or the receiver is being jammed on L1, then L2 serves as a backup.
    2. 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).

    power_levels.jpg

    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.

    structure_of_GPS.jpg 2.7.4. Signal at L1

    The L1 in-phase 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.

    equation4.jpg

    Where

    I is the satellite index
    Ap and Ac are the in phase and quadrature signal amplitudes respectively in (volt, volt),
    D is the navigation data bit.
    ω1 is the L1 center frequency (rad/sec) and
    γ1 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.

    equation5.jpg

    where

    Bp is the signal amplitude of L2,
    ω2 is the center frequency of L2 in (rad/sec) and
    γ2 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- GPS-200C (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.

    spreadfactor.jpg 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 p-code 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 sub-frames, each sub-frame 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. Sub-frames 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.

    1. Time and satellite clock information.
    2. Correction data to compensate for signal delay
    3. Satellite orbit information
    4. Satellite health status
    gps_navigation.jpg 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

    1. 0.1-4 mm in local surveys(10m-100km base line lengths)
    2. 4-10 mm in regional surveys( 100-1000km base line lengths)
    3. 1-2 cm in global surveys (1000-10,000km 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 (geoid-ellipsoid 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.

    1. Establishment of high precision zero order geodetic national survey control network of GPS stations.
    2. Strengthening, densification and readjustment of existing primary control networks using GPS stations.
    3. Connecting remote islands to mainland geodetic control networks.
    4. Determination of a precise geoid using GPS data
    5. Earth rotation and polar motion studies from GPS data.
    6. Estimating gravity anomalies using GPS.
    7. Marine geodesy: positioning of oceanic stations and buoys etc.
    8. 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 m-velocity 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 Anti-Spoofing (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 (ECEF-Earth centered earth fixed) and defined to a high degree of accuracy by defence mapping agency, USA (DMA). The relationship between WGS-84 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 WGS-84 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 (x-y) 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).

    frames.jpg 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 co-ordinates 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.

    Geodetic 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 right-handed, Earth Centered, Earth Fixed (ECEF) orthogonal coordinate system, measured in the plane of the CTP equator, 90o East of the X-axis. Earth-fixed 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 earth-mass, 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.

    earth-centered
    PARAMETER NAME WGS84
    Semi major axis A 6378137 m
    Flattening F 1/298.257223563
    Angular velocity Ω 7.292115*10-5rad s-1
    Geocentric gravitational constant(mass of earth’s atmosphere included) GM 398600.5 km3+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, earth-fixed, X, Y and Z, Cartesian coordinates (XYZ) define three dimensional positions with respect to the center of mass of the reference ellipsoid.

    1. The z-axis points toward the North Pole.
    2. The X-axis is defined by the intersection of the plane defined by the prime meridian and the equatorial plane.
    3. The Y-axis completes a right handed orthogonal system by a plane 90o east of the X-axis 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 large-scale 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

    transverse zone_system utm

    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 WGS-84 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 co-ordinate 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 u-axis is parallel to the centerline and v-axis is perpendicular to this line as shown in the given figure 14.

    2.18.2.5. Advantages of UTM
    1. UTM provides a constant distance relationship anywhere on the map.
    2. 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.
    3. Since land navigation is done in a very small part of the world at any one time using large-scale 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
    1. Full geo reference requires the zone number, easting and northing (unless the area of the data base falls completely within a zone).
    2. Rectangular grid superimposed on zones defined by meridians cause axes on adjacent zones to be skewed with respect to each other.
    3. No simple mathematical relationship exists between coordinates of one zone and an adjacent zone.
    hotline 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:

    1. Conformal & Conical
    2. Parallels that are unequally spaced arcs of concentric circles and are more closely spaced near the center of the map.
    3. Scale is true along two standard parallels, normally or along just one.
    4. Meridians are equally spaced radii of the same circles thereby cutting parallels at right angles.
    5. Pole in same hemisphere as standard parallel is a point, other pole is at infinity.
    6. It is used for maps of countries and regions with predominant east west expanse.
    7. Coalfield companies use it in India extensively for geographical maps, IMW maps, and grid in respect of topographical maps.
    8. It is used as state plane coordinate system (SPCS) in USA.
    9. 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.

    conformal 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 y-axis and a line perpendicular to it as x-axis. 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

    1. Simple and easy to understand.
    2. All cities, towns etc. can be referred to in meters. Easy to compute distances and bearings.
    3. Takes care of scale error, and keeps it within control.
    4. 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: 24o07’11”.26
    Longitude of Origin: 77o39’17”.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: 19o27’06”.39

    Indian Geodetic datum based on Everest Spheroid is a local geodetic datum, which appropriately suits the Indian sub-continent to a certain extent. It is not a geocentric ellipsoid, and its origin is far away from the geocentric. The geodetic co-ordinates based on Everest spheroid differ considerably (in many cases even hundreds of meters) as compared to WGS-84 and other international ellipsoids. The parameters of the Everest and WGS84, their differences and translation parameters are given in tables 3 and 4.

    Everest WGS-84
    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)(WGS84-Everest) 835.757
    ▲f*104(WGS84-Everest) 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 (International-Everest) 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 WGS-84 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 17o31’36”900 78o41’27”.457 -0”.465 -3”.314 +9.799
    1 B 17o32’03”.859 78o23’09”.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 17o31’36”435 78o41’24”.143
    2 B 17o32’03”.385 78o23’06”.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.