CE 200

INTRO TO SURVEYING
New Jersey Institute of Technology
Professor Allison Lapatka, PE, PLS

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 GLOBAL POSITIONING SYSTEMS
• Global Positioning System (GPS) emerged in the 1970s, and grew out of the space program. It
relies upon signals transmitted from satellites for its operation, and has become a system for
global navigation and guidance.
• Since other countries have recently developed their own systems, all of the difference systems
are now referred to as GNSS, or global navigation satellite systems, such as GLONASS,
Galileo, and Beidou.
• These systems provide precise timing and positioning information anywhere on the Earth with
high reliability and low cost.
• This has resulted in a departure from conventional surveying procedures, since surveyors no
longer need to rely on observed angles and distances for determining point position.
• The first satellite positioning system was the Navy Navigation Satellite System (NNSS,
commonly called TRANSIT system), which was developed in 1958, and was used to aid in the
navigation of the US Navy’s Polaris submarine fleet.
• The first authorized civilian use was in 1967, and was quickly adopted by the surveying
community. The US Dept. of Defense began development of the Navigation Satellite Timing and
Ranging (NAVSTAR) Global Positioning System, with the first satellite going into orbit in 1978,
and became fully operational in December 1993.

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 GLOBAL POSITIONING SYSTEMS
• In satellite surveying, the satellites are reference or control stations, and the ranges (distances) to these
satellites are used to compute the positions of the receiver.
• GPS can be broken in to 3 parts
• Space segment – 24 satellites operating in six orbital planes spaced at 60 o intervals around the
equator. Four additional satellites are held in reserve as spares. The orbital planes are inclined to the
equator at 55o, which provides for 24 hour satellite coverage between the latitudes of 80 oN and 80oS.
The satellites travel in near-circular orbits that have a mean altitude of 20,200 km above the Earth and
an orbital period of 12 sidereal hours (+/- 4 min. shorter than a solar day). Precise atomic clocks are
used to control the timing of the signals they transmit.
• Control segment – monitoring stations which monitor the signals and track the positions of the
satellites over time. The initial GPS monitoring stations are at Colorado Springs, and on the islands of
Hawaii, Ascension, Diego Garcia, and Kwajalein. The DoD has since added additional tracking
stations to the control network. Tracking information is relayed to the master control station in the
Consolidated Space Operations Center (CSOC) located at Schreiver Air Force base in Colorado
Springs, which uses the data to make precise, near-future predictions of the satellite orbits, and their
clock correction parameters.
• User segment – two categories of receivers that are classified by their access to two services that the
system provides – Standard Position Service (SPS), and Precise Positioning Service (PPS). SPS is
provided on the L1 broadcast frequency and more recently the L2 at no cost to the user. The PPS
broadcasts on both the L1 and L2 frequencies, and is only available to military and authorized users.

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 GLOBAL POSITIONING SYSTEMS
• GPS uses “one-way” communication and depend on precise timing of the transmitted signal.
• The orbiting GPS satellites continually broadcast a unique signal on the 2 carrier frequencies
(L1 & L2 microwave radio frequencies)
• In order for receivers to independently determine the ground positions of the stations they
occupy in real time, a system was devised for accurate measurement of signal travel time from
satellite to receiver. In GPS, this was accomplished by modulating the carriers with
pseudorandom noise (PRN) codes. The PRN codes consist of unique sequences of binary
values (zeros and ones) that appear to be random but are generated according to a special
mathematical algorithm using devices known as tapped feedback shift registers. Satellites
transmit two or more different PRN codes. The L1 frequency is modulated with the precise
code, or P code, and also wit the coarse/acquisition code, or C/A code, which allows receivers
to acquire the satellites as well as determine the approximate positions.
• Modernized satellites are being equipped with new codes, including a second civilian code on
the L2 signal called the L2C. The P code is also being replaced by two new military codes,
caleld M codes. A 3rd civilian signal, L5, was added in 1999 to provide safety of life applications
to GPS

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 GLOBAL POSITIONING SYSTEMS
• To determine the positions of points on Earth from satellite observations, three different
reference coordinate systems are needed, and are specified in the space related satellite
reference coordinate systems, which are 3D rectangular systems defined by the satellite
orbits.
• Satellite positions are then transformed into a 3D rectangular geocentric coordinate
system, which is physically related to the Earth. Positions of points on the Earth are
determined in this coordinate system.
• Geocentric coordinates are transformed into the more commonly used and locally
oriented geodetic coordinate system.

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 GLOBAL POSITIONING SYSTEMS
• Satellite movements vary somewhat from their ideal paths because of gravitational forces
exerted by the sun and moon, the movement of the Earth, and forces due to solar
radiation.
• If all forces except for the Earth’s gravitational pull are ignored, a satellite’s ideal orbit is
elliptical, and has one of its foci at G, the Earth’s mass center.
• The perigee is the point where the satellite is the closest to G, and the apogee is the point
where the satellite is the farthest from G. These points are joined by the line of apsides,
which passes through the two foci, and is the reference axis Xs.
• The satellite reference coordinate system is Xs, Ys,, and Zs
• Ys axis: mean orbital plane
• Zs axis: perpendicular to Y s plane.

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 GLOBAL POSITIONING SYSTEMS
• The objective of satellite systems is to locate points on the surface of the Earth. It is
necessary to have a “terrestrial” frame of reference, which enables relating points
physically to the Earth, and uses the geocentric coordinate system.
• This image illustrates a quadrant of a reference ellipsoid, with a geocentric coordinate
system (Xp, Yp, Zp) superimposed
• The origin is at the mass center of the Earth
• Xe axis passes through the Greenwich meridian
(in the plane of the equator)
• Ze axis coincides with the Conventional
Terrestrial Pole (CTP)
Ye axis lies in the plane of the equator and creats a
Right handed coordinate system.

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 GLOBAL POSITIONING SYSTEMS
• 4 angular parameters are required to convert from the satellite reference coordinate
system to the geocentric system, which define the relationship between the satellite’s
orbital system and key reference planes and lines on the Earth.
• Inclination angle, i: angle between the orbital plane and the Earth’s equatorial plane
• Argument of perigee, Ѡ: angle in the orbital plane from the equator to the
line of apsides
• Right Ascension of the ascending node, Ω: angle in the plane of the Earth’s
equator from the vernal equinox to the line of intersection between the
orbital and equatorial planes
• Greenwich hour angle of the vernal equinox, GHAg : angle in the equatorial
plane from the Greenwich meridian to the vernal equinox
• These parameters are known in real time for each satellite based upon
predictive mathematical modeling of the orbits.

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 GLOBAL POSITIONING SYSTEMS
• Coordinates calculated in the geocentric coordinate system (previously described) are
inconvenient for use by surveyors because
• Geocentric coordinates are typically extremely large values, since their origin is the
Earth’s center
• With the X-Y plane in the plane of the equator, the axes are unrelated to the
conventional directions of north-south or east-west on the surface of the Earth
• Geocentric coordinates give no indication about relative elevations between points.
• Therefore, geocentric coordinates are converted to geodetic coordinates of latitude (∅),
longitude (λ), and height (h) so that the reported point positions become more meaningful
and convenient for users. – (X,Y,Z) becomes (∅,λ,h)

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 GLOBAL POSITIONING SYSTEMS
• To convert geodetic coordinates to geocentric coordinates of a point P
• XP = (RNP + hP)cos∅P cosλP
• YP = (RNP + hP)cos∅P sinλP
• ZP = [(RNP(1-e2) + hP]sin∅P
• RNP =
∅P
• XP, YP, ZP are the geocentric coordinates of any point P
• e = eccentricity of the WGS84 ellipsoid=0.08181919084
• RNP = radius in the prime vertical of the ellipsoid at P
• a = semi major axis of the ellipsoid.
• North latitudes & east longitudes are positive
• South latitudes & west longitudes are negative

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 GLOBAL POSITIONING SYSTEMS
• To convert geocentric coordinates of a point P to geodetic coordinates
1. DP = +
2. Longitude, λP = 2tan-1 (DP – XP / YP)
3. Approximate Latitude, ∅o = tan-1 (ZP/ DP(1-e2)
4. Calculate the approximate radius of the prime vertical, R N, using ∅o above
∅o
5. Calculate an improved value for the latitude from ∅ = tan-1 ( )
6. Repeat the computations of steps 4 & 5 until the change in ∅between iterations becomes negligible.
This final value, ∅P , is the latitude of the station.
7. Use the following formulas to compute the geodetic height of the station. For latitudes less than 45 o,
use
hp = - RNP
∅P
8. For latitudes greater than 45o, use
hp = - RNP(1-e2)
∅P

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 GLOBAL POSITIONING SYSTEMS
• Geodetic heights via satellite surveys are measured with respect to the ellipsoid.
Therefore, the geodetic height of a point is the vertical distance between the ellipsoid and
a point on the Earth’s surface. Since these are not equivalent to elevations or orthometric
heights given with respect to the Geoid, the geoid height (vertical distance between the
ellipsoid and the geoid) must me calculated, by H = h – N
• H = elevation above the geoid, or orthometric height
• h = geodetic height determined by satellite surveys
• N = geoidal height

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 GLOBAL POSITIONING SYSTEMS
• If 2 satellites are in the same orbital plane, we can say that, for each satellite,
• XP = r*cos(f)
• YP = r*sin(f)
• The distance between the satellites would simply be the distance formula.
• f is the true anomaly, which is an angular parameter which defines the position of a
satellite orbiting the Earth
• r is the radial distance from the center of mass

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