gps error part -1

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GNSS Surveying, GE 205
Lecture 3, March 8, 2015
GPS Error

• Kutubuddin ANSARI
• kutubuddin.ansari_at_ikc.edu.tr

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GPS Errors
GPS measurements are both affected by several
types of random errors and systematic errors
which affects the accuracy of measurements
X
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GPS Errors
Originating at the satellites
Originating signal propagation or
atmospheric refraction
Originating at the receiver
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Satellites Errors

• 1. Ephemeris or Orbital Error
• Satellite positions are a function of time
• Forces acting on the GPS satellites are
  not perfect
• Errors in the estimated satellite positions
  known as ephemeris errors.

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Thumb Rule to estimate Orbital Error
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2. Selective Availability
Selective availability (SA) is a technique to
deny accurate real-time autonomous
positioning to unauthorized users.

• d -process is achieved by dithering the
  fundamental frequency of the satellite clock.
• e-error is the truncation of the orbital
  information in the transmitted navigation message
  so that the coordinates of the satellites cannot
  accurately be computed.
• SA turned on, nominal horizontal and vertical
  errors could be up to 100m and 156m,
  respectively.

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SA is off
SA is on
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3. Satellite and Receiver Clock Errors
Each GPS Block II and Block IIA satellite
contains two cesium and two rubidium atomic
clocks. The satellite clock error is about 8.64
to 17.28 nanoseconds per day. The corresponding
range error is 2.59 m to 5.18 m GPS receivers,
in contrast, use inexpensive crystal
clocks. The receiver clock error is much larger
than that of the GPS satellite clock.
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Receiver Error
Multipath Error

• A signal that bounces of a smooth object and hits
  the receiver antenna.
• Increases the length of time for a signal to
  reach the receiver.
• A big position error results.
• Gravel roads
• Open water
• Snow fields
• Rock walls
• Buildings

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PHASE
Phase is the fraction of a wave cycle which has
elapsed relative to an arbitrary point
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Multipath Error


If a and f denote the amplitude and the phase of
the signal
direct signal a cosf indirect signal ß a
cos(f? f) Where ß is a damping factor
The superposition of signals is represented by

Let us consider

where the subscript M indicates multipath


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• ß may vary between 0 and 1

• ß 0 (no reflected signal and no multipath)
• ßM 1 and ?fM 0
• the resultant signal is identical to the
  direct signal

• ß 1 (The strongest possible reflection )

• The best way to eliminate multipath error is to
  construct the observation site with no reflecting
  surface and objects in its locality.

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Signal Propagation or Atmospheric Refraction
Errors
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1. Ionosphere

• The uppermost part of the earths atmosphere (50
  km and 1000 km), ultraviolet and X-ray radiations
  coming from the sun interact with the gas
  molecules and atoms.
• These interactions result in gas ionization, a
  large number of free, negatively charged,
  electrons and positively charged, atoms and
  molecules, such a region of the atmosphere where
  gas ionization takes place is called the
  ionosphere.

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• The electron density within the ionospheric
  region is not constant, it changes with
  altitude. As such, the ionospheric region
  is divided into sub regions, or layers,
  according to the electron density
• The altitude and thickness of those layers vary
  with time, as a result of the changes in the
  suns radiation and the Earths magnetic field.
• The ionosphere is a dispersive medium,
  which means that it bends the GPS radio
  signal and changes its speed as it passes
  through the various ionospheric layers to reach a
  GPS receiver

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Dispersive Medium
The dispersion is the phenomenon in which
the phase velocity of a wave depends on its
frequency and such type of medium is called
dispersive medium
In a dispersive prism, material dispersion causes
different colors to refract at different angles,
splitting white light into a rainbow.
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Phase and Group velocity
The phase velocity of a wave is the rate at which
the phase of the wave propagates in space (red
dot). 
The group velocity of a wave is the velocity with
which the overall shape of the waves amplitudes
propagates through space (green dot).
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Phase and Group velocity

• For a single electromagnetic wave propagating
  in space with wavelength ? and frequency f
• The phase velocity

The group velocity
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Rayleigh Equation
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Refractive Index
The refractive index  n of a material is a
dimensionless number that describes how light
propagates through that medium. It is defined as
where c is the speed of light in vacuum and v is
the phase velocity of light in the medium
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Modified Rayleigh Equation

• Depends on Refractive Index (n)

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Modified Rayleigh Equation
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Ionospheric Refraction

• The ionosphere extending in various layers
  from about 50 km to 1,000 km above earth is a
  dispersive medium with respect to the GPS radio
  signal. Following Seeber series ..
• Neglect higher order terms

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Ionospheric Refraction

• Ionosphere dispersive relative to GPS Radio
  Signal

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Pseudorange
Pseudorange Geometric range Range
correction (Measured Range) (Actual Range)
Error
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Total Electron Content (TEC)
TEC is an important descriptive quantity for the
ionosphere of the Earth. TEC is the total number
of electrons integrated between two points, along
a tube of one meter squared cross section. The
TEC is measured in a unit called TECU, where
1TECU11016electrons/m2
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GPS Frequencies

• Each satellite sends down exactly the same two
  radio frequencies
• L1 at 1575.43 MHz
• L2 at 1227.60 MHz
• At these microwave frequencies the signal are
  highly directional and hence are easily blocked,
  as well as highly reflected by solid objects and
  water surfaces

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Total Electron Content (TEC)
For the dual frequency (L1, L2) observation, TEC
in the slant direction can be calculated from the
pseudo range (P) and phase observations (?) as
Here, P1 and P2 are pseudoranges and ?1 and ?2
are phases of carriers L1 and L2 respectively.
For simplification
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Slant Total Electron Content (STEC)


STEC is the total electron content calculated on
the path different than local zenith. The value
of TEC consists of both the STEC along a
satellite receiver ray path and instrumental bias
B (constant)

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Vertical Total Electron Content (VTEC)
The electron content calculated on the local
zenith path is called Vertical Total Electron
Content (VTEC)
where a is the elevation angle, RE the radius of
the earth (RE6378 km) and hmax (350 km) is the
height of the ionospheric shell above the surface
of the earth
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Total Electron Content

• TEC is a very complicated quantity depends on
  sunspot activities line of sight (includes
  elevation and azimuth of satellites) position of
  observation etc.
• Determination of TEC is essential
• TEC effects needs to be measured, estimated,
  modelled or eliminated

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Elimination

• Various time its very difficult to measure ,
  estimate or model the value of TEC
• Most efficient method is to eliminate the value
  of TEC
• Its very easy to eliminate it by using two
  signals with different frequencies and this the
  main reason why the GPS signal has two carrier
  waves L1 and L2
• It can be done by linear combination of
  pseudorange models so that ionospheric refraction
  cancels out

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Elimination

• Start with Code Pseudorange model
• with ionosphere affects

• fL1, fL2 frequency of the two carriers
• Linear Combination
• RL1, L2n1RL1 n2RL2

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Elimination
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Elimination
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Ionosphere free linear combinations

• Code ranges
• This is the ionospheric free linear
  combination for code ranges. A similar
  ionospheric free linearcombination for carrier
  phase may be derived as Carrier phases

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