GPS Error-2

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GNSS Surveying, GE 205
Lecture 4, March 15, 2015
GPS Error-2

• Kutubuddin ANSARI
• kutubuddin.ansari_at_ikc.edu.tr

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2. Troposphere

• The troposphere is the lowest layer of the
  atmosphere that lies next to the Earths surface.
  
• Most of the air that makes up the atmosphere is
  found in the troposphere
• It extends to about 14 kilometers (around 9
  miles) above the Earth and is where virtually
  all weather takes place.

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Troposphere

• As you move up into the troposphere the
  temperature decreases.
• At the top of this layer the air temperature is
  about - 60C.
• Environmental Lapse rate 6.5 0C/km

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Tropospheric Delay

• The troposphere is the electrically neutral
  atmospheric region that can be extend up to about
  50 km from the surface of the earth.
• The troposphere is a non-dispersive medium for
  radio frequencies below 15 GHz, as a result, it
  delays the GPS carriers and codes identically.
• That is, the measured satellite to receiver range
  will be longer than the actual geometric range,
  which means that a distance between two receivers
  will be longer than the actual distance.

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The above equation in terms of Zenith Total
Delay (ZTD) can be expressed with sum of a
hydrostatic part Zenith Hydrostatic Delay (ZHD)
and a wet part Zenith Wet Delay (ZWD)
ZTD ZHD ZWD
About 90 of the troposphere refraction arise
from the dry and about 10 from the wet
component.

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Precipitable Water Vapor (PWV)

• Precipitable water vapor (PWV) is the amount of
  water vapor present in a column above the surface
  of the Earth
• Measured in units of inches or millimeters
• It represents the maximum amount of water that
  could fall down to the surface as precipitation
  if all the water vapor converted into a liquid or
  a solid

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Precipitable Water Vapor (PWV)

• ZWD is proportional to PWV as
• ZWDQ.PWV
• where factor Q is depending by the vertical
  mean temperature Tm,
• 
  
• Q is a dimensional quantity variable in space and
  time, however in mean is equal to 6.5.
• The Zenith Total Delay (ZTD), is the sum of ZHD
  and ZWD
• ZTD ZHD Q.PWV
• Generally 10 mm PWV corresponds to approximately
  65 mm of ZWD .

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Mapping function

• Basic form of mapping function was deduced by
  Marini (1972) and matches the behavior of the
  atmosphere at near-zenith and low elevation
  angles. Form is with constants (k)

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Relation with Temperature
A multiple linear regression method and neural
network method are performed to retrieve the
relation between PWV verses temperature . The PWV
has lower correlations with tropospheric
temperature. To check what type of prelateship
PWV constrains with temperature, let us consider
an equation of PWV with atmospheric temperature
(T) has been given by
If ? is error between observed and modeled value
of PWV then the equation can be written by least
square method in following form
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Relation with Temperature
To calculate the value of a and b, let the
partial derivatives of error with respect to a
and b are zero
After solving the equation the two equations can
be obtained in following form
Where n is number of observations. The values of
constants a and b will explain the modelled
relationship among PWV and temperature
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Sources of GPS Error

• Source Amount of Error
• Satellite clocks 1.5 to 3.6 meters
• Orbital errors lt 1 meter
• Ionosphere 5.0 to 7.0 meters
• Troposphere 0.5 to 0.7 meters
• Receiver noise 0.3 to 1.5 meters
• Multipath 0.6 to 1.2 meters
• Selective Availability (see notes)
• User error Up to a kilometer or more

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Geometry Measure
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Ideal Satellite Geometry
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Poor Satellite Geometry
S
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Good Satellite Geometry
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Poor Satellite Geometry
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Good Satellite Geometry
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Poor Satellite Geometry
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GPS Satellite Geometry

• Satellite geometry can affect the quality of GPS
  signals and accuracy of receiver trilateration
• Dilution of Precision (DOP) reflects each
  satellites position relative to the other
  satellites being accessed by a receiver
• There are five distinct kinds of DOP

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Dilution Of Precision
PDOP Position Dilution Of Precision (Commonly
Used) GDOP Geometric Dilution Of Precision VDOP
Vertical Dilution Of Precision HDOP
Horizontal Dilution Of Precision TDOP Time
Dilution Of Precision
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GPS Satellite Geometry

• Its usually up to the GPS receiver to pick
  satellites which provide the best position
  triangulation.
• Some GPS receivers allow DOP to be manipulated by
  the user.
• Position Dilution of Precision (PDOP) is the DOP
  value used most commonly in GPS to determine the
  quality of a receivers position.

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Dilution Of Precision (DOP)
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Dilution Of Precision (DOP)
when measuring must have good DOP and good
visibility may not always be possible
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The cofactor matrix Q
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The cofactor matrix Q
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The cofactor matrix Q
When the topocentric local coordinate system with
its axes along the local north, east, and up .
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How to check?
QUALITY PDOP Very Good 1-3 Good 4-5 F
air 6 Suspect gt6
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Wide Area Augmentation System (WAAS)
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Wide Area Augmentation System

• The WAAS is an air navigation system
  to expand the GPS, with the goal of improving its
  accuracy, integrity, and availability.
• The WAAS specification requires it to provide a
  position accuracy of 7.6 meters or better for
  both lateral and vertical measurements.
• The ground segment is composed of multiple
  Wide-area Reference Stations (WRS). These ground
  stations monitor and collect information on the
  GPS signals, then send their data to three
  Wide-area Master Stations (WMS).
• 38 WRS stations , 20 in USA, 7 in Alaska, 1 in
  Hawaii, 1 in Puerto Rico, 5 in Mexico, and 4 in
  Canada

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Wide Area Augmentation System

• The space segment consists of multiple
  geosynchronous of communication satellites  which
  broadcast the correction messages generated by
  the WAAS Master Stations for reception by the
  user segment
• The user segment is the GPS and WAAS receiver,
  which uses the information broadcast from each
  GPS satellite to determine its location and the
  current time, and receives the WAAS corrections
  from the Space segment

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How It Works ?

• The signals from GPS satellites are received by
  Wide Area Reference Stations (WRS) sites.
• The GPS information collected by the WRS sites is
  forwarded to the WAAS Master Station (WMS).
• At the WMS, the WAAS augmentation messages are
  generated. These messages contain information
  that allows GPS receivers to remove errors in the
  GPS signal, allowing for a significant increase
  in location accuracy and reliability.

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How It Works ?

• The augmentation messages from the WMS to be
  transmitted to Geostationary communications
  satellites.
• The Receivers receive the WAAS augmentation
  message from Geostationary communications
  satellite and processes to estimate the position
  .
• WAAS also provides indications to receivers of
  where the GPS system is unusable due to system
  errors or other effects.

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How good is WAAS?

• With Selective Availability set to zero, and
  under ideal conditions, a GPS receiver without
  WAAS can achieve fifteen meter accuracy most of
  the time.
• Under ideal conditions a WAAS equipped GPS
  receiver can achieve three meter accuracy.
• Precision depends on good satellite geometry,
  open sky view, and no user induced errors.

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Local Area Augmentation System (LAAS)
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Local Area Augmentation System (LAAS)

• The Local Area Augmentation System (LAAS) is an
  all-weather aircraft landing system based on
  real-time differential correction of
  the GPS signal
• Basically LAAS is complement of the WAAS with
  seamless satellite based navigation system.
  Practical terms, this means that at locations
  where the WAAS is unable to meet existing
  navigation the LAAS is used to fulfill those
  requirements.
• The International Civil Aviation
  Organization (ICAO) calls this type of system is
  a Ground Based Augmentation System (GBAS). 

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Local Area Augmentation System (LAAS)
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How It Works ?

• Local reference receivers located around the
  airport send data to a central location at
  the airport.
• This data is used to formulate a correction
  message, which is then transmitted to users.
• A receiver on an aircraft uses this information
  to correct GPS signals, which then provides a
  standard  display for Landing System.

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Ambiguity Resolution
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Code Pseudorange
The pseudorange is the "distance" between the GPS
satellite at some transmit time and the receiver
at some receive time. Because the transmit time
and the receive time are different, it is
impossible to measure the true range between the
satellite and the receiver. The basic definition
of the pseudorange observable is
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Phase Pseudorange
Another observable, based on the carrier phase of
the signal, does not require the actual
information being transmitted. The basic
definition of the phase observable is
where N is the integer number of cycles
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Ambiguity
The integer number of cycles, N, is typically not
known and varies for every receiver-satellite
combination. As long as the connection between
the receiver and the satellite is not broken, N
remains constant while the fractional beat phase
changes over time. Because of the ambiguous
nature of N, it is referred to as the ambiguity
and can either be solved for by using the code
pseudoranges, or estimated.
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Ambiguity Resolution
1. Single-Frequency Phase Data
When phase (F)measurements for only one frequency
are available, the most direct approach is as
follows-
The ambiguity is denoted by N. As soon as the
ambiguity is determined as an integer value, the
ambiguity is said to be resolved or fixed.
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2. Dual-frequency phase data
This situation for the ambiguity resolution
improves significantly when using dual frequency
phase data. There are many advantages implied in
dual-frequency data because of the various
possible linear combinations that can be formed
like the wide-lane and narrow-lane techniques.
Denoting the phase data referring to the
frequencies f1 and f2 by F1 and F2 then-
Wide Lane F1 - F2 Narrow Lane F1 F2
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2. Dual-frequency phase data
The phase models in the modified form
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3. Combining dual-frequency carrier phase and
code data
The models for dual-frequency carrier phases and
code ranges, both expressed in cycles of the
corresponding carrier, can be written in the form-
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3. Combining dual-frequency carrier phase and
code data
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4. Combining triple-frequency carrier phase and
code data
The technique based on three carriers is denoted
as three carrier ambiguity resolution (TCAR).
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