Embed Size (px)
Citation preview
• The troposphere is the lowest layer of the atmosphere that lies next to the Earth’s 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.
2. Troposphere
Troposphere
• As you move up into the troposphere the temperature decreases.
• At the top of this layer the air temperature is about - 60°C.
• Environmental Lapse rate 6.5 0C/km
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.
Tropospheric Delay
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.
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
• ZWD is proportional to PWV as: ZWD=Q.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 .
Precipitable Water Vapor (PWV)
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):
1
2
3
1( )sin( )
sin( )sin( )
sin( )
m kk
k
where is elevation angle
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:
PWV aT b
If ϵ is error between observed and modeled value of PWV then the equation can be written by least square method in following form:
2 2= (PWV )aT b
To calculate the value of a and b, let the partial derivatives of error with respect to a and b are zero:
2 2
= 0 = 0anda b
After solving the equation the two equations can be obtained in following form:
2
0
0
PWV a T nb
PWV T a T b T
Where n is number of observations. The values of constants a and b will explain the modelled relationship among PWV and temperature
Relation with Temperature
Sources of GPS ErrorSource Amount of Error
Satellite clocks: 1.5 to 3.6 meters Orbital errors: < 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
Geometry Measure
N
S
W E
Ideal Satellite Geometry
S
N
W E
Poor Satellite Geometry
Good Satellite Geometry
Poor Satellite Geometry
Good Satellite Geometry
Poor Satellite Geometry
GPS Satellite Geometry
• Satellite geometry can affect the quality of GPS signals and accuracy of receiver trilateration
• Dilution of Precision (DOP) reflects each satellite’s position relative to the other satellites being accessed by a receiver
• There are five distinct kinds of DOP
Dilution Of Precision
PDOP = Position Dilution Of Precision (Commonly Used)
GDOP = Geometric Dilution Of PrecisionVDOP = Vertical Dilution Of PrecisionHDOP = Horizontal Dilution Of PrecisionTDOP = Time Dilution Of Precision
• It’s 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 receiver’s position.
GPS Satellite Geometry
Dilution Of Precision (DOP)
Good DOP
Poor DOP
when measuring must have good DOP and good visibility
…may not always be possible
Dilution Of Precision (DOP)
The cofactor matrix Q
1( )T
Q A A
1
1 0 1 0 1 0
1 1
2 0 2 0 2 0
2 2 2
3 0 3 0 3 0
3 3 3
4 0 4 0 4 0
4 4 4
x x y y z zc
x x y y z z cA
x x y y z z c
x x y y z z c
2 2 20 0 0x x y y z z
The cofactor matrix Q
When the topocentric local coordinate system with its axes along the local north, east, and up .
The cofactor matrix Q
QUALITY PDOPVery Good 1-3Good 4-5Fair 6Suspect >6
How to check?
Wide Area Augmentation System (WAAS)
•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
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
Wide Area Augmentation System
•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.
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.
How It Works ?
±3m
±15m
•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.
How good is WAAS?
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).
Local Area Augmentation System (LAAS)
Local Area Augmentation System (LAAS)
•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.
How It Works ?
Ambiguity Resolution
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:
Code Pseudorange
R c t
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
R c t N
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.
Ambiguity Resolution1. Single-Frequency Phase Data
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.
When phase (Φ)measurements for only one frequency are available, the most direct approach is as follows-
1 1 Ionof N
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 Φ1 and Φ2 then-
Wide Lane = Φ1 − Φ2
Narrow Lane = Φ1 + Φ2
1 1 1 2 2 21 2
21 1 2
21 1 2 21 1 2
21 21 211 2
1 11 1 2 21 1 2
21 21
,
Let ide lane = - ,
1 1 = a f + N - b f
N
b baf N af Nf f
wand f f f N N N
f
f f N a f ff f
2. Dual-frequency phase data
The phase models in the modified form
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-
From the above equations
3. Combining dual-frequency carrier phase and code data
4. Combining triple-frequency carrier phase and code data
The technique based on three carriers is denoted as three carrier ambiguity resolution (TCAR).
After the successful computation of the N1 ambiguity, the same procedure may be applied accordingly to get the other two carrier ambiguities N2 and N3.
4. Combining triple-frequency carrier phase and code data
