Attitude Determination by Means of Dual Frequency GPS Receivers
Single and Dual Frequency Solution In GPS
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SINGLE AND DUAL FREQUENCY
SOLUTION IN GPS
Presented by:
JITHIN RAJ K
M.Tech (Communication Systems 2013-2014)
Hindustan University, Chennai
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1. Single Frequency Solutions:
Single frequency users cannot take advantage of the full
capacity of all GPS signals to eliminate ionoshperic effects.
To support single frequency users broadcast message contain
ionosphere model data which allows the computation of
approximate ionosphere group delay.
The code and carrier phase can be given as:
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Differencing both Eq 9.32 & 9.33 at epoch time ‘t’ we get:
It is function of:
1. Group delay
2. Initial ambiguity
3. Receiver and satellite hardware delay
4. The multhipath
If some delays are eliminated or ignored, then also it is
difficult to model.
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1.1 Ionospheric plate model:
Ionosphere is approximated at a particular receiver
location by a flat plate of equal thickness having
homogenous distribution of free electrons.
It does not consider the curvature of earth.
Vertical group delay can b given by:
Now combining Eq 9.35 and 9.34, neglecting hardware
and multipath terms:
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Vertical group delay and ambiguity can be eliminated from
code and phase observations.
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1.2 Daily Cosine Model
Slightly advanced model.
Consider earth rotation and daily motion of sun W.R.T
receiver location.
Ik,I,,P(t)=Vertical group delay
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1.3 Ionospheric Point Model:
Ionosphere begins at height of about 50km rather than at
earth’s surface.
Usually a mean ionospheric height of about 350km is
assumed.
Eq 9.35 can be replaced with:
Θ term is the elevation angle of satellite at ionosphere point.
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The projection of ionospheric point on the earth is called
subionosheperic point.
Factor F
It is called slant factor or obliquity.
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1.4 Generalization in Azimuth & Altitude:
It consider azimuth dependency of vertical group delay.
The variation in vertical angle is modeled by sine function.
It helps to measure the ionospheric delay more accurately.
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1.5 Broadcast Message & Ionospheric Model:
The satellite message contains 8 coefficients.
It uses cosine model for daily variation of ionosphere(Similar
to expression 9.37).
The amplitude and period of the cosine term are functions of
geomagnetic latitude and represented by third degree
polynomials.
The coefficients of these polynomials are transmitted as part
of navigation message.
The algoritham is shown below:
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F= Slant factor or obliquity
Ψ= Earth’s central angle between the user location and
ionospheric point.
ΨIP & λIP = geodetic latitude and longitude of ionospheric
point.
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2. Dual Frequency Ionospheric-Free Solution
Ionospheric delays and advances are frequency dependent.
It is possible to eliminate ionospheric effects using dual
frequency receivers.
Difficulty arises from a modulation offset between L1 and L2
satellite & possibly at receiver.
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The offset is determined by control segment, which is measured
by satellite manufacturer during broadcast message.
We allow a code offset fro the receiver and assume a relation
similar to 9.43, Now Psuodorange equations become
For a navigation solution of at least 4 satellites,the receiver code
offsets & other error components common to the station, are
absorbed by rxr clock estimate.
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Objective is to find a function of codes that does not depend on
ionosphere.
The ionosphere free function serves this purpose:
Eq 9.46 is not a function of ionospheric term.
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The dual frequency phase expression in units of cycles given
as:
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The ionospheric free carrier phase function is:
The multiplier for L1 carrier phase is given in Eq 9.47 and new
multiplier L2 carrier phase is:
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3.Dual Frequency Ionospheric Solutions:
Because of code phase delays and multipath ,the
determination of absolute ionosphere is not straight forward.
The code difference of 9.44 and 9.45 given as:
This function shows difficulties encountered when measuring
the ionosphere or TEC with dual frequency receivers.
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The ionospheric function for carrier phases follows readily 9.49
and 9.50 as
This function reflects the time variation of TEC.
From single freq. solution 9.34, it is clear that the code and
phase offsets cancel as long as the relations 9.43 and 9.53 are
valid.
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The complete form is:
Similar equation can be written for L2 carrier also.
The initial ambiguity and code phase offsets cancel completely
when differenced over time,as long as effects are const.
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The Eq 9.57 is called range difference equation.
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Thank You!!!!!!