GPS-RO
Study on " multipath " propagation during a radio occultation
1 Radio Occultation
Theory
2 Objective of my
study
3 EGOPS simulator :
Forward modeling part, Inverse Retrieval part
exemple of radio occultation simulation with exponential atmospphere
4 Simulation of
multipath effect with existing tool
5 Implementation of a
raytracing algorithm adapted to simulate multipath propagation
6 Quantifiyng
the refractivity gradients which can produce multipath
7 Conclusion and futur works
1 Radio Occultation Theory
residual time Dt1-Dtdirect (due
to atmosphere) ® Excess phase D j [s], [m], [rad]
- D
tdirect ® Calculated from precise orbital
positions of LEO and GPS
- D
t1 ® Observation
Set of measurement of Excess phase D j
n(r ,P,T)
2 Objective of my study
High refractivity gradients in the low atmosphere may cause two or more signals to
arrive simultaneously at the receiver " Multipath "
- The signal emitted by the GPS at two times t1 and t2 both arrive
at the LEO at the same time (case 1 of multipath)
- It is also possible that two rays emitted in two directions at same time arrive
simultaneously at the LEO (case 2 of multipath)
- The superposition of two signals into the receiver is S1mod+S2mod.
The standard PLL (phase lock loop) track the signal with strong amplitude.
- When signals are close in amplitude and frequency, the PLL can lose lock
- Objective:
Quantifiyng the refractivity gradients which can
produce multipath during a radio occultation
3 EGOPS Simulator
Forward modeling part
Inverse Retrieval part
Overall effect parameters of the atmosphere on the signal:
a
Impact parameter: a
Tangeant point: rt
Bouger’s rule :
Doppler shift : D j
+ RLG ®
®a , a
Oignon peeling
n(ri)
=
(abel
transform)
Profiles retrieval
N : refractivity
P : atmospheric pressure [mbar]
Pw : water vapor [mbar]
ne : electron number density per cubic meter [number of electron/m3]
f : transmitter frequency [Hz]
w : liquid water content [g/m3]
dry atmosphere (Pw = w = 0)and ionospheric correction (estimation
of ne to remove it)
Density:
Rd = 287 J deg-1 kg-1
: Gas constant for 1 kg dry air
Pressure can be obtain from density by integrating the equation of hydrostatic
equilibrium:
Pressure:
g = 9.81 m s-2
For a exponential model of atmosphere : 
: 
, 
or 
In theory, the upper integration limits of this hydrostatic
integral extend to an infinite altitude whereas the occultation observations do not. This
limitation introduce error in refractivity, density, pressure and temperature at altitudes
below zu
From the pressure profile, it is now possible to retrieve the
temperature profile.
Temperature:
Example of simulation
Model atmospher/ionosphere
Atmosphere : Exponential Atm 1D(RefAtm_Uog)
No Humidity included (moist air)
Ionosphere : No Ion
Retrieval Chain
Ionosphere Correction & Bending angle tool : IMG/UoG
BenAngle Ion.Corr. & Bend. Angle Retrieval.
Refractivity Profiles Retrieval/Inversion Tool : DMI Abel
Transform Refractivity Profile Retrieval.
Geographic Maps
Forward modeling part
Inversion modeling part
D
j ® a , a Bouger’s rule and Doppler shift
Profile of bending angle a
in function of a
4 Introduced a disturbance dN in forward profile
in order to simulate multipath effect on excess phase and amplitude
5 Implementation of a raytracing algorithm adapted to
simulate multipath propagation
Algorithm of raytracing
Initialisation
Detection
Signal from GPS is emitted in all direction. We
must find the direction of the ray which intercects the LEO
Time reference : (XL,YL)
® t = 0 periode of measurement te
Dichotomie on the initial angle f ® f i ® RG,i
= (XG,i,YG,i), j
i
Reception time LEO n.te ® Emission time GPS n.te-j i,n
Orbit propagateur gives real position RG,i,real = (Xg,i,real,Yg,i,real)
of GPS at time n.te-j i,n
When d = | RG,i,real
- RG,i | < e ® RG,n
= RG,i, j G,n = j i
Range of measurement : t = 0 ® t = M.te (Flag = 0)
Result of Detection
e = 100 m
t=0,te,2.te,3te
Extend to the case of multipath : heuristic
algorithm
6 quantifiyng the magnitude
of refractivity gradients which can produce multipath
Case 2 of multipath : two rays emitted in two directions at
same time arrive simultaneously at the LEO (these ray have two different tangeant point rt and have the same excess phase D
j )
- At an epoch of measurement during a radio occultation, there is the situation as follow:
sweep from the LEO to find from which position of GPS is emmitted the signal
Diagrame of gradient change to have multipath (case 2)
With this diagrame and the algorithm of detection in multipath mode, we
will be able to simulate multipath because the diagram gives the necessery gradient to
provoke multipath in the appropriate region (the region where is situated the GPS during
the radio occultation).
7 Conclusion
The existing tools can not simulate multipath propagation
Implementation of a raytracing simulator
- Extend to the case of multipath
Futur works
Diagrame of refractivity change to produce multipath (case 2) in all regions
quantifiyng the refractivity gradients which can produce multipath in case 1
- In case of multipath quantifiyng the magnitude of refractivity gradients which can
produce enough multipath to PLL lost lock.
Necessity to simulate the attenuation in amplitude on the ray during the propagation
Page last modified 27 August-1999
Mail to jh@acri.fr