Review of tropospheric, ionospheric and multipath
data and models
for Global Navigation Satellite Systems
Antonio Martellucci#1A, Roberto Prieto Cerdeira #2
#
European Space Agency, ESTEC, TEC-EEP
Keplerlaan 1, PB 299, NL-2200 AG Noordwijk, The Netherlands
1
Antonio.Martellucci@esa.int
Roberto.Prieto.Cerdeira@esa.int
2
Abstract— The implementation of the European Galileo
navigation system and the design of its future evolution require a
proper modelling of the effects introduced by the atmosphere
(tropospheric and ionospheric) and by multipath from the
environment surrounding the navigation receiver. All those
effects combine to reduce the performance (accuracy, integrity,
availability and continuity) of the navigation system and they
have to be proper accounted into the design and the operation of
the system. Those impairments may also impact system
performance by affecting ground segment operations such as
sensor station measurements or satcom data networks.
Examples of their application in GNSS related activities range
from design of the system and performance assessment by means
of system simulators, definition of the proper receiver correction
algorithms according to their application and utilization, design
of mitigation algorithms, characterization of the ground segment
monitoring stations, in-orbit validation and performance
monitoring; and the development of satellite-based and regional
augmentation systems.
The paper presents a review of the input data and models for the
tropospheric path delay, the ionospheric delay and scintillations
and multipath effects for different environments (sensor stations,
pedestrian, land mobile, aeronautical and indoor). The
propagation issues related to the development of GNSS system at
C band will also be discussed.
I. INTRODUCTION
Galileo will be the European civil Global Navigation
Satellite Systems (GNSS), interoperable with other GNSS
such as GPS or GLONASS and providing several services:
Open, Commercial, Safety of Life and Public Regulated
Services. In preparation for the deployment of the Galileo
System, the European Space Agency (ESA) initiated the
development of an overall Galileo System Test Bed (GSTBV2) including two Galileo In-Orbit Validation Element
(GIOVE) satellites: GIOVE-A (launched on 28th December
2005) and GIOVE-B (launched 27th April 2008) with several
objectives including: secure frequency spectrum allocated for
Galileo by ITU, validate signal in space performance,
characterise On-Board clocks and radiation environment, and
finally collect lessons on Ground Mission Segment and Space
Segment.
EGNOS (European Geostationary Navigation Overlay
System) is the SBAS (Satellite-based Augmentation System)
represents the European contribution to the first generation of
Global Navigation Satellite Systems (GNSS-1). EGNOS
augments GPS and GLONASS, providing real-time integrity
and accuracy for aeronautical, maritime and land mobile
trans-European network applications. It is interoperable with
other SBAS such as WAAS and MSAS and complies with
standards defined by the International Civil Aviation
Organization (ICAO).
GNSS are based on the broadcasting of electromagnetic
ranging signals. Those signals are based on one (or more) high
symbol rate pseudorandom sequences (PRNs) modulated with
a given spreading shape and they may suffer a number of
propagation impairments impacting the performance
(accuracy, availability, continuity or integrity) of the system.
For GNSS working in L-band the main effects are due to
Earth’s atmosphere and the characteristics of the local
environment of the receiver. On this sense, Earth’s
atmosphere can be classified on troposphere, whose main
effect is a group delay on the navigation signal due to water
vapour and the gas components of the dry air, this delay is
non-dispersive (independent of frequency); and the ionosphere,
the ionised part of the atmosphere, that induces a dispersive
group delay that is several of orders of magnitude larger than
the one from the troposphere. Others ionospheric effects such
as scintillations and refraction may be present.
The local environment may affect the navigation signal in
various ways such as: fading due to shadowing (the signal is
scattered and/or diffracted by obstacles (buildings,
vegetation, …) between satellite and receiver; multipath,
where replicas of the signal arrive to the receiver with a
certain delay and phase due to reflexion and diffraction with
surrounding objects. Ambient noise and interference, although
not considered propagation effects, they may impact
navigation performance.
Likewise, within ESA’s GNSS evolutions programme,
other candidate frequency bands are being studies such as C
and S-band. Studies on propagation impairments for GNSS at
C-band have been carried out recently, see [1],[10].
II. TROPOSPHERIC EFFECTS
Due to the refractive index N of the earth’s neutral
atmosphere (N > 1) GNSS microwave signals suffer from
tropospheric propagation delays. The total tropospheric delay
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in direction of a particular satellite - slant path delay (SPD) can be divided into a hydrostatic and a wet component. Using
mapping functions, these two delays are projected into zenith
direction and viceversa.
SPD(ε ) = m h (ε ) ⋅ ZHD + m w (ε ) ⋅ ZWD
(1)
SPD(ε) = slant path delay [m] along elevation angle ε
ZHD = zenith hydrostatic delay [m]
ZWD = zenith wet delay [m]
mh(ε) , mw(ε) = mapping functions of the hydrostatic
and wet path delay along elevation angle ε
For the the mapping functions, mh(ε) , mw(ε) , the model of
Niell [1] is currently used.
The ZHD and ZWD are related to the air refractivity N,
which in turn is determined by values of air total pressure, P
[hPa], temperature, T [K], and water vapour pressure, e [hPa].
e
e
N = K 1 ( P − e) + K 2 + K 3 2 ≡
T
T
(2)
e
e ⎞ −1
⎛
−1
k 1 ( P − e) Z d + ⎜ K 2 + K 3 2 ⎟ Z v
T
T ⎠
⎝
Zd and Zv are the compressibility factors of dry air and
water vapour. Capital K is used for the formulation that does
not include compressibility. In the following tables some
experimental values of air refractivity coefficients available
from different authors are given. The uncertainty of air
refractivity parameters, with particular regard to K3, produces
an rms fluctuation of the ZTD of about 6 mm on a global scale.
TABLE I
COEFFICIENTS OF THE NON-DOSPERSIVE AIR REFFACTIVTY
Author(s)
Smith&
Wintraub [2]
Thayer
[3]
Hasegawa and
Strokesb. [4]
Liebe
[5]
Bevis
weighted [6]
Bevisunweighted [6]
Rueger best avail. [7]
Rueger best aver [7]
K1
1/hPa
77.607
± 0.013
77.64
± 0.014
77.6
± 0.032
77.676
± 0.023
77.6
K2
K/hPa
71.6
± 8.5
64.79
± 0.08
69.4
±0.146
71.631
K3*10-5
K2/hPa
3.747
± 0.013
3.776
± 0.004
3.701
± 0.003
3.74656
69.4
3.701
77.6
± 0.05
77.695
± 0.013
77.689
± 0.0094
70.4
±2.2
71.97
± 10.5
71.295
± 1.3
3.739
± 0.012
3.75406
± 0.03
3.75463
± 0.0076
∞⎛
e ⎞
e
ZWD = 10 − 3 ⋅ ∫ ⎜ K 2′ + K 3 2 ⎟dh
(4)
h0
T
T
⎠
⎝
M
K 2′ = K 2 − K1 w = 22.1 [K/hPa]
Md
Md = 28.9644 ; Mw = 18.0152 are the Molar weights
of dry and wet air [g/mol]
The zenith wet delay can also be estimated, with a reduced
accuracy, from the vapour pressure at the height of the
receiver, e0, and the local climatological parameters, λ and Tm
related to the vertical profiles of air total pressure, temperature
and water vapour pressure.
R ⎛
K ⎞ e
ZWD (e0 , λ , TM ) = 10 −6 ⋅ d ⋅ ⎜⎜ K 2′ + 3 ⎟⎟ ⋅ 0 ≈
TM ⎠ λ + 1
gm ⎝
(5)
Rd K 3 e0
−6
≈ 10 ⋅
g m TM λ + 1
This equation is assumed to be valid under the following
λ +1
condition: e = e 0 ( p p 0 )
Rd = 287.054 [J/(Kg K)]
∞
∞
e
e
Tm = ∫ dh ∫ 2 dh = Effective Mean temperature of the
T
T
h0
h0
water vapor column above the receiver [K]
g m = g (ϕ , h0 ) = 9.784 ⋅ (1 − 0.00266 ⋅ cos(2 ⋅ ϕ ) − 0.00028 ⋅ h0 ) =
Gravity acceleration at the mass center of air [m/s2]
In the framework of the Galileo project ESA used the
European Centre for Medium-Range Weather Forecasts
(ECMWF) reanalysis product ERA15 covering the period
from 1979 to 1993 to derive the input parameters and the
coefficients for the calculation of ZHD ZWD. ERA15 global
fields are characterized by a horizontal resolution of 1.5 x 1.5
deg, a vertical resolution of 31 levels and a temporal
resolution of 6 hours (00, 06, 12, 18 UTC),. The 31 levels are
defined in terms of pressure (hPa), with a higher resolution in
the planetary boundary layer, where the levels follow the earth
surface. Values of temperature (K) and specific humidity
(kg/kg), associated with these pressure levels, are also
provided with the dataset. The analysis produced among the
others, monthly statistics (unconditioned and conditioned to
the hour of the day) of “surface data”, P, e, Tm, λ, with a
world-wide coverage.
Air total pressure, P, is assumed to be affected by a
seasonal variation:
The zenith hydrostatic delay ZHD can be modelled using
total pressure at the antenna site. The model of Saastamoinen
(see [6]) is a rather accurate hydrostatic model:
0.0022767 ⋅ p
(3)
ZHD =
1 − 0.00266 ⋅ cos 2ϕ − 0.00028 ⋅ h
ϕ:
Ellipsoidal latitude
h:
Surface height above the ellipsoid in [km]
p:
Total Surface pressure in [hPa]
Therefore the ZWD is given by the following integral along
the atmospheric profile:
(
)
D y − a 3i ⎤
⎡
X i D y = a1i − a 2 i cos ⎢2π
⎥
365.25 ⎦
⎣
a1i = average value of the parameter
a2i = seasonal fluctuation of the parameter
a3i = day of the minimum value of the parameter
Dy.= day of the year [1 ..365.25]
( )
(6)
In addition Tm, e and λ are assumed to be affected by both
seasonal and diurnal fluctuations:
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(
)
(
( ))
D y − a3 i ⎤
⎡
X i D y , H d = a1i − a 2 i cos ⎢2π
⎥
365.25 ⎦
⎣
(7)
H d − b3 i D y ⎤
⎡
−b 2 i D y cos ⎢2π
⎥
24
⎣
⎦
Hd= hour of the day [0..24)
b2i = amplitude of daily fluctuation.
b3i,= hour of the day at which the minimum value occur.
The model has been validated using and independent ECMWF
global product covering the period from March to October
2002 with a spatial resolution of 1 x 1 deg. The global map of
the model rms error is given in Figure 1. The overall rms
errors of ZTD, ZHD and ZWD are 4.5, 1.6 and 4.4 cm with
biases of 9, 0.6 and 8 mm, respectively. Those errors can be
reduced by using as input actual meteorological ground
measurements and as an additional step actual values of λ.
(
)
( )
error is dispersive, it can be estimated and eliminated by
GNSS receivers working at two or more frequencies.
The group delay experienced by an electromagnetic wave
propagating through the ionosphere, σiono, is directly
proportional to the Total Electron Content (TEC), neglecting
higher order terms which usually account for less than 0.1 %
of the delay), as follows:
40.3
40.3
(9)
σ iono =
⋅ N ⋅ dl =
⋅ sTEC
f
2
∫
path
f
2
where σiono is the group delay error [m], f is frequency [Hz], N
is electron density [electrons.m-3], sTEC is slant Total
Electron Content [electrons.m-2], and path is the propagation
path between receiver and satellite. The sTEC may also be
expressed in TECU (TEC units), where 1 TECU = 1016
electrons.m-2. At the L1 frequency (1575.42 MHz), the delay
is approximately 16 cm for 1 TECU. The value of TEC
depends on different factors such as time of the day, location,
season, solar activity (which is related to the epoch within the
solar cycle) or level of disturbance of the ionosphere, such as
those due to geomagnetic storms. An example of VTEC map
is shown in figure 2.
Fig. 1 Map of the rms error of the tropospheric model in blind mode
The input parameters of the model can be scaled from
surface to height h by assuming:
Tm (h) = Tms − α m ⋅ (h − hs )
(8)
am= lapse rate of the mean temperature
of water vapour, [K/km], also derived from ERA15.
As an example the error of the model at 5000 m, in the upper
part of the troposphere, the model error rms reduces to 2.5, 2.2
and 1 cm for ZTD, ZHD and the ZWD.
III. IONOSPHERIC EFFECTS
The ionosphere is a region of the Earth’s atmosphere
ionised by solar radiation and lying between about 50
kilometres up to several thousand kilometres from Earth’s
surface. The ionosphere affects radio wave propagation in
different ways such as refraction, absorption, Faraday rotation,
group delay, time dispersion or scintillations, and those effects
are dispersive.
For GNSS, working in L band, one of the most important
ionospheric effect is the pseudo-range error introduced by the
group delay on navigation signals (which is identical but with
opposite sign to the carrier phase advance). This delay, if not
corrected, can induce ranging errors up to several tens of
meters in L band for days with high levels of electron density
and low elevation satellites. As the ionospheric group delay
Fig. 2 VTEC map in a grid of 5x5 degrees derived with NeQuick.
EGNOS and other SBAS systems use a thin-shell
approximation of the ionosphere and broadcast VTEC values
for predefined grid points. A receiver, in order to correct
ionospheric delay, first estimates the VTEC at the pierce-point
(intersection between line-of-sight link from GPS satellite to
user terminal and the thin shell layer) by interpolation from
the surrounding grid points, and then applies a vertical-toslant mapping that depends on zenith angle at the pierce point.
Galileo single frequency receivers will implement an
algorithm for single frequency ionospheric corrections based
NeQuick electron density climatological model and broadcast
parameters
estimated
using
dual-frequency
TEC
measurements from a network of Ground Sensor Stations. The
algorithm estimates an Effective Ionisation Level (Az) for
each sensor station, applicable for a period of typically 24
hours. In order to cope with potential mismodellings
depending on location with respect to the magnetic field, the
Az parameter is fitted to a second order polynomial function
of the Modified Dip Latitude (MODIP):
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Error! Objects cannot be created from editing field codes.(
10)
where µ is MODIP (in degrees) and a0, a1, a2 are the Az
coefficients which are broadcast in Galileo Signal in Space
[11]. The Az is used in Galileo receivers as input parameter
for the NeQuick ionospheric model. The performance of the
algorithm has been analysed in several publications using IGS
data [12] and also data from GIOVE ground sensor stations
[13],[14]. Multi-frequency receivers can eliminate first order
ionospheric delay by combination of two or more frequencies.
For the accurate representation of instantaneous
ionospheric TEC, when dual frequency observables from
several stations are available, more accurate results are found
using a two layer model, such as the one proposed with the
WARTK technique [15].
Other effect related to TEC appears in receiver that uses
carrier smoothing filtering. Carrier smoothing is used in GPS
receivers to reduce the effects of multipath and thermal noise.
The noisy code measurements are used to estimate the bias on
more precise but ambiguous carrier measurements by means
of averaging with a Hatch filter. However, the code-carrier
divergence, i.e. the effect on which the code is delayed
proportionally to the TEC and the carrier is advanced by
nearly the same amount, limits the use of the smoothing
method by introducing a bias when large temporal ionospheric
gradients are encountered. In solar maximum conditions, rates
of change above 8 mm/s may occur in Europe with a
probability of 0.001 for a quiet day, and 0.01 for a day with
large geomagnetic storm [16]. For a 100-seconds smoothing, 8
mm/s is equivalent to a filter bias of -1.6 meters.
Ionospheric scintillation is the other main propagation
effect from the ionosphere on navigation signals. Ionospheric
scintillations are rapid fluctuations of amplitude and phase of
the radiowave signal caused by small-scale irregularities
which modify the ionospheric refractive index. The
development of Global Navigation Satellite Systems with
safety of life services, such as Galileo, has shown that
radionavigation signal propagation impairments due to
ionospheric scintillations are a key driver of the system
performance. Current analysis are based on ionospheric
models and data for nominal averaged situations, however,
extreme cases which happen more often during solar
maximum years have not been understood completely and
therefore the effects on GNSS under those situations is not
fully characterised.
The most commonly used parameter to characterise
intensity fluctuations is the amplitude scintillation index S4,
defined by equation:
12
⎛ I2 − I 2
⎞
⎟
(11)
S4 = ⎜
2
⎜
I ⎟
⎝
⎠
Likewise, phase scintillations are characterised by the
standard deviation of the phase variations σφ.
Strong scintillations can induce cycle slips and loss-of-lock
in GNSS receivers on one or more signals simultaneously.
Scintillations depend on location, time-of-day and solar
activity. During nominal conditions, strong levels of
scintillation are rarely observed in mid-latitudes, but they may
be encountered daily during post-sunset hours in low latitude
regions. Also in polar and auroral regions, non-negligible
levels of phase scintillations have been observed.
Ionospheric modelling is a challenging domain, depending
on solar activity and its interactions with geomagnetic field;
the ionosphere may deviate from its nominal behaviour. This
happens, for instance, during severe geomagnetic storms. In
those cases, it is essential for a safety of life system to confirm
that the integrity of the computed corrections is still
maintained while minimising the impact on availability and
continuity of service. For this reason, accurate models or
realistic synthetic/measured data of a disturbed ionosphere are
needed for a complete qualification.
The GISM model [17] is the model used as baseline for the
analysis of ionospheric scintillations in the different Galileo
segments. GISM is based on physical principles and statistical
analysis of ionospheric characteristics (phase and amplitude
PSD and PDF) and driven by an electron density
climatological model (NeQuick) behind. Figure 3 shows a
map of vertical S4 derived with GISM. A simple engineering
model for the analysis of amplitude scintillation based on
GISM outputs is presented in [18].
Fig. 3 Map of vertical S4 derived with GISM model
IV. MULTIPATH EFFECTS
Different propagation mechanisms (diffraction, reflection
and scattering) are combined together originating signal
variations that affect receiver performance. Shadowing and
blockage due to obstacles, frequency selective fading due to
multipath or large building penetration losses are some
examples of the impairments which GNSS receivers may
encounter due to the local environment.
In a GNSS receiver, after antenna, RF and A/D conversion,
the signal processing module, performs the autocorrelation of
the incoming signal with locally generated replicas of the
PRN codes in order to estimate the transit time of the signal
from the satellite and thus the pseudorange. In the presence of
multipath, the autocorrelation function is distorted, shifting
the zero-crossing of the discriminator function and thus
creating an error on the pseudorange estimation.
Multipath is characterised by: amplitude, phase, time delay
and phase rate of change. The phase rate of change is also
referred to as Doppler fading bandwidth and represents the
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relative Doppler frequency change between the direct and
multipath signal. For the analysis of multipath in static
receivers, the multipath code phase error envelope has been
extensively used in literature. This error envelope indicates
the error bounds of a single specular multipath ray at any
delay from the direct signal. It is often presented for a
maximum delay of 1.5 the chip period assuming that longer
delays do not affect the pseudorange estimation (true for
negligible sidelobes in the autocorrelation function). For
instance, Figure 4 plots the code phase multipath error
envelope for some of the Galileo signals for a Signal to
Multipath Ratio (SMR) of 6dB, bandwidth of 15 MHz, and
different discriminator spacings.
One of the current challenges for the analysis of multipath
is to derive a clear methodology to implement realistic and
reliable multipath models into any hardware and software
simulation environment, and that allows assessing multipath
performance in an unambiguous manner. A preliminary
method and results into this work is given in [21]. An example
of tracking error of BOC(1,1) signal for a given urban
vehicular simulation is shown in Figure 5.
Fig. 5 BOC(1,1) tracking for a simulation in urban environment.
Fig. 4 Code phase multipath error envelope for different signals and
discriminator spacings.
The analysis of single specular multipath gives a good
qualitative tool to understand different effects on the receiver.
However, this kind of multipath is not representative of most
environments and thus, complex channel models including a
large number of reflectors should be used. In several cases,
signal design with respect to multipath performance is
performed using the error envelope, which may lead to
misleading conclusions depending on the environment and
type of application.
For the Galileo Land Mobile case, a wideband channel
model based on [19] can be used. It is based on a Tap Delay
Line and it can be used in urban and rural (pedestrian and
vehicle) and fixed environments. The output of the model is a
complex fading time-series for each tap. The model is simple
enough to be adapted into hardware signal simulators for
receiver testing but it has several limitations such as a nonrealistic reduced number of taps to represent the delay
spreaded energy and a lack of elevation dependency. A more
versatile model is the proposed in [20] for Land mobile users.
The model includes deterministic and stochastic
representation of the multipath and the environment and it is
able to generate a time-varying direct signal and a large
number of reflections (in the order of 50) with varying delay,
phase and amplitude. The model takes into account satellite
elevation and azimuth, and changes in velocity of the vehicle
during the simulation. The major limitation of this model is
that the large number of output parameters is difficult to adapt
into hardware or software simulations.
V. CONCLUSIONS
It is important to understand the origin and impact of the
propagation effects discussed in this paper, and also to
develop reliable models and design adequate mitigation
techniques in order to achieve the required performance.
There are some effective impairment mitigation techniques for
some of them but in other cases they represent a challenge, in
particular for applications that require not only high accuracy
but also integrity of the signal, such as safety-of-life
applications.
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