Signal Processing - September 2017 - 88

clocks. This is achieved through the usage of atomic clocks
GNSS signals reach the receiver antenna passing through
such as Cesium and RubidiumD. With the development of
active layers of the atmosphere. GNSS signal propagation
the Galileo system, new clock technologies have been inis affected by the ionosphere and the troposphere, which
troduced [18]. Along with Rubidium Atomic Frequency
delay the signals and can introduce disturbances such as
Standards, Galileo satellites are also equipped with passive
ionospheric scintillation. TF analysis proves effective in
hydrogen maser clocks. Since an error in time implies an
characterizing ionospheric events. Four TF techniques for
error in position, it is fundamental to conthe analysis of GNSS carrier phase meatinuously monitor the health status of the
surements affected by ionospheric disturJammers can emit singleGNSS clocks on the satellites and in the
bances are investigated in [13]. A network
or multicomponent
ground stations.
of closely spaced GNSS receivers was used,
The key performance indicator of an
and the respective receiver measurements
nonstationary signals
atomic clock is stability, the standard defiwere analyzed. The correlation between
that assume time-varying
nition of which is the Allan variance (AVAR)
receiver TFRs was used to estimate the
frequency characteristics.
[19]. The dynamic AVAR (DAVAR) is a
relative delays between the observations
representation of the time-varying stabilof an ionospheric event from the differity of an atomic clock [14]. The DAVAR is computed by slident receivers. Since the receivers were placed in known
ing the AVAR on the clock data and is a function of time and
positions, it was possible to estimate the drift velocity of
the observation interval. Since the AVAR has a simple conionospheric irregularities. This approach was practically
nection to the Haar wavelet and the power spectrum [20], the
demonstrated in [24].
DAVAR can be seen as a mixed time-scale/TFR. When the
In addition to natural propagation phenomena, GNSS sigclock behaves according to the specifications, the DAVAR
nal reception can be impaired by RF interference, i.e., by the
does not change in time and depends only on the observapresence of unwanted RF emissions in the GNSS frequency
tion interval. When an anomaly occurs, the DAVAR changes
band. TF analysis provides effective tools for interference
with time, and its shape depends on the type of anomaly
detection and mitigation [3], [9], [10], [25] and is usually
occurred [21]. The DAVAR is used in the Galileo system to
applied after analog-to-digital conversion on the samples
monitor the clocks of the precise timing facility, which genprovided by the GNSS front end, indicated as y [n] in Figure 3.
erates the Galileo system time, as well as to validate all of
A general approach for interference detection and mitigation
the atomic clocks on-board the Galileo satellites.
in a single-antenna receiver is discussed in the "Interference
The mesh plot in Figure 4 shows the dynamic Allan deviDetection and Excision" section. The availability of multiantenna
ation (DADEV), i.e., the square root of the DAVAR, of a
GNSS receivers provides additional opportunities for nonstasignal made by the sum of a white phase noise (WPN) and
tionary jamming suppression, where the spatial dimension is
a white frequency noise, two common noise components of
incorporated in the TF analysis framework [15], [16]. This
atomic clocks. The joint observation of the DADEV and its
advanced TF application is analyzed in the "From Single- to
confidence surface (solid red) [22] highlights an increase in
Multiantenna Receivers" section.
the WPN intensity at small observation interval x and large
After interference suppression, GNSS signals are protime t values, hardly noticeable from the corresponding
cessed by the signal processing blocks of the receiver,
ADEV v y (x) in Figure 4, which averages out this anomawhich produce measurements such as pseudoranges, Doplous behavior. The results provided in Figure 4 are merely an
pler frequencies, and carrier phase observations. In this
example of the benefits of TF approaches for the monitoring
case, TF analysis can also be beneficial, e.g., for smoothof GNSS clocks.
ing the measurements and reducing the impact of propagation impairments such as multipath. Although multipath
can be readily addressed within the framework described
in the "From Single- to Multiantenna Receivers" section,
multipath of satellite signals and its effect and remedia5.38e-011
tion are not discussed in this article.
y-(t )
-4.31e-011
1e-11

σy (τ )

Interference detection and excision

σy(t,τ )
1e-12
1e3
τ (s)
1e4

6
t (s)

10
× 105

FIGURE 4. Clock monitoring: the mesh plot and its confidence surface
(solid red) highlight the anomalous behavior of an atomic clock [23].

Most TF interference mitigation approaches for GNSS can be
described as a four-step process: TFR, interference detection,
interference excision, and TF synthesis or time-domain signal
reconstruction. The process is illustrated in Figure 5, which
also provides the functional relationships between the different steps. Depending on the application, some of the functional
blocks depicted in Figure 5 may not be present, and different
configurations may be obtained. In the first step, denoted as
TF analysis, the input samples provided by the receiver front

IEEE SIGNAL PROCESSING MAGAZINE

September 2017

Table of Contents for the Digital Edition of Signal Processing - September 2017