arXiv:1001.0025v1  [cs.CR]  30 Dec 2009GNSS-based Positioning: Attacks and Countermeasures
Panos Papadimitratos and Aleksandar Jovanovic
EPFL
Switzerland
Email: firstname.lastname@epfl.ch
Abstract
Increasing numbers of mobile computing devices, user-
portable, or embedded in vehicles, cargo containers, or the
physical space, need to be aware of their location in order
to provide a wide range of commercial services. Most often,
mobile devices obtain their own location with the help of
Global Navigation Satellite Systems (GNSS), integrating,
for example, a Global Positioning System (GPS) receiver.
Nonetheless, an adversary can compromise location-aware
applications by attacking the GNSS-based positioning: It
can forge navigation messages and mislead the receiver into
calculating a fake location. In this paper, we analyze this
vulnerability and propose and evaluate the effectiveness of
countermeasures. First, we consider replay attacks, which
can be effective even in the presence of future cryptographic
GNSS protection mechanisms. Then, we propose and an-
alyze methods that allow GNSS receivers to detect the re-
ception of signals generated by an adversary, and then re-
ject fake locations calculated because of the attack. We
consider three diverse defense mechanisms, all based on
knowledge, in particular, own location ,time, andDoppler
shift, receivers can obtain prior to the onset of an attack.
We find that inertial mechanisms that estimate location
can be defeated relatively easy. This is equally true for the
mechanism that relies on clock readings from off-the-shelf
devices; as a result, highly stable clocks could be needed.
On the other hand, our Doppler Shift Test can be effective
without any specialized hardware, and it can be applied to
existing devices.
1 Introduction
As wireless communications enable an ever-broadening
spectrum of mobile computing applications, location or
position information becomes increasingly important for
those systems. Devices need to determine their own posi-
tion,1to enable location-based or location-aware function-
ality and services. Examples of such systems include: sen-
sors reporting environmental measurements; cellular tele -
phones or portable digital assistants (PDAs) and comput-
ers offering users information and services related to their
1In this paper, we are not concerned with the related but ortho g-
onal localization problem of allowing a specific entity to de termine
and ascertain the location of other devices.surroundings; mobile embedded units, such as those for
Vehicular Communication (VC) systems seeking to pro-
vide transportation safety and efficiency; or, merchandize
(container) and fleet (truck) management systems.
Global navigation satellite systems (GNSS), such as the
Global Positioning System (GPS), its Russian counter-
part (GLONAS), and the upcoming European GALILEO
system, are the most widely used positioning technology.
GNSS transmit signals bearing reference information from
a constellation of satellites; computing platforms nodes),
equipped with the appropriate receiver, can decode them
and determine their own location.
However, commercial instantiations of GNSS systems,
which are within the scope of this paper, are open to
abuse: An adversary can influence the location informa-
tion,loc(V), a node Vcalculates, and compromise the node
operation. For example, in the case of a fleet management
system, an adversary can target a specific truck. First, the
adversary can use a transmitter of forged GNSS signals
that overwrite the legitimate GNSS signals to be received
by the victim node (truck) V. This would cause a false
loc(V) to be calculated and then reported to the fleet cen-
ter, essentially concealing the actual location of Vfrom the
fleet management system. Once this is achieved, physical
compromise of the truck (e.g., breaking into the cargo or
hijacking the vehicle) is possible, as the fleet management
system would have limited or no ability to protect its as-
sets.
This is an important problem, given the consequences
such attacks can have. In this paper, we are concerned
with methods to mitigate such a vulnerability. In partic-
ular, we propose mechanisms to detect and reject forged
GNSS messages, and thus avoid manipulation of GNSS-
based positioning. Our investigation is complementary
to cryptographic protection, which commercial GNSS sys-
tems do not currently provide but are expected to do so
in the future (e.g., authentication services by the upcom-
ing GALILEO system [5]). Our approach is motivated by
the fundamental vulnerability of GNSS-based positioning
toreplay attacks [9], which can be mounted even against
cryptographically protected GNSS.
The contribution of this paper consists of three mecha-
nisms that allow receivers to detect forged GNSS messages
and fake GNSS signals. Our countermeasures rely on in-
formation the receiver obtained before the onset of an at-
1tack, or more precisely, before the suspected onset of an
attack. We investigate mechanisms that rely on own (i)
location information, calculated by GNSS navigation mes-
sages, (ii) clock readings, without any re-synchronization
with the help of the GNSS or any other system, and (iii)
received GNSS signal Doppler shift measurements. Based
on those different types of information, our mechanisms
can detect if the received GNSS signals and messages orig-
inate from adversarial devices. If so, location informatio n
induced by the attack can be rejected and manipulation
of the location-aware functionality be avoided. We clarify
that the reaction to the detection of an attack, and mecha-
nisms that mitigate unavailability of legitimate GNSS sig-
nals is out of the scope of this paper.
We briefly introduce the GNSS operation and related
work in Sec. 2. We discuss the adversary model and specific
attack methods in Sec. 3.2. We then present and analyze
the three defensive mechanisms in Sec. 4. Our findings
support that highly accurate clocks can be very effective
at the expense of appropriate clock hardware; but they
can otherwise be susceptible, when off-the-shelf hardware
is used. Location-based mechanisms can also be defeated
relatively easily. On the contrary, our Doppler Shift Test
(DST) provides accurate detection of attacks, even against
a sophisticated adversary.
2 GNSS Overview
2.1 Basic Operation
Each GNSS-equipped node Vcan receive simultaneously
a set of navigation messages NAV ifrom each satellite Si
in the visible constellation . Satellite transmitters utilize a
spread-spectrum technique and each satellite is assigned a
unique spreading code Ci. These codes are a priori pub-
licly known. Navigation messages allow Vto determine its
position, loc(V) = (XV, YV, ZV), in a Cartesian system, as
well global time, by obtaining a clock correction or time
offset,tV, also called the synchronization error . At least
four satellites should be visible in order for a receiver to
compute position and exact time, the so-called PVT (Po-
sition, Velocity and Time) or navigation solution [6]. This
computation relies on the pseudo-range measurements per-
formed by V, one pseudo-range per visible satellite, that is,
estimating the satellite-receiver distance based on the es ti-
mated signal propagation delay, ρi. For each pseudo-range
ρiestimated at V, the following equation is formed:
ρi=|si−loc(V)|+c·tV (1)
The satellite Siposition is si, the receiver position is
loc(V),cis the speed of light, and tVis the synchronization
error for V.2.2 Future Cryptographic GNSS Protec-
tion
Cryptographic protection ensures the authenticity and in-
tegrity of GNSS messages, i.e., ensures that NAV messages
generated solely by GNSS entities, with no modification,
are accepted and used by nodes. Currently, cryptography is
used in military systems, but it is not available for commer-
cial systems to provide authenticity and integrity. Public
or asymmetric key cryptography is a flexible and scalable
approach that does not require tamper-resistant receivers .2
Independently of the number of receivers present in the sys-
tem (possibly, millions or eventually hundreds of millions ),
a pair of private/public keys ki, Kican be assigned to each
satellite Si, with the public key bound to the satellite iden-
tity via a certificate provided by a Certification Authority.
Each receiver obtains the certified public keys of all satel-
lites in order to be able to validate NAV messages digitally
signed with the corresponding ki.Navigation Message Au-
thentication (NMA) [5] will be available as a GALILEO
service.
To further enhance protection, a different public-key
NMA approach was proposed in [7]. Each Sichooses a
secret spreading code for each NAV message but discloses
this, along with a hidden timing marker , in a delayed and
authenticated manner to the receiving nodes. If nodes can
maintain accurate clocks by means other than the GNSS
system alone, they can then safely detect messages that are
forged or replayed between the time of their creation and
the code disclosure. A similar idea using Secret Spreading
Codes (SSC) was presented in [11].
3 Attacking GNSS
3.1 Adversary model
The location (position) GNSS-equipped nodes obtain can
be manipulated by an external adversary, without any ad-
versarial control on the GNSS entities (the system ground
stations, the satellites, the ground-to-satellite commun ica-
tion, and the receiver). If any cryptographic protection
is present, we assume that cryptographic primitives are
not breakable and that the private keys of satellites can-
not be compromised. The adversary can receive signals
from all available satellites (depending on the locations o f
the adversary-controlled receivers). It is also fully awar e
of the GNSS implementation specifics and thus can pro-
duce fully compliant signals, i.e., with the same modula-
tion, transmission frequency equal to the nominal one, ft,
or any frequency in the range of received ones, fr; similarly,
transmitted and received signal powers, as well as message
preambles and body format (header, content).
We classify adversaries based on their ability to re-
produce GNSS messages and signals, considering ones
equipped with:
2To prevent the compromise of a single, system-wide symmetri c
key, shared among the GNSS and all nodes.
21. Single or multiple radios, each transmitting at the
same constant power, Pc
t, and frequency fc
t.
2. Single or multiple radios, each being ability to adapt
its transmission frequency, fj
t, over time; jis an index
of adversarial radios.
3. Multiple radios with adaptive transmission capabili-
ties as above, and additionally the ability to estab-
lish fast communication among any of the adversarial
nodes equipped with those radios.
Adversarial radios in all above cases can record GNSS
signals and navigation messages for long periods. For all
adversaries above, we consider a nominal range R, within
which adversarial transmissions can be received, with this
value varying for different adversarial radios. We denote
this as the area under attack . Clearly, the more powerful
and the more numerous radios an adversary has, the higher
its potential impact can be. In the sense, it can influence a
larger system area and potentially mislead more receivers.
We assume that the area under attack does not coin-
cide with the wireless system area. In other words, the
adversary has limited physical presence and communica-
tion capabilities. This implies that nodes can lock on ac-
tual GNSS signals for a period of time before entering an
area under attack. We do not dwell on how frequently and
under what circumstances nodes are under attack. Rather,
we investigate the strength of different defense mechanisms
given that a node is under attack. We abstract the phys-
ical properties of the adversarial equipment and consider
the periods of time it can cause unavailability and maintain
the receiver locked on the spoofed signal.
We emphasize that our attack model is notthe worst
case; this would be a receiver under attack during its cold
start, that is, the first time it is turned on and searches for
GNSS signals to lock on. However, our adversary model
corresponds to a broad range of realistic cases and it is a
powerful one. For example, returning to the cargo example
of the introduction: It will be hard for an adversary to
control a receiver from its installation, e.g., on a contain er,
and then throughout a trip. But it would be rather easy to
select a location and time to mount its attack. Regarding
the strength of the attacker, it is noteworthy that attacks
are possible without any physical access to and without
tampering with the victim node(s) software and hardware.
3.2 Mounting Attacks against GNSS Re-
ceivers
The adversary can construct a transmitter that emits sig-
nals identical to those sent by a satellite, and mislead the
receiver that signals originate from a visible satellite. H ow-
ever, the attacker has to first force the receiver to lose
its “lock” on the satellite signals. This can be achieved
byjamming legitimate GNSS signals, by transmitting a
sufficiently powerful signal that interferes with and ob-
scures the GNSS signals [12]. Jammers are simple to con-
struct with low cost and very effective: for example, withReceived GNSS signal delayed 
Transmit after  treplay NAV message buffering 
Preamble 
detection 
Victim receiver 
V
Total 
delay treplay Adversary 
Figure 1: Illustration of the replay attack: the adversary
captures and replays the signal after some time treplay =
tmin
replay +τ, with the τ≥0 chosen by the adversary, and
tmin
replay >0 imposed by the specifics of the attack configu-
ration and the adversary capabilities.
1 Watt of transmission power, the reception of GNSS sig-
nals is stopped within a radius of approximately 35 km
radius [6,12].
Then, the adversary can spoof GNSS signals, i.e., forge
and transmit signals at the same frequency and with power
thatexceeds that of the legitimate GNSS signal at the re-
ceiver’s antenna. Satellite simulators are capable of broa d-
casting simultaneously signals carrying counterfeit navi ga-
tion data from ten satellites.3The spoofed signal can also
be generated by manipulating and rebroadcasting actual
signals ( meaconing ). As long as the lock of the victim re-
ceiver Von the spoofed signal persists, loc(V) is under the
influence or full control of the adversary.
Apart from jamming, the adversary could take advan-
tage of gaps in coverage , i.e., areas and periods of time for
which Vcannot lock on to more than three satellite sig-
nals. Clearly, this can be often possible in urban areas or
because of the terrain, such as tunnels or obstructions from
high-rise buildings. We do not consider further this case,
as such loss of satellite signals is not under the control of
the attacker. Nonetheless, the tests we propose here are ef-
fective independently of what causes receivers to loose loc k
on GNSS signals.
3.3 Replay attack
Thereplay attack can be viewed as a part of a more general
class of relay attacks : the attacker receives at one location
legitimate GNSS signals, relays those to another location
3The adversary can deceive the receiver after down-conversi on
of the satellite signal, with one component in-phase and one in-
quadrature:
I(t) =aiCa(t)M(t)cos(ft) (2)
Q(t) =aqCa(t)M(t)sin(ft) (3)
Cais the C/A (Course/Aquisition) code, M(t) is the NAV message,
and coefficients aiandaqrepresent the signal attenuation. The at-
tacker could pick the amplifying coefficients aiandaqsuch that the
received signal power exceeds the nominal power od a GPS sign al [13].
3where it retransmits them without any modification. This
way the adversary can avoid detection if cryptography is
employed, while it can “present” a victim with GNSS sig-
nals that are not normally visible at the victim’s location.
In this paper, we abstract away the placement of adversar-
ial nodes, and we characterize the replay attack by two fea-
tures: (i) the adversarial node capability to receive, reco rd
and replay GNSS signals, and (ii) the delay treplay between
reception and re-transmission of a signal.
The GNSS signal reception and replay can be done
at the message or symbol level, or it can be done by
recording the entire frequency band and replaying it with-
out de-spreading signals. The latter, more involved and
thus costly, would enable the attacker to mount an at-
tack against the delayed-disclosure secret spreading code
approach, as pointed out in [7], not only for long replay-
ing delays but also for very short ones. Clearly, such an
instantiation of the replaying attack implies a more sophis -
ticated adversary than one replaying symbols or messages.
For example, the adversary would need to infer, possibly by
possessing a legitimate receiver, the start of NAV messages
to replay signals accordingly
Thetreplay delay between reception and re-transmission
depends on the attack configuration (e.g., the distance be-
tween the receiving and re-transmitting adversarial radio s,
the physics of the signal propagation, and, when applica-
ble, the delay for the adversary to decode the GNSS signal).
We capture such factors by considering tmin
replay >0, a min-
imum delay that the adversary cannot avoid. Beyond this,
the attacker can choose some additional delay τ≥0, such
that it replays the signal after treplay =tmin
replay +τ. We
illustrate a replay attack in Fig. 1: The recording of the
NAV message starts after its beginning is detected, due to
the preamble 10001011, with length of eight chips, and the
decoding of the NAV message first bit. This corresponds
totmin
replay = 20ms: the transmission rate of 50 bit/s implies
that 20ms are needed for the first bit to be received by an
adversarial radio.
The adversary can choose different treplay values for sig-
nals from different satellites, even though “blind” replayi ng
of all NAV signals with the same delay can be effective. The
selection of which signals (from which satellites) to relay of-
fer flexibility. But even the “blind” replaying of all NAV
signals (the entire band) can be effective: treplay controls
the “shift” in the PVT solution. Essentially, treplay con-
trols the “shift” in the PVT solution the adversary induces
to the victim node(s).
Fig. 2 shows the impact of a replay attack as a function
of the spoofing stage of the attack: (i) the location offset
or error, i.e., the distance between the attack-induced and
the actual victim receiver position, and (ii) the time offset
or error, that is, the time difference between the attack-
induced clock value and the actual time. We consider for
this example trelay= 20ms, as the first bit decoding de-
lay dwarfs the preamble detection and propagation delays.
This is indeed a very subtle attack we refer to [9] for a range
oftreplay values, which shows that the larger the treplay, as0 50 100 150 200 250 300010002000300040005000600070008000900010000
Attack duration  [s]Distance offset  [m]
(a)
0 50 100 150 200 250 300050100150200250300350
Attack duration [s]Time offset   [ms]
  
(b)
Figure 2: Impact of the replay attack, as a function of
thespoofing attack duration. (a) Location offset or er-
ror: Distance between the attack-induced and the actual
victim receiver position. (b) Time offset or error: Time
difference between the attack-induced clock value and the
actual time.
the adversary tunes its τvalue, the higher the location and
time offsets.
Even for a very low treplay, while the mobile node re-
ceiver is still locked on the attacker-transmitted signals , the
location error increases, with the victim receiver “dragge d”
away from its actual position. Each millisecond of trelay
translates approximately into 300m of location offset for
each pseudorange (as the speed of light, c, is taken into
account), with the actual “displacement” of the victim de-
pending on the geometry (e.g., position of the satellite
whose signals were replayed).
As for the time offset, which can be viewed as a side-
effect of the attack: it is in the order of less than one mil-
lisecond per second, and it can very well go easily unnoticed
by the user. With a given trelay, every time the victim re-
ceiver re-synchronizes, typically at the end of a NAV mes-
sage that lasts 30 sec, treplay will emerge as tVfrom the
PVT solution and thus will be accumulated as part of the
time offset shown in Fig. 2.
4 Defense mechanisms
We investigate three defense mechanisms that rely on a
common underlying three-step idea. First, the receiver col -
lects data for a given parameter during periods of time it
deems it is not under attack; we term this the normal mode .
4Second, based on the normal mode data, the receiver pre-
dicts the value of the parameter in the future. When it
suspects it is under attack, it enters what we term alert
mode. In this mode, the receiver compares the predicted
values with the ones it obtains from the GNSS functional-
ity. If the GNSS-obtained values differ, beyond a protocol-
selectable threshold, from the predicted ones, the receive r
deems it is under attack . In that case, all PVT solutions
obtained in alert mode are discarded. Otherwise, the sus-
pected PVT solutions are accepted and the receiver reverts
to the normal mode.
In this work, we consider three parameters: location ,
time, andDoppler Shift , and we present the corresponding
detection mechanisms, Location Inertial Test ,Clock Offset
Test, andDoppler Shift Test . We emphasize again that all
three mechanisms rely on the availability of prior informa-
tion collected in normal mode. But they are irrelevant if
the receiver starts its operation without any such informa-
tion (i.e., a cold start ).
To evaluate the proposed schemes, we use GPS traces
collected by an ASHTECH Z-XII3T receiver that out-
puts observation and navigation (.obs and .nav) data into
RINEX ( Receiver Independent Exchange Format ) [8]. We
implement the PVT solution functionality in Matlab, ac-
cording to the receiver interface specification [8]. Our im-
plementation operates on the RINEX data, which include
pseudoranges and Doppler frequency shift and phase mea-
surements. We simulate the movement of receivers over a
period of T= 300 s, with their position updated at steps of
Tstep= 1sec.
4.1 Location Inertial Test
At the transition to alert mode, the node utilizes own lo-
cation information obtained from the PVT solution, to
predict positions while in attack mode. If those positions
match the suspected as fraudulent PVT ones, the receiver
returns to normal mode. We consider two approaches for
the location prediction: (i) inertial sensors and (ii) Kalm an
filtering.
Inertial sensors , i.e., altimeters, speedometers, odome-
ters, can calculate the node (receiver) location indepen-
dently of the GNSS functionality.4However, the accuracy
of such (electro-mechanical) sensors degrades with time.
One example is the low-cost inertial MEMS Crista IMU-15
sensor (Inertial Measurement Unit).
Fig. 3 shows the position error as a function of time [4],
which is in our context corresponds to the period the re-
ceiver is in the alert mode. As the inertial sensor inaccurac y
increases, the node has to accept as normal attack-induced
locations. Fig. 4 shows a two-dimensional projection of
two trajectories, the actual one and the estimated and er-
roneously accepted one. We see that over a short period
4They have already been used to provide continuous navigatio n
between the update periods for GNSS receivers, which essent ially are
discrete-time position/time sensors with sampling interv al of approx-
imately one second0102030405060708090100050100150200250300
GNSS unavailability period [s]Inertial navigation error [m]
  
Figure 3: Location error of Crista IMU-15 inertial sensor,
as a function of the GNSS unavailability period.
3.456 3.458 3.46 3.462 3.464 3.466 3.468
x 1065.295.35.315.325.335.345.355.365.375.38x 105
 
X coordinate [m] Y coordinate [m]
Attacker−induced trajectory
Actual trajectory
Figure 4: Illustration of location error using inertial sen -
sors: Actual vs. estimated when under attack trajectory.
of time, a significant difference is created because of the
attack.
A more effective approach is to rely on Kalman filtering
of location information obtained during normal mode. Pre-
dicted locations can be obtained by the following system
model:
Sk+1= Φ kSk+Wk (4)
withSkbeing the system state, i.e., location ( Xk, Yk, Zk)
and velocity ( V xk, V yk, V zk) vectors, Φ kthe transition
matrix, and Wkthe noise. Fig. 5 illustrates the location
offset for a set of various trajectories. Unlike the case that
only inertial sensors are used, with measurements of iner-
tial sensors (with the error characteristics of Fig. 3 used
as data when GNSS signals are unavailable, filtering pro-
vides a linearly increasing error with the period of GNSS
unavailability.
Overall, for short unavailability periods, inertial mech-
anisms can be effective. As long as the error (Y axes of
Figs. 4, 5) does not grow significantly, the replay attack
can be detected. But for sufficiently high errors, the re-
play attack impact can remain undetected. We remind the
reader that the x-axes in Fig. 2 provide the duration of the
spoofing attack - the transmission (replay) of GNSS signals
- and they are not to be confused with the duration of the
GNSS period of unavailability in the x-axis of Figs. 4, 5.
50 50 100 150 200 250 300020040060080010001200
Time [s]Distance offset [m]
Figure 5: Distance error of inertial mechanisms with
Kalman filtering, as a function of the GNSS unavailabil-
ity period.
0 5 10 15 20 25 30−9−8.5−8−7.5−7−6.5−6x 10−3
Time  [30s step]Time offset  [s]
  
Figure 6: Clock offset for the ASHTECH Z-XII3T receiver,
during a 900 sec period with no re-synchronization.
4.2 Clock Offset Test
Each receiver has a clock that is in general imprecise, due
to the drift errors of the quartz crystal. If the reception
of GNSS signals is disrupted, the oscillator switches from
normal to holdover mode. Then, the time accuracy de-
pends only on the stability of the local oscillator [2,6]. Th e
quartz crystals of different clocks run at slightly different
frequencies, causing the clock values to gradually diverge
from each other (skew error).
A simulation based study [2] of quartz clocks claims that
coarse time synchronization can be maintained at microsec-
ond accuracy without GPS reception for 350 sec in 95%
cases. This means that quartz oscillators can maintain
millisecond synchronization for few hours, including ran-
dom errors and temperature change inaccuracies. Indeed,
in such a case, the adversary would need to cause GNSS
availability for long periods of time, for example, tens of
hours, before being able to mount a relay attack that causes
a time offset in the order of tens of milliseconds.
However, without highly stable clocks, mounting attacks
against the Clock Offset Test can be significantly easier.
This can be the case for a ASHTECH receiver, for which
time offset values are shown at successive points in time,
each 30 seconds apart, in Fig. 6. We clarify this is notto be perceived as criticism for a given receiver or to be
the basis for the suitability of the Clock Offset Test. As
explained above, the stability of the receiver clock deter-
mines the strength of this test. But the data in Fig. 6,
over a period of 900 seconds, exactly demonstrates that
for commodity receivers significant instability is observe d;
time offset values are in the order of ten milliseconds (or
slightly less). Consequently, the adversary would need to
jam for roughly a couple of minutes, force the receiver to
consider as acceptable a time offset of 20 to 32 millisec-
onds, and thus be mislead by a replay attack as detailed in
Sec. 3.
Finally, we note that we do not consider here the case
of synchronization by means external to the GNSS system.
For example, if the receiver could connect to the Internet
and run NTP, it could obtain accurate time. But this would
be an infrequent operation (in the order of magnitude of
days), thus useful only if highly stable clock hardware were
available.
4.3 Doppler Shift Test (DST)
Based on the received GNSS signal Doppler shift, with
respect to the nominal transmitter frequency ( ft=
1.575GHz), the receiver can predict future Doppler Shift
values. Once lock to GNSS signals is obtained again, pre-
dicted Doppler shift values are compared to the ones cal-
culated due to the received GNSS signal. If the latter are
different than the predicted ones beyond a threshold, the
GNSS signal is deemed adversarial and rejected. What
makes this approach attractive is the smooth changes of
Doppler shift and the ability to predict it with low, es-
sentially constant errors over long periods of time. This
in dire in contrast to the inertial test based on location,
whose error grows exponentially with time.
The Doppler shift is produced due to the relative motion
of the satellite with respect to the receiver. The satellite
velocity is computed using ephemeris information and an
orbital model available at the receiver. The received fre-
quency, fr, increases as the satellite approaches and de-
creases as it recedes from the receiver; it can be approxi-
mated by the classical Doppler equation:
fr=ft·(1−vr·a
c) (5)
where ftis nominal (transmitted) frequency, frreceived
frequency, vris the satellite-to-user relative velocity vector
andcspeed of radio signal propagation. The product vr·
arepresents the radial component of the relative velocity
vector along the line-of-sight to the satellite.
If the frequency shift differs from the predicted shift for
each visible satellite Siin the area depending on the data
obtained from the almanac (in the case when the naviga-
tion history is available), for more than defined thresholds
(∆fmin,∆fmax) or estimated Doppler shift from naviga-
tion history differs for more than the estimated shift, know-
ing the rate ( r), the receiver can deem the received signal
as product of attack.
650 100 150 200 250 3002300235024002450250025502600265027002750
Time [s]Frequency offset [Hz]
  
Measured Doppler shift [Hz ] 
Linear approximation
Prediction bounds
Figure 7: Measured and approximated Doppler frequency
shift.
TheAlmanac contains approximate position of the satel-
lites, ( Xsi, Y si, Zsi), time and the week number ( WN, t ),
and the corrections, such that the receiver is aware of the
expected satellites, their position, and the Doppler offset .
Because of the high carrier frequencies and large satel-
lite velocities, large Doppler shifts are produced ( ±5kHz),
and vary rapidly (1 Hz/s). The oscillator of the receiver
has frequency shift of ±3KHz, thus the resultant frequency
shift goes therefore up to ±9KHz. Without the knowledge
of the shift, the receiver has to perform a search in this
range of frequencies in order to acquire the signal. The
rate of Doppler shift receiving frequency caused by the rel-
ative movement between GPS satellite and vehicles approx-
imately 40 Hz per minute to the maximum. These varia-
tions are linear for every satellite. If the receiver is mobi le,
the Doppler shift variation can be estimated knowing the
velocity of the receiver( [3]).
In our simulations, Doppler shift is analyzed for each
available satellite (number of available satellites varie s). To
be consistent with results shown for other mechanisms, we
present results for DST for the 300sec period.
We observe in Fig. 7 the Doppler shift variation based
on data collected by an ASHTECH receiver: the maximum
change in rate is within + /−20Hz around a linear curve
fitted to the data. This clues that with sufficient samples,
the future Doppler Shift rate, and thus the shift per se,
values can be predicted. In practice, we observe that 50
sec of samples, with one sample per second, appear to be
sufficient.
More precisely, the rate of change of the frequency shift,
Di(t), is computed for each satellite, Si, as:
ri=dDi(t)
dt(6)
which can be approximated by numerical methods. Based
on prior samples for each Di, available for some time win-
dow the frequency shift can be predicted based those sam-
ples and the estimate rate of change of the Doppler shift.
Based on prior measured statistics of the signal at the re-
ceiver, the variance σ2of a random component, assumed
to beN(0, σ2), can be estimated. This random component0 50 100 150 200 250 300−10000100020003000
Time [s]Frequency offset [Hz]SV−1
0 50 100 150 200 250 300−10000−50000
Time [s]Frequency offset [Hz]SV−4
  
0 50 100 150 200 250 3000200040006000
Time [s]Frequency offset [Hz]SV−7
0 50 100 150 200 250 3000100020003000
Time [s]Frequency offset [Hz]SV−13
0 50 100 150 200 250 300−4000−20000
Time [s]Frequency offset [Hz]SV−20
0 50 100 150 200 250 300−10000100020003000
Time [s]Frequency offset [Hz] SV−24
0 50 100 150 200 250 300−4000−20000
Time [s]Frequency offset [Hz] SV−25
Figure 8: Doppler shift attack; unsophisticated adversary .
The dotted line represents the predicted and the solid line
the measured frequency offset.
is due to signal variation (including receiver mobility, RF
multipath, scattering). Its estimation can serve to deter-
mine an acceptable interval around the predicted values.
The adversary is mostly at the ground and static or mov-
ing with speed that is much smaller than the satellite ve-
locity, which is in a range around 3km/s. Thus, the adver-
sary will not be able to produce the same Doppler shift as
the satellites, unless it changes its transmission frequen cy
to match the one receivers would obtain from GNSS sig-
nals due to the Doppler shift. An unsophisticated attacker
would then be easily detected. This is illustrated in Fig. 8:
After a “gap” corresponding to jamming, there is a striking
difference, between 100 and 150 seconds, when comparing
the Doppler shift due to the attack to the predicted one.
The case of A sophisticated adversary that controls its
transmission frequency (the attack starts at 160 s)is shown
in the Fig. 9. The adversary has multiple adaptive ra-
dios and it operates according to the following principle: i t
predicts the Doppler frequency shift at the location of the
receiver, and it then changes its transmission frequency
accordingly. If the attacker is not precisely aware of the
actual location and motion dynamics of the victim node
(receiver), there is still a significant difference between t he
predicted and the adversary-caused Doppler shift. This
is shown, with a magnitude of approximately 300 Hz, in
Fig. 9; a difference that allows detection of the attack.
5 Conclusion
Existing GNSS receivers are vulnerable to a number of
attacks that manipulate the location and time the re-
ceivers compute. We qualitatively and quantitatively ana-
lyze those in this paper, and identify memory-based mech-
anisms that can help in securing GNNS signals. In particu-
lar, we realize that location-based inertial mechanisms an d
a clock offset test can be relatively easily defeated, with th e
adversary causing (through jamming) a sufficiently long
period of unavailability. In the latter case, only special-
ized highly stable clock hardware could enable detection of
fraudulent GNSS signals. Our Doppler Shift Test provides
70 50 100 150 200 250 300020004000
Time [s]Frequency offset [Hz]SV−1
  
0 50 100 150 200 250 300−10000−50000
Time [s]Frequency offset [Hz]SV−21
  
0 50 100 150 200 250 3000500010000
Time [s]Frequency offset [Hz]SV−7
  
0 50 100 150 200 250 300020004000
Time [s]Frequency offset [Hz]SV−25
  
0 50 100 150 200 250 300−4000−20000
Time [s]Frequency offset [Hz]SV−9
  
0 50 100 150 200 250 3000100020003000
Time [s]Frequency offset [Hz]SV−29
  
0 50 100 150 200 250 300−4000−20000
Time [s]Frequency offset [Hz]SV−13
  
Figure 9: Doppler shift attack; sophisticated adversary.
The dotted line represents the predicted and the solid line
the measured frequency offset.
resilience to long unavailability periods without special ized
equipment.
Our results are the first, to the best of our knowledge,
to provide tangible demonstration of effective mechanisms
to secure mobile systems from location information manip-
ulation via attacks against the GNSS systems.
As part of on-going and future work, we intent to further
refine and generalize the simulation framework we utilized
here, to consider precisely the effect of counter-measures
that only partially limit the attack impact. Moreover, we
will consider more closely the cost of mounting attacks of
differing sophistication levels, especially through proof -of-
concept implementations.
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