IEEE - Aerospace and Electronic Systems - June 2022 - 26

GPS Spoofing Detection by Neural Network Machine Learning
Figure 6.
GPS spoofing detection neural network data flow.
ADJUSTING WEIGHTS
The incremental changes in the weights Dwl
jk can be
obtained from the gradients of the error function with
respect to the weights as
Dwl
jk ¼
@Ex
@wl
¼
jk
@Ex
@sl
j
@wl ¼ dl
@sl
j
jk
where Equation (19) can be rewritten in a vector-matrix
form as
DWl ¼ dl al1T
:
(20)
To keep the error close to zero, the Gradient Descent
(GD) method is used. The weights are changed in small increments
using the calculation of the derivative (or gradient) of
the error function. Applying the Steepest Descent (SD) algorithm
for minimizing the error function, the corrections to the
synaptic weights are made in the direction ofdecreasing error.
The change in the weights is thus proportional to the incremental
change and a learning rate parameter where 0 <
< 1 such that
wl
jk ¼ wl
jkdl
jal1
k
(21)
where Equation (21) can be rewritten in a vector-matrix
form as
Wl ¼ Wl
N
dl al1T
:
(22)
Figure 6 shows the overall data flow for the NN forward
propagation and backward propagation.
LEARNING ALGORITHM
The GD algorithm is a first-order iterative optimization algorithm
for finding a local minimumofa differentiable function.
If there are multiple local minima, then there is no guarantee
that the procedure will find the global minimum. Stochastic
Gradient Descent (SGD) replaces the actual gradient (calculated
from the entire dataset) by an estimate thereof (calculated
from a randomly selected subset of the data).
Computational burden is reduced for high-dimensional
26
j al1
k
(19)
problems achieving faster iterations although at the cost of a
slower convergence rate. For faster convergence, an adaptive
learning rate is used. Root Mean Square Propagation
(RMSProp) is a method where the learning rate is adapted for
each of the parameters by dividing the learning rate for a
weight by a running average of the magnitudes of recent gradients
for that weight. A further refinement is the Adaptive
Moment Estimation (Adam) method [20] where the running
averages ofboth the gradient and the second moments of the
gradient are used. The method is straightforward to implement,
computationally efficient, with low memory requirements,
appropriate for problems with noisy and/or sparse
gradients.
SPOOFING DETECTION TRAINING AND TESTING
DATASETS GENERATION
Datasets need to be generated for training the NN. The inputs
to the NN-based spoofing detector consist of the direct
authentic signals from GPS satellites and delayed spoofed signals.
Actually, the inputs are the metrics calculated from the
mixture ofauthentic and spoofed signals. To create such datasets,
the direct authentic signals transmitted from GPS satellites
are recorded and saved. The saved authentic GPS signals
are then used to generate the spoofed signals. The recorded
signals are first sampled at the frontend, down-converted to
the intermediate frequency (IF) range, and filtered before analog-to-digital
(A toD) conversion, as shown in Figure 7.
The next step is to generate the delayed spoofed signals
from the digitized authentic signals. The digitized
authentic signals are fed to a GPS simulator. The signal
power level is estimated. This is done in order to adjust
the power of the spoofing signals [11]. The authentic GPS
signals are then delayed and despread an appropriate
amount. The delayed and despread signals are then combined
with the authentic GPS signals to produce a mixture
of authentic and spoofed signals. Finally, the power level
of the combined signal is adjusted to be proportional but
slightly higher than the authentic GPS signals. The combined
mixed (direct authentic and delayed spoofed) signal
set shown in Figure 7 is used in the offline training of the
NN. Multiple datasets can be created by changing the
delay and amplitude specifications of the spoofing signal.
IEEE A&E SYSTEMS MAGAZINE
JUNE 2022
IEEE - Aerospace and Electronic Systems - June 2022

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