IEEE - Aerospace and Electronic Systems - June 2022 - 24

Table 1.
GPS Spoofing Detection by Neural Network Machine Learning
ACTIVATION FUNCTION
Each hidden layer contains one or more neurons and the output
ofeach neuron goes through an activation function,which
introduces nonlinearity, limits the amplitude of the neuron
output, and propagates the output of a neuron forward.
Table 1 presents the plot, function, derivative, and range ofa
few commonly used activation functions such as Linear,
Step, Sigmoid, Hyperbolic tangent (tanh), and Rectified Linear
Unit (ReLU). When the activation function is nonlinear,
the universal approximation theorem states that a two-layer
NN can be proven to be a universal function approximator.
Activation functions with finite range tend to be more stable
with gradient-based training methods, whereas those with
infinite range, training is generally more efficient. Except for
the Step and the ReLU, all other activation functions displayed
in Table 1 are continuously differentiable, which is a
desirable property when using gradient-based optimization
methods. Typically, an NN with one or more hidden layers,
together with their nonlinear activation functions, enables it
to achieve a desired nonlinear mapping ofinput to output.
TRAINING PROCESS
Training the NN implies learning the values of the parameters
(weights and biases) ofthe NN. This learning process in
anNN is an iterative process of " going forward and returning
backward " by the layers of neurons, as shown in Figure 4.
The " going forward " is a forward propagation ofinformation
and the " returning backward " is the back propagation of
error. The forward propagation occurs when the NN is

IEEE - Aerospace and Electronic Systems - June 2022

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