IEEE - Aerospace and Electronic Systems - August 2023 - 18

An Integrated INS/GNSS System With an Attention-BasedDeepNetwork forDrones in GNSSDeniedEnvironments
of the network. This ceases the learning of initial layers
parameters [21]. LSTMs are RNNs capable of selectively
recognizing long sequences. LSTM can determine the
complicated temporal dynamics of drone movement by
directly correlating its current and previous states. As
illustrated in Figure 4, LSTM comprises several gates and
a memory cell to store information. The input and output
gates regulate the information flow into and out of the
cell. Many pieces of literature thoroughly study LSTM
networks [31]. One can model an LSTM cell without caring
about its inner working simply by writing
Figure 6.
Test platform and data acquisition instruments. UAV is equipped
with an autopilot and a flight data recorder to gather the needed
data. Spatial INS is used for reference data.
pooling layers. The resulting outputs are then fed to an
LSTM cell to be used in the final attention layer. The input
consists of 256 consecutive IMUs of the vehicle's accelerations
and angular velocities.
ACLSTM
Due to the sequentiality of the equations describing the
motion of a moving body, one of the best candidates to
implement the above NN design is to use LSTM networks
introduced to overcome the vanishing gradient in time
series estimations using RNNs. The main reason for gradient
vanishing in the learning process is that the back propagation
algorithm back propagates the prediction error of
the network through many successive nonlinear layers,
each of which multiplies the error by a small number
(<1), resulting in an almost zero error at the initial layers
Table 1.
Frequency Domain Specification of the SPATIAL
Parameters
Dynamic range
Non-linearity
Scale factor stability
Noise density
Bandwidth
0:0040
< 0.05%
< 0.05%
p
s
400 Hz
hk ¼ fLSTMh hk1;uk;ck1ðÞ
ck ¼ fLSTMc
ðÞhk1;uk;ck1
(2)
where hk, uk; and ck denote the output, input, and the
memory value ofan LSTM cell at time step k.
To improve furthermore on the capabilities of an
LSTM network, another level of data abstraction can be
used before the LSTM cell, extending NN's complexity.
LSTM cells are designed to extract temporal relationships
between input data, but fall short of extracting spatial
data. Multiple convolutional layers can be added to cover
this shortcoming before feeding input data to an LSTM.
The architecture used in this study utilizes two stacked 1D
CNN layers with a kernel size of9 and widths of248 and 240.
The idea behind using convolutional layers before an LSTM
cell is to extract spatial features of the INS data through
abstraction achieved using multiple layers of convolutions.
By feeding the resulting spatial feature to LSTM cells, one
can extract hidden temporal relationships between these spatial
features. This deep convolutional LSTM (CLSTM) network
is applicable to model spatiotemporal series without
considering increased computational complexity.
A max-pooling layer of size one and a 20% dropout is
applied following the two CNNs to reduce the effect of
the CNN's sensitivity to extracted feature's location and
avoid overfitting in the learning process. The max pooling
Gyroscope
2000 deg/sec
Accelerometer
16 g
< 0.05%
< 0.06%
ffiffiffiffiffiffi
Hz
100 mgffiffiffiffiffiffi
Hz
p
400 Hz
Magnet
4G
8G
< 0.08 %
< 0.09 %
210 mgffiffiffiffiffiffi
Hz
p
100 Hz
Barometer
10-120 KPa
-
-
0.56 Pa
p
50 Hz
This table presents thefrequency domain specifications ofthe sensors used in SPATIAL INS. Multiple sensors in this INS aid the navigation
with additional measurementsfor accurate navigation.
18
IEEE A&E SYSTEMS MAGAZINE
AUGUST 2023
ffiffiffiffiffiffi
Hz

IEEE - Aerospace and Electronic Systems - August 2023

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