Evaluating the Impact of Convolutional Neural Network Layer Depth on the Enhancement of Inertial Navigation System Solutions

International Journal of Computer Networks & Communications (IJCNC) Vol.16, No.5, September 2024
DOI: 10.5121/ijcnc.2024.16504 59
EVALUATING THE IMPACT OF CONVOLUTIONAL
NEURAL NETWORK LAYER DEPTH ON THE
ENHANCEMENT OF INERTIAL NAVIGATION
SYSTEM SOLUTIONS
Mohammed AFTATAH and Khalid ZEBBARA
IMISR Laboratory, Applied Sciences Faculty Ait Melloul, Ibn Zohr University, Agadir,
Morocco
ABSTRACT
Secure navigation is pivotal for several applications including autonomous vehicles, robotics, and
aviation. The inertial navigation system estimates position, velocity, and attitude through dead reckoning
especially when external references like GPS are unavailable. However, the three accelerometers and
three gyroscopes that compose the system are exposed to various types of errors including bias errors,
scale factor errors, and noise, which can significantly degrade the accuracy of navigation constituting also
a key vulnerability of this system. This work aims to adopt a supervised convolutional neural network
(ConvNet) to address this vulnerability inherent in inertial navigation systems. In addition to this, this
paper evaluates the impact of the ConvNet layer's depth on the accuracy of these corrections. This
evaluation aims to determine the optimal layer configuration maximizing the effectiveness of error
correction in INS (Inertial Navigation System) leading to precise navigation solutions.
KEYWORDS
Inertial Navigation Systems, INS Errors, Convolutional Neural Networks, Layer Depth, Secure Navigation
1. INTRODUCTION
Inertial Navigation Systems (INS) come in various types, each suited for different applications
based on their accuracy, cost, and technological sophistication. Here are the primary types of
INS: fiber optic-based gyroscope, Ring laser-based gyroscope, and gyroscopes of the
mechanical type, and MEMS (Micro Electro Mechanical Systems) use tiny integrated circuits
incorporating accelerometers and gyroscopes. The raw accelerations across the three axes (x, y,
and z) are measured by the three-axis accelerometers (axial acceleration), while angular velocity
(rotation) is measured by the three-axis gyroscopes around these axes [1]. These systems are
much cheaper and smaller than traditional gyroscopic systems, making them ideal for commercial
applications like smartphones and drones [2]. However, they are generally less accurate over long
periods.
The loss of precision over extended periods for the MEMS-INS type arises from several error
sources including scale factor, noise, and bias, which significantly impact their performance.
Bias, a constant error that can drift over time, leads to cumulative inaccuracies in navigation
outputs [3]. Scale factor errors, which are inconsistencies in the sensor's response relative to the
actual motion, cause deviations proportional to the true movement. Noise, comprising both
random and systematic variations, further degrades measurement precision, complicating
accurate navigation [4]. Recently, many groups of researchers have investigated several neural

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networks to address these issues, including RNNs (Recurrent Nets), DRL (Deep learning-based
reinforcement), and ConvNets [5]. Furthermore, using additional layers enables neural networks
to better model and learn the complex relationships between the true motion of the system and
the raw measurements of the inertial sensors [6].
The approach proposed by the authors of [7], used a ConvNet (Convolutional Network) with the
aim of de-noising inertial measurements. Under constant specific forces and rotations, the
researchers gathered measurements from two distinct IMUs: a low-cost IMU and a high-grade
IMU. The algorithm used the high-grade IMU dataset to learn patterns and features in the
low-cost IMU measurements, ultimately generating a model based on ConvNet. The
results from their experiment demonstrate that ConvNet can effectively reduce sensor errors and
perform the accuracy. However, the authors have applied the methodology in a simulation-world
navigation setup. Furthermore, this methodology does not conclusively show how deep learning
can reduce error drifts for inertial sensors in real-world sensors. In [8], the authors employed
SRU-RNN for de-noising MEMS gyroscope signals, achieving substantial improvements in
reducing noise, bias instability, and angle random walk.
OriNet is a method detailed in [9], which inputs to the network of memory cells (Long Short-
Term Memory) the signals from a 3D gyroscope to produce corrected gyroscope signals. A loss
function was defined and minimized to measure the difference between the estimated and
actual orientations, training the LSTM model. OriNet was evaluated using a data pool from a
public drone, which demonstrated an approximate 80% enhancement in attitude performance. In
[10], the reinforcement-learning algorithms are employed to identify optimal parameters for
inertial calibration algorithms.
In 2019, Zhu et al. [11] introduced a NAS-RNN model to suppress noise in MEMS gyroscope
data, demonstrating significant improvements over traditional LSTM-RNN methods, with further
decreases in standard deviation values and attitude errors. The authors of [12] described an
approach, where a gyroscope is calibrated using a ConvNet, resulting in high accuracy in attitude
estimation. Wang et al. proposed in their work [13] a hybrid method integrating CNN-LSTM and
PSO-SVM to address temperature-induced errors in MEMS gyroscopes, resulting in a significant
reduction of temperature drift and improved gyroscope accuracy.
Moreover, a review paper by Podder et al. [14] provided a comprehensive analysis of artificial
intelligence applications in MEMS sensors, underscoring methods such as CNN, RNN, LSTM,
and ANN for process optimization, signal de-noising, and error correction, highlighting the
potential and effectiveness of artificial intelligence in performing MEMS sensors.
Numerous researchers have employed ConvNet and other AI (Artificial Intelligence) algorithms
to mitigate errors in inertial navigation systems. While these approaches have shown promise in
reducing such errors, the impact of the depth of layers within these networks has not been
thoroughly explored. This gap in the literature suggests that further investigation into the depth of
ConvNet layers could provide significant insights and potentially lead to more optimized
solutions for addressing INS errors.

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Table 1. A summarized table of existing methods for machine-learning-based correction of inertial
sensors.
Authors Year Model Learning Target sensors of correction
Chen et al. [7] 2018 ConvNet Supervised Accelerometer, gyroscope
Jiang et al. [8] 2018 Simple
Recurrent Unit
RNN (SRU-
RNN)
Supervised MEMS Gyroscope
Esfahani et al. [9] 2019 Orinet Supervised Gyroscope
Nobre and
Heckman [10]
2019 Reinforcement
learning
algorithms
Unsupervised Optimal parameters for
inertial calibration
Zhu et al. [11] 2019 NAS-RNN Supervised MEMS Gyroscope
Brossard et al.
[12]
2020 ConvNet Supervised IMU Gyroscope
Wang and Cao
[13]
2022 CNN-LSTM
and PSO-SVM
Supervised MEMS Gyroscope
Podder et al. [14] 2023 Artificial
intelligence
Applications
Supervised MEMS-Based Sensors
This paper can be summarized by its primary objectives as follows:
 Modeling INS sensors from a reference trajectory;
 Modeling the main errors affecting accelerometers and gyroscopes, specifically focusing
on bias, scale factor, and noise;
 Developing a CovNet algorithm to mitigate the errors of the MEMS sensors including
both accelerometers and gyroscopes;
 Exploring the adaptability of the CNN architecture through the manipulation of the
number of layers, assessing its impact on error mitigation;
 Comparison of the performance of the INS estimated positions before and following
the use of the proposed algorithm.
Six distinct sections are written to organize this paper: Firstly, Section 1 introduces this work.
Secondly, Section 2 contains a review of the literature, an outline of the primary contributions of
this paper, an explanation of INS, a discussion of the INS sensors' modeling and their inherent
errors, and an introduction to the ConvNets algorithm. Thirdly, the methodology employed to
implement the ConvNets algorithm is explained in Section 3 details. Fourthly, Section 4 details
the experiment. Additionally, Section 5 presents the findings in terms of the effectiveness of the
CNN algorithm in reducing errors in the output of the MEMS-INS. Finally, Section 6 provides
the conclusion of the paper by synthesizing the findings and discussing the future work planned
by our group.
2. BACKGROUND INFORMATION
2.1. Introduction To Inertial Navigation
An Inertial Navigation System operates independently (qualified as an autonomous navigation
system) and computes through a process known as dead reckoning the velocity, position, and
attitude of a mobile without the need for external references. This system utilizes six internal
sensors, three gyroscopes, and three accelerometers, respectively measuring raw angular

62
velocities and linear accelerations. These data from the internal sensors are integrated twice over
time, enabling the system to estimate with high accuracy the trajectory of the object.
Two well-known types of INS are Micro-Electro-Mechanical Systems INS (MEMS-INS) and
Gimbaled INS. This paper focused on MEMS-INS due to many advantages including small
dimensions, low cost, and power efficiency, turning them into a perfect choice for an extensive
range of applications.
2.1.1. Importance of MEMS-INS
The importance of MEMS-INS is evaluated by the extensive use of these sensors in multiple
industries. This significance is justified by several key factors:
- Firstly, the ability to operate independently of external signals such as GPS;
- Secondly, the deliverance of continuous navigation ;
- Thirdly, the high-speed computation is ideal for real-time processing and output;
- Fourthly, the resistance to jamming and spoofing attacks;
- Finally, the providence of a wide range of information including velocity, position, and
attitude in 3D.
2.1.2. Mems-Ins Mechanization
MEMS-INS Mechanization is a set of INS sensors' equations employed to derive navigation
outputs, including the mobile’s position, velocity, and attitude, from the measurements of inertial
sensors, specifically the accelerations, and rotations. In this study, two references are
frequently used: the ENU frame (East, North, Up) and the chassis frame (body frame).
Upcoming, the dynamic equations are expressed in the ENU frame. Additionally, the ENU
system will be referred to as the navigation frame. The chassis frame is defined at the center of
the inertial system. These equations are given in (1), (2), and (3) [15, 16, 17]:
LLa n
r DV
 (1)
n n b n n n n
b ib ie en
v C f (2 ) v g
      
(2)
n n b
b b nb
C C (S( ))
  (3)
Here,  
T
n
r    
refers to the latitude, longitude, and altitude in the ENU frame,
 
T
n
e n u
v v v v

presents the linear velocity,
b
ib
f
are the accelerometer's raw measurements in the body frame,
n
b
C
and
b
n
C
are used to convert values from the chassis frame to the ENU coordinate system and to
transform values from the ENU coordinate system to the chassis frame, respectively. They
depend on three angles yaw, pitch, and roll (ψ, θ, and φ: Euler angles).
b
nb

is the angular velocities directly measured by the gyroscopes about the three axes of the INS
after removing
b
ie

and
b
en

,
n
ie

is the expression in the ENU frame of the Earth's rotation rate,
n
en

is the ENU frame’s rotation rate vector relative to the Earth,

63
n
g presents the vector of the gravity,
D presents a matrix to transform values from the navigation frame to the LLA (latitude,
longitude, and altitude) frame as given in (4).
m
n
1
0 0
R h
1
D 0 0
(R h)cos
0 0 1
 
 

 
 
  
 
 
 
 
  (4)
Where,
m
R the radii of curvature in the meridian,
n
R is the prime vertical,
2 2
2
2
a b
e
a


is the Earth’s eccentricity,
a is the Earth’s semi-major axis,
b is the Earth’s semi-minor axis,
Then, the dynamic equations in the ENU frame can be expressed as:
n n
P V

Where,  
T
n
e n u
P P P P

refers to the vector of 3D positions.
Figure 1. The mechanization of MEMS-INS, kindly taken form [18, 19]

64
2.1.3. Mems-Ins Inherent Errors
Although the INS can provide real-time navigation data, even in environments where external
references are unreachable. However, INS sensors are exposed to many forms of errors that can
significantly affect their consistency and accuracy. These errors in INS sensors include biases,
scale factor errors, and noise, all of which affect the accelerometers and gyroscope
measurements.
Bias errors are constant or slowly varying added to the true value, causing a drift in both
angular rate and acceleration measurements. Additionally, scale factor errors result from
the deviation of the sensor's sensitivity from its ideal value. Furthermore, noise in INS
sensors, including random walk and white noise, complicates the readings even more.
Taking into consideration all these types of errors, the measured acceleration and angular rate can
be expressed as (5)(6):
(1 )*
measured gyroscope true gyroscope gyroscope
SF b
  
   
(5)
(1 )*
measured accelerometer true accelerometer accelerometer
a SF a b 
    (6)
Where,
true
a and true
 are the true acceleration and angular rates, while accelerometer
 and
gyroscope

represent noise in the measurements,
accelerometer
b and gyroscope
b
represent the bias in the accelerometer and gyroscope respectively,
accelerometer
SF
and gyroscope
SF
the scale factor errors for accelerometers and gyroscopes,
respectively.
Figure 2. MEMS-INS modeling
2.2. ConvNet
ConvNet (Convolutional Neural Network, simply Convolutional Network) is considered as a
class of deep neural networks specializing in dealing with grid-structured data, such as visual
imagery. However, they have recently been adapted for sequential data tasks like speech
recognition and error correction of inertial navigation systems. Subsequently, it provides several
advantages, including the ability to handle large volumes of data and automatically detect
relevant features without manual intervention. This makes them particularly suitable for detecting
features and patterns of INS inherent errors, which traditional methods might not effectively treat.

65
A CNN typically comprises three key layers: a conv layer, a pool layer, and an FC (fully
connected) layer. Its main structure is illustrated in Figure 3 [20, 21, 22].
Figure 3. ConvNet’s main structure
2.2.1. Convolution Layer
The convolutional layer starts by processing the INS estimated positions. These calculated
positions contain errors due to three main factors such as bias and sensor noise. The role of this
layer is to capture spatial characteristics and patterns from the INS estimates. The convolution is
expressed as (7) [23, 24]:
1 1
(1) (0) (1) (1)
( )( )
0 0
( . )
M N
ij i m j n mn
M N
h x b
 
 
 
 
 
  (7)
Where (0)
( )( )
i m j n
x   represents the input estimated position data, (1)
mn
 are the weights of the
convolutional kernel in the first layer, (1)
b refers to the bias term, and σ presents the function of
activation.
2.2.2. Pooling Layer
After processing the estimated positions by the convolutional layer to extract spatial features, the
representation is minimized in spatial dimensions by the pooling layer while preserving the most
relevant information, which decreases the necessary total of computation and weights. To capture
the most significant features detected by the preceding layer, the Max pooling operation is given
by (8) [25]:
(1) (1)
( , ) ( , )
max
ij mn
m n P i j
p h

 (8)
Here, (1)
mn
h is the output from the convolutional layer at position, P(i,j) represents the pooling
region around position, (1)
ij
p is the pooled output.
2.2.3. Fc Layer
After the two layers of convolution and pooling, comes the role of the FC layer (Or the dense
layer), which is used in artificial neural networks to connect each neuron or node from the
preceding layer to each neuron of the present layer. In this layer, the input vector is linearly
converted by the node using a matrix of weights. Then, a non-linear conversion is applied to the

66
result through a non-linear activation function. The Equation for a non-linear transformation for a
FC layer is defined as (9) [25]:
(2) (2) (1) (2)
( )
k kj j k
j
y p b
 
 
 (9)
Where (1)
j
p represents the output from the pooling layer, (2)
kj
 are the weights matrix, (2)
k
b is the
bias term, (2)
k
y denotes the output of the FC layer after passing through a function of activation σ
introducing the non-linearity.
2.2.4. Activation Function
Several activation functions are present in the literature and are used with ConvNets, such as
tanh, sigmoid, and ReLU. However, ReLU is the most commonly used due to its numerous
advantages. ReLU is more expressive with the non-linear model, which allows the network to
deal with complex features and functions. Simplicity and efficiency are the main advantages of
ReLu in terms of overcoming the gradient problem that can occur when based on sigmoid or tanh
as activation functions. Its output equals directly the input if the input is positive; otherwise, it
equals zero. The ReLu function is given by (10) [26, 27]:
Re ( ) max(0, )
Lu x x
 (10)
Where x presents ReLU’s function input.
3. METHODOLOGY
The accuracy of the MEMS-INS navigation solution relies on several elements, as discussed in
the previous section, and is significantly influenced by the quality and the grade of the
accelerometers and gyroscopes and the capability to redress its inherent errors. The ability of the
machine learning-based CNN algorithm to mitigate the inertial sensor’s errors by training the
estimated positions of the INS using the positions from the reference trajectory is the primary
objective of this work.
This study investigates diverse depths of CNN layers to perform the accuracy of the MEMS-INS
navigation solution. We will evaluate multiple CNN architectures with varying depths to identify
the most effective model for correcting INS errors. By systematically comparing the performance
of these models, we aim to determine the optimal depth that minimizes these errors.
The proposed machine learning-based CNN algorithm comprises two distinct phases: firstly, the
training phase followed by the testing phase secondly. The first phase is detailed in Figure 4.
Figure 4. The block diagram representing the first phase (training phase) of machine learning-based CNNs

67
The proposed algorithm machine learning–based–CNNs for MEMS-INS navigation solution
improvement is a process of the following steps:
Input: Result of mechanization of three gyroscopes and three accelerometers in terms of INS 3D
estimated positions and the reference position.
Step 1: Prepare and set the machine learning-based-CNNs configuration (input data, output data,
number of layers, types of layers, activation function, and epochs/iterations).
Step 2: Consists of the training phase.
Step 3: Produce the machine learning-based-CNNs model.
Step 4: Includes the testing phase (evaluate and apply the machine learning-based-CNNs on the
residual data).
Step 5: Examine the output of the machine learning-based-CNNs (improved INS positions).
Step 6: Calculate the percentage of enhancement caused by the proposed model using the
comparison between the reference positions and the machine learning-based-CNNs values (Root
Mean Square Error given by (11)) [28, 29].
2
, ,
1
( )
n ref n CNNs
n
RMSE P P
n
 
 (11)
Where, ,
n CNNs
P and ,
n ref
P are trained positions and reference positions, respectively.
Figure 5. The block diagram detailing the second phase (testing phase) of machine learning-based-CNNs
where the generated model is applied to the estimated positions by MEMS-INS and comparing the
generated values with the reference once.
The algorithm detailed below will be tested on the INS estimated positions data with three
variants: a superficial ConvNet, a medium-depth ConvNet, and a deep ConvNet. These variants
are designed to explore the impact of network depth on performance. The configurations of these
three variants are detailed in Table 2.

68
Table 2. The configurations of superficial ConvNet, medium-depth ConvNet, and deep ConvNet
Superficial
ConvNet
Medium-depth
ConvNet
Deep ConvNet
Number of
layers
2 Conv + 2
Pooling + 1 Fully
Connected
4 Conv + 2
Pooling + 2
Fully Connected
8 Conv + 4
Pooling + 3 Fully Connected
Configuration Conv Layer 1: 32
filters, kernel size
3x3, ReLU
activation
Pooling Layer 1:
Max pooling,
pool size 2x2
Conv Layer 2: 64
filters, kernel size
3x3, ReLU
activation
Pooling Layer 2:
Max pooling,
pool size 2x2
Fully Connected
Layer 1: 128
units, ReLU
activation
Output Layer:
Softmax
activation (for
classification)
Conv Layer 1:
32 filters, kernel
size 3x3, ReLU
activation
Conv Layer 2:
64 filters, kernel
size 3x3, ReLU
activation
Pooling Layer
1: Max pooling,
pool size 2x2
Conv Layer 3:
128 filters,
kernel size 3x3,
ReLU activation
Conv Layer 4:
256 filters,
kernel size 3x3,
ReLU activation
Pooling Layer
2: Max pooling,
pool size 2x2
Fully Connected
Layer 1: 512
units, ReLU
activation
Fully Connected
Layer 2: 256
units, ReLU
activation
Output Layer:
Softmax
activation (for
classification)
Conv Layer 1: 32 filters, kernel size
3x3, ReLU activation
Pooling Layer 1: Max pooling, pool
size 2x2
size 2x2
size 2x2
size 2x2
Fully Connected Layer 1: 1024 units,
ReLU activation
ReLU activation
ReLU activation
Output Layer: Softmax activation (for
classification)
4. EXPERIMENTS
4.1. Experimental Setup
Verification of the proposed machine-learning model's effectiveness was conducted using
simulated MEMS-INS data instead of real MEMS-INS sensors. The experimental work was
performed within a simulation environment using Matlab. The reasons behind this choice come
from enabling tests in various scenarios without physical investment and the flexibility and
scalability they offer.
From a reference trajectory, we modeled the three accelerometers and three gyroscopes that
compose an INS system to generate raw INS measurements, including specific forces and angular
velocities. Bias, scale factor, and noise, as inherent INS errors, were then introduced into the data.

69
These errors were added with specific values commonly affecting the low-grade MEMS-IMU
sensors. This method permits to creation of a controlled environment for testing the proposed
machine-learning model’s performance under conditions that mimic real-world sensor
inaccuracies. The performance characteristics of the simulated MEMS-IMU are presented in
Table 3 below.
Table 3. Performance characteristics of the simulated MEMS-IMU and real MEMS-IMU
MEMS-IMU Real IMU Simulated IMU
Output data rate From 100 Hz to 1 kHz 100 Hz
Warm-up time around 1 to 5 seconds 5 seconds
Gyroscopes
Scale factor 1% to 5% 5%
Bias 10° to 100°/hour 100°/hour
Noise 0.01 to 0.1°/s/√Hz 0.1°/s/√Hz
Accelerometers
Scale factor 0.1% to 1% 1%
Bias 100 to 1,000 µg 1,000 µg
Noise 100 to 500 µg/√Hz 500 /√Hz
4.2. Simulation Environment
The simulated trajectory, developed within a MATLAB simulation environment, includes both
curved paths and straights to effectively emulate real scenarios. Indeed, curved segments
introduce more complex changes in attitude and velocity, while straight paths represent simple
linear motion. The following figures (Figure 6 and Figure 7) illustrate the initial simulated
trajectory in both 2D and 3D, highlighting the challenges posed by different motion dynamics.
Figure 6. Overview of the 2D simulated trajectory

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Figure 7. Summary of the 3D simulated trajectory
5. RESULTS & DISCUSSION
The simulated trajectory, accurately reflecting real-world conditions, was employed to evaluate
our proposed ConvNet variants within the MATLAB environment. At the frequency of 1 Hz, this
trajectory consists of 3000 points, corresponding to a duration of 3000 seconds. This duration
translates to 50 minutes, providing a substantial dataset for assessing the performance and
robustness of our ConvNet models in various scenarios. By utilizing this extensive trajectory
data, the error correction algorithms were thoroughly tested and validated, ensuring their practical
applicability and reliability.
The three configurations of the ConvNet were applied to the erroneous data in a two-phase
process. In the first stage, 50% of the position data from the reference trajectory was utilized to
generate the three machine-learning-based ConvNet models. Following this, the three proposed
models were applied to the remaining INS erroneous data set to measure their performance. This
approach allowed for an initial training phase using a substantial portion of the accurate data,
ensuring the models were well-calibrated before evaluating their effectiveness on the unseen,
erroneous portion of the dataset.
In all upcoming figures, the following color scheme was utilized to distinguish between the
different datasets: red was used to represent the reference trajectory. The data processed by the
first ConvNet configuration is shown in blue. The second ConvNet configuration's results are
depicted in green. Finally, the data corrected by the third ConvNet configuration is displayed in
magenta.
The East, North, and Up position components are compared in Figures 8-10. By analyzing these
figures, the obtained position components using the proposed ConvNet models were substantially
closer to the reference position components. Furthermore, the findings indicate that the accuracy
of the position estimation improved with the increasing depth of the ConvNet architecture.
Specifically, deeper ConvNet models resulted in positional outputs that were more closely
aligned with the reference data. This suggests that deeper neural network structures have
enhanced capability in mitigating INS errors and refining positional accuracy, thereby validating

71
the efficacy of employing deeper ConvNet configurations for improved inertial navigation
performance.
However, it was also observed that the computational time required is proportional to the network
depth. This increase in computation time underscores the substantial use of CPU (Central
Processing Unit) resources necessary to handle deeper network structures. Consequently, while
deeper ConvNet configurations offer superior accuracy, they also demand greater computational
power and resources, highlighting a trade-off between performance accuracy and computational
efficiency. This balance must be carefully managed to optimize both the effectiveness and
efficiency of the INS error correction process.
(a)
(b)
Figure 8. Evaluation of the three ConvNet models targeting the east component of positional data (a) &
zoomed-in view (b)

72
(a)
(b)
Figure 9. Evaluation of the three ConvNet models targeting the north component of positional data (a) &
zoomed-in view (b)
Figure 10. Evaluation of the three ConvNet models targeting the up component of positional data
The overall 2D and 3D trajectory comparisons are presented in Figure 11. As demonstrated by
the illustrations, the machine learning-based ConvNet technique effectively mitigates the inherent
errors of MEMS-INS, leading to an improved INS navigation solution. Furthermore, the
ConvNet3 architecture produces the most significant and relevant results. The obtained trajectory
by the ConvNet3 closely tracked the reference path, particularly through the curve segments.

73
(a)
(b)
Figure 11. Results after applying the three ConvNet configurations to the trajectory in both 2D (a) and 3D
(b)
Table 4 provides the RMSE (Root Mean Square Error) analysis of the INS solution's position
components. This analysis underscores the improved accuracy achieved with the ConvNet3
method, outperforming the ConvNet1 and ConvNet2 architectures in reducing INS errors and
enhancing trajectory accuracy. However, the RMSE in the up direction remains high even with
the deepest architecture provided by the ConvNet3, due to gravity fluctuations caused by
variations in the Earth's gravitational field.
Table 4. RMSE analysis of East, North, and Up position components for the ConvNet variants
Position RMSE Superficial ConvNet Medium depth
ConvNet
Deep ConvNet
East (m) 23.63 5.08 2.39
North (m) 22.10 6.93 6.31
Up (m) 81.50 66.47 14.10
The following table (Table 5) summarizes the findings by comparing the key parameters of
performance, including CPU utilization, accuracy, and RMSE’s average, for the three ConvNet
variants. ConvNet3 demonstrates superior accuracy and lower RMSE but requires higher
computational time and resource utilization. On the other hand, ConvNet1 and ConvNet2 provide
a more balanced trade-off between accuracy and efficiency.

74
Table 5. Summary of the findings by comparing the three ConvNet variants: A Detailed Comparison
Parameter Superficial ConvNet Medium depth
ConvNet
Deep ConvNet
Architecture 2 conv + 2 pooling + 1
FC
4 conv + 2 pooling + 2
FC
8 conv + 4 pooling
+ 3 FC
Activation
function
ReLu
Framework Matlab environment
CPU Utilization Low Medium High
RMSE average
over 3D in meters
(East, North, and
Up)
42.41 26.16 7.60
Accuracy 69.70% 70.20% 91.72%
6. CONCLUSIONS & FUTURE WORK
To summarize this paper, our work highlights the fundamental role of layer depth in enhancing
the MEMS-INS navigation solution performance within the context of supervised machine
learning, specifically relying on the ConvNet model. Using a dataset obtained by modeling and
mechanizing the INS system from a reference trajectory that was generated to reflect real
scenarios. Three variants of ConvNet were applied to this dataset to improve the accuracy in
correcting INS inherent errors. The results demonstrate that ConvNet3 achieves high accuracy
and outperforms the two other variants, but it requires more CPU resources. ConvNet 3, the deep
convolutional neural network, achieved an accuracy of 91.72%. In comparison, the two other
variants did not exceed an accuracy of 80%. On the other hand, ConvNet1 and ConvNet2 offer a
better balance between efficiency and accuracy. This study highlights the critical trade-offs
between computational resource consumption and model performance, guiding future
developments in the field of MEMS-INS error correction.
While mitigating inherent errors in inertial navigation systems (INS) is crucial, it is not sufficient
to ensure secure navigation for intelligent systems. To achieve robust navigation, especially in
challenging GNSS environments, further steps are necessary. As a next step, we will combine
this work with either machine learning techniques or the Kalman Filter to bridge GPS outages.
This integration aims to provide a more secure and resilient solution for intelligent systems in
GPS-denied environments where their signals are unreliable or unavailable.
CONFLICTS OF INTEREST
The authors declare no conflict of interest.
ACKNOWLEDGEMENTS
The contributors of this paper appreciate the cooperation and collaboration of our laboratory
members.

75
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AUTHORS
Mohammed AFTATAH obtained a state engineer degree in Network and
Telecommunications from ENSA Marrakech, Cadi Ayyad University, Marrakech,
Morocco. Presently, he is a trainer at OFPPT in Network, Systems, and Cybersecurity and
is actively pursuing his Ph.D. in Artificial Intelligence and its application to secure
navigation for intelligent systems.
Dr. Khalid ZEBBARA earned his Ph.D. in Computer Systems from Ibn Zohr University,
Agadir, Morocco. He is currently a Professor at the Faculty of Applied Sciences, Ibn Zohr
University, Agadir. In addition, he heads the Imaging, Embedded Systems, and
Telecommunications (IMIS) research team at the Faculty of Applied Sciences, Ibn Zohr
University, Agadir.

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