=Paper=
{{Paper
|id=Vol-2874/paper2
|storemode=property
|title=Deep Learning-Based Method for Detecting Cassini-Huygens Spacecraft Trajectory Modifications
|pdfUrl=https://ceur-ws.org/Vol-2874/paper2.pdf
|volume=Vol-2874
|authors=Ashraf ALDabbas,Zoltán Gál
}}
==Deep Learning-Based Method for Detecting Cassini-Huygens Spacecraft Trajectory Modifications==
https://ceur-ws.org/Vol-2874/paper2.pdf
Deep Learning-Based Method for Detecting
Cassini-Huygens Spacecraft Trajectory
Modifications∗
Ashraf ALDabbasa , Zoltán Gálb
a
University of Debrecen, Doctoral School of Informatics
Ashraf.Dabbas@inf.unideb.hu
b
University of Debrecen, Faculty of Informatics
Gal.Zoltan@inf.unideb.hu
Proceedings of the 1st Conference on Information Technology and Data Science
Debrecen, Hungary, November 6–8, 2020
published at http://ceur-ws.org
Abstract
During the last 13.5 year motion cycle of the interplanetary research
project, there were necessary flight path modifications of the Cassini space-
craft. In the order of signal travel time (approximatively 80 minutes) on the
Earth-Cassini long sized channel, complex event detection of orbital mod-
ifications requires special investigation and analysis of the collected large
trajectory dataset. This paper presents a sophisticated, in-depth learning
approach for detecting Cassini spacecraft’s trajectory modifications in post-
processing mode. The model uses neural networks with Long Short-Term
Memory (LSTM) to extract useful data and learn the time series’ inner data
pattern, together with the penetrability of the LSTM layers distinguish de-
pendencies between the long- and short-term phases.
Keywords: Cassini-Huygens interplanetary project, complex event, sensory
data, big data, artificial intelligence, pattern processing, knowledge represen-
tation
AMS Subject Classification: 65C60, 60G35, 68T05, 68T20
Copyright © 2021 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
∗ This work was supported by the construction EFOP-3.6.3-VEKOP-16-2017-00002. The
project was supported by the European Union, co-financed by the European Social Fund. The
paper was supported by the QoS-HPC-IoT Laboratory, too.
19
1. Introduction
A complex event’s significance is related to processing several events, followed
by paying attention to discriminate distinct occurrences within a time series of
events [2]. There are situations where the obtainable knowledge to represent some
method or device is merely observation inspection; with the scale of big data,
there is an significant simplification of the problem, which is to identify an ex-
treme event [5]. The spacecraft launched in October 1997 arrived at its target on
1 Jul 2004 [8]. This case is called Cassini-Huygens’ Saturn Orbit Insertion (SOI).
It took the spacecraft 6.7 years from Earth’s launch to reach Saturn’s destination
(SOI). For reaching Saturn manoeuvres for correcting the orbital momentum of
the spaceraft relative to Sun were necessary. They were gravity assisted by doing
flybys of planets. Then flybys of Titan, the biggest moon of Saturn were carried
out for further gravity assisted orbit corrections needed for reaching other moons
of Saturn [3]. Visualization of the large-scale trajectory shown in Figure 1 be-
low represents the last 393,977 pieces of Cassini trajectory coordinates sampled
between Earth and Saturn planets [9]. The last 13.5 years of the trajectory de-
fined by roughly large-scale semi-ellipse and evaluated by us begins with a circular
marker in the bottom, while the top square symbolizes the end of the trajectory
on September 14, 2017. In our research framework we focus on detecting Cassini’s
orbiter trajectory changes.
Figure 1. Cassini large scale trajectory around Sun.
The trajectory represented contains just the last 13.5 Earth years including
approaching phase, SOI event and orbiting around the Saturn of the Cassini space-
craft. This duration is approximately half period time of the Saturn trajectory
around the Sun. The star, circle, and square characters mark the Sun, the first
sample, and the last sample, respectively. After the SOI, the Cassini trajectory is
a dynamic curve compound by an ellipse-based helicoid around Saturn, orbiting
around the Sun in its own ellipse. It should be mentioned that the first amount
20
of samples are before SOI, consequently the time interval between SOI and end of
project is just 13.3 years. With the established method, we aim to detect events in
post processing mode relevant to Cassini’s trajectory modifications. To this end,
we put forward our model that uses the capacity of Long-Short Term Memory
neural networks to produce useful data and learn the internal data structure of the
trajectory time series and leverage the memory dependence LSTM potential.
In section 2 we provide a brief literature review of several related studies within
the field. Section 3 describes extraction of sampling and trajectory characteris-
tics of the Cassini database (Imaging Science Subsystem (ISS), Saturn EDR Data
Sets (Volume 1 – Volume 116) [9], which was indexed by National Aeronautics and
Space Administration of the USA (NASA). Section 4 discusses spacecraft trajec-
tory modifications detection by LSTM based artificial intelligence algorithm along
with the adopted method for the detection of trajectroy changes. Section 5 con-
tains the experimental results of the trajectory manoeuvres detection and section
6 summarizes our research conclusions.
2. Related Work and Previous Studies
Cassini’s project’s trajectory was separated into three classes of activities occur-
ring in phases: i) launching and journey to Saturn, ii) approaching and arrival
at Saturn, and iii) science phase. Controlling the trajectory required processing
a variety of status information including certain step length, velocity, etc. The
approaching and arrival process provided complete project trajectory information.
Basic role of trajectory maps in the science phase is to position the spacecraft in a
specific location related to Saturn, which has been meticulously planned and has
sufficient entrance conditions consistent with spacecraft velocity and path angle.
Paper [11] offers recent research results on the Cassini project orbiter remodeling
and mostly shifting our view of the Cassini orbiter; like in the last half of 2016, one
of Cassini’s near flybys changed the trajectory of Cassini to form a sequence of 20
rings containing marvelous orbits.
Paper [7] surveyed artificial intelligence developments in the concept of space-
craft control and guidance dynamics and focused on evolutionary logic and deep
learning as the cornerstone to potential systemic space science. The method in-
cludes artificial intelligence and automatic logic to monitor the navigation and the
remote sensing of the external space mission trajectories. Gated Recurrent Unit
(GRU) provides a periodic neural network algorithm for real-time trajectory pre-
diction, where its parameters are acquired as an initial step by batch processing,
then the qualified feedback for trajectory prediction [6]. In work [10] a model-based
reinforcement learning is proposed to conduct almost quintessential reconfiguration
in establishing flying spacecraft. Along with two other algorithms, the LSTM layer
network and reverse reinforcement learning were used to remodel and forecast pos-
sible trajectories to acquire collision-free maneuvers. These merits encouraged us
to use LSTM networks, where the LSTM approach suits our study field.
21
3. Extracting Sampling and Trajectory Characteris-
tics of the Cassini-Huygens Database
There were two pieces of the spacecraft: Huygens probe and Cassini orbiter.
Cassini-Huygens (C-H) arrived at Saturn in 2004, sending useful data back to
Earth. Huygens moved through Titan’s atmosphere, Saturn’s biggest moon, plunged
down by parachute to the furthest point so far, landed on his surface. Huygens took
samples, testing them, and submitting the findings to Cassini, who then returned
these signals to Earth. Remote sensing devices gathered data from vast distances
remotely. The acquired image data was provided by NASA’s Imaging Science Sub-
system (ISS). The ISS comprises of two detached wide-angle video cameras and a
narrow-angle camera. The dataset of ISS picture volumes comprises an immense
number of images and their corresponding labels. The dataset is freely accessible
by reference [9]. Table 1 shows the project’s time stamp.
Table 1. Tasks time stamps of main phases (UTC).
Task Starting Date Ending Date
C_H Project 15 October 1997 15 September 2017
Analyzed DB by us 6 February 2004 15 September 2017
Prime Mission 1 July 2004 1 July 2008
Equinox Mission 1 July 2008 11 October 2010
Solstice Mission 11 October 2010 15 September 2017
We evaluated the 116 volumes of the data collection from the above NASA
source. The staring study had time stamp 02:07:06 on February 6, 2004, and end
stamps on September 14, 2017, all clarified in UTC (Coordinated Universal Time).
The C-H project’s five key objectives (i.e., Saturn study, Moon Titan, Saturn
rings, ice satellites, and magnetosphere) involved trajectory maneuvers. Reference
[4] gives the amount of expected and performed adjustments in the trajectory of
each mission. Table 2 provides the number of Saturn orbits along with the planned
and executed maneuvers. The percentage of performed and expected trajectory
maneuvers for the Prime and Equinox project is 69.5% and 67.3%, respectively.
Table 2. Number of Saturn orbits and manoeuvres.
Trajectory Maneuvers Trajectory Maneuvers
Mission No. of Orbits
Planned Executed
Prime 75 161 112
Equinox 64 104 70
Solstice 155 206 141
With no official details on the Solstice mission’s performed trajectory modifi-
cations, our forecast is 68.4 percent (average of the previous two) of the scheduled
22
maneuvers, providing 141 trajectory modifications.
4. Conditions of the Complex Event Detection of the
Cassini Trajectory
Our classifier’s key purpose is to specify complex events from sensory produced
data; we expanded the sensory data index to detect temporal semantics for com-
plex event detection. Potential dynamic data set occurrences are where observation
sequences shift. We consider severe trajectory adjustment as the Cassini orbiter
velocity vector shifts more than a threshold metric. Since velocity is a measure
vector, extreme trajectory occurrences mean satisfying either of the following two
conditions: extreme alteration of the velocity direction or of the acceleration vec-
tor’s magnitude.
4.1. Modification per Time of the Velocity Vector Direction
The speed of the angle modification ∆𝜙𝑖 between consecutive velocity vectors 𝑣𝑖
and 𝑣𝑖+1 is given by the following formula:
(︁ )︁
𝑖+1 ·𝑣𝑖
∆𝜙𝑖 cos ‖𝑣𝑖𝑣‖·‖𝑣 𝑖+1 ‖
= , 𝑖 = 1, 2, . . . , 𝑁 − 1 (4.1)
∆𝑡𝑖 𝑡𝑖+1 − 𝑡𝑖
where 𝑣𝑖 and 𝑣𝑖+1 are two consecutive velocity vectors of the orbiter, ‖𝑣𝑖 ‖ is the
magnitude of the vector, ∆𝑡𝑖 is the time interval between two consecutive samplings
and 𝑖 = 1, 2, . . . , 𝑁 −1. The number of vectors is the total number of samples in the
Prime, Equinox and Solstice missions: 𝑁 = 407, 303 − 13, 326 = 393, 977. Value
around 0 of the ∆𝜙/∆𝑡 means a very small modification of the direction per unit
of time. Such cases were at the beginning of the project (see values before 2005 on
the Figure 2a).
This amount of samples analysed by us belongs to the last 13.3 years of the C-H
project. Starting with the SOI event, the angle of the consecutive samplings of the
velocity direction modified in a higher range per unit of time. The spacecraft tra-
jectory has been updated many times, but no specific knowledge on these incidents
is accessible to the public. NASA’s open 116-volume archive includes samples of
high time dispersion. Values of the ∆𝜙/∆𝑡 in the scale of over 1 rad/sec were
sampled in case of relatively short delay time between consecutive samplings. The
distribution of the ∆𝜙/∆𝑡 is exponential conform to the right hand side histogram
of Figure 2.
4.2. Modification of the Acceleration Vector Magnitude
Trajectory adjustment happens as the magnitude of velocity vector v (𝑣𝑥 , 𝑣𝑦 , 𝑣𝑧 )
varies during successive sampling by a higher value than the threshold 𝑇 ℎ𝑣 . The
23
(a) Angle modification vs. date. (b) Histogram of angle modification.
Figure 2. Basic properties of angle modification velocity vs. date.
Majority of angle velocity are less than 0.01 rad/sec.
estimation of the adjustment magnitude per unit of time of the velocity vector be-
tween two consecutive samples (being the moving average acceleration) is centered
on the velocity components defined in the database as follows:
𝑣 = 𝑣𝑥 + 𝑣𝑦 + 𝑣𝑧 (4.2)
‖∆𝑣𝑖 ‖ ‖𝑣𝑖+1 − 𝑣𝑖 ‖
𝑎𝑖 = = , 𝑖 = 1, 2, . . . , 𝑁 − 1. (4.3)
∆𝑡𝑖 𝑡𝑖+1 − 𝑡𝑖
The magnitude of velocity modification can be derived using the following re-
lation:
‖𝑣𝑖+1 − 𝑣𝑖 ‖2 = (∆𝑣𝑥,𝑖 )2 + (∆𝑣𝑦,𝑖 )2 + (∆𝑣𝑧,𝑖 )2 (4.4)
where ∆𝑣𝑥,𝑖 , ∆𝑣𝑦,𝑖 , ∆𝑣𝑧,𝑖 are the modification of the orthogonal velocity com-
ponents in the sampling interval 𝑖, and 𝑖 + 1. The acceleration magnitude of the
Cassini can be seen on the left-hand side of Figure 3. It can be observed that
the distribution of the acceleration magnitude is power function conform to the
right-hand side histogram of Figure 3.
The histogram denotes a structure in which the amplitude of acceleration events
calculated in a specified magnitude duration is spread through possible magnitude
values. Each level within the generated histogram expresses the acceleration rate
among the acceleration span. A linear function, resulting in the histogram’s power
function dependency, will approximate the log-log scale histogram.
4.3. Complex Event Detection of the Cassini Orbiter Trajec-
tory
Our classifier’s key purpose is to specify complex events from sensory produced
data; we expanded the sensory data index to detect temporal semantics for complex
24
(a) Acceleration magnitude vs. date. (b) Histogram of acceleration magnitude.
Figure 3. Acceleration magnitude of the Cassini vs. date. Majority
of the magnitudes of a are less than 1 km/s2 .
event detection. Potential dynamic data set occurrences are where observation
sequences shift. Let’s have trajectory adjustment indexes where 𝐼 set unique events:
∆𝜙𝑖
𝐼𝜙 = {1 < 𝑖 < 𝑁 − 1 | ≥ 𝑇 ℎ𝜙 } (4.5)
∆𝑡𝑖
𝐼𝑎 = {1 < 𝑖 < 𝑁 − 1 | 𝑎𝑖 ≥ 𝑇 ℎ𝑎 } (4.6)
𝐼 = 𝐼𝜙 ∪ 𝐼𝑎 (4.7)
𝐽 = 𝐼𝜙 ∩ 𝐼𝑎 (4.8)
where 𝐼𝜙 and 𝐼𝑎 are sample indexes of the analyzed NASA database for which
the velocity direction modifications or the acceleration magnitude are greater than
the corresponding threshold values. Set 𝐽 is used to sense the individual effect
simultaneously of the two conditions mentioned in subsections 3.1 and 3.2. If the
set 𝐽’s cardinality is low, then conditions (4.5) and (4.6) are not strongly dependent
and both of them help to detect complex events on the trajectory. The resulting
set 𝐼 contains all the sampling indexes detected by the proposed complex event
detector.
𝐼 = 𝑖1 , 𝑖2 , . . . , 𝑖𝑘 (4.9)
After the SOI phase in 2004, the spacecraft performed many trajectory ad-
justments in compliance with the Earth commands sent by the supervisor squad.
Cardinality 𝑘𝐼 and 𝑘𝐽 of the sets 𝐼 and 𝐽, respectively, give the number of ex-
treme events called Cassini trajectory modifications dependent on circumstances
(4.7) or (4.8) over the last 13.3 years of the project studied. Obviously, number
of trajectory variations should be less than the amount of observations listed in
Table 2.
25
Working points are represented with red bubble markers and are placed in
the extreme modification coordinates of the gradient of the surfaces. Based on
Table 1. the amount of conducted maneuvers is considered 323. By leveraging
the dependence of severe values on the threshold values 𝑇 ℎ𝜙 and 𝑇 ℎ𝑎 within our
model, we may evaluate the working point in three-dimensional space. Figure 4
sets out this dependency as a surface plot. The working point on both surfaces is
placed on cordinates with extreme modification of the surfaces. To fulfill the total
number of trajectory manoeuvres the values of the thresholds are (𝑇 ℎ𝜙 , 𝑇 ℎ𝑎 ) =
(2.85𝑟𝑎𝑑/𝑠, 33.84𝑘𝑚/𝑠2 ). For these threshold values, the cardinality of the set 𝐼
and 𝐽 were found to be (𝑘𝐼 , 𝑘𝐽 ) = (323, 1). It was found that approximately two
times more extreme events appear in set 𝐼𝜙 than in set 𝐼𝑎 . These two sets are not
disjunctive because in several samples, both of the conditions (4.5) and (4.6) fulfill.
The union of these two sets gives precisely 323 extreme trajectory adjustment cases.
In the continuation, we demonstrate the approach for detecting these trajectory
maneuvers with recurrent neural network.
(a) Cardinality of set 𝐼 vs. thresholds. (b) Cardinality of set 𝐽 vs. thresholds.
Figure 4. Dependence of the cardinality of sets 𝐼 and 𝐽.
4.4. Deep Learning Method of Detecting Trajectory Modifi-
cations
The work presented in [1] aids in analyzing the effect on the trajectory of spacecraft,
depending on how two or more ideas or artifacts are related between the orbital
elements. Any framework’s productive research includes the time-domain scientific
findings reference. The suggested solution is an amalgamated structure that may
define trajectory adjustments in the C-H expedition project. Trajectory analysis
enables knowledge to be gained, not only regarding spacecraft motion but also
for improved machine learning-based motion analysis. Our system collects the
trajectory data as inputs and analyses them momentarily and spatially based on
the sample number and pacing alongside the spacecraft’s velocity.
26
The input to the RNN system is a sequence of sample ID, 𝑖 ∈ {1, . . . , 𝑁 − 1 =
393,976}, sampling intervals ∆𝑡𝑖 = 𝑡𝑖+1 −𝑡𝑖 , modification of the position coordinates
(∆𝑥𝑖 , ∆𝑦𝑖 , ∆𝑧𝑖 ) and modification of the velocity components (∆𝑣𝑥,𝑖 , ∆𝑣𝑦,𝑖 , ∆𝑣𝑧,𝑖 )
among the last 13.3 years of the studied time interval. The input 𝑋 of the neural
network is a 7𝑥𝑁 type matrix conform to the formula below:
𝑋 = [𝑋1 , 𝑋2 , . . . , 𝑋𝑁 −1 ], (4.10)
where column vectors 𝑋𝑖 have the following elements:
𝑋𝑖 = [∆𝑡𝑖 , ∆𝑥𝑖 , ∆𝑦𝑖 , ∆𝑧𝑖 , ∆𝑣𝑥,𝑖 , ∆𝑣𝑦,𝑖 , ∆𝑣𝑧,𝑖 ]𝑇 . (4.11)
The data set having 𝑁 −1 samples is divided into the subsets of objects conform
to Table 3. We used half of the samples for learning and the remaining half of
samples is divided equally for validation and testing. Based on the formula (4.11)
each matrix has 7 rows and 𝑁 columns.
Table 3. Dimension of the data subsets.
Start Column End Column No. of Matrix No. of Matrix
Data Subset
Index Index Rows Columns
XTrain 1 (N-1)/2 7 (N-1)/2
YTrain 1 (N-1)/2 7 (N-1)/2
XValidate (N-1)/2+1 3*(N-1)/4 7 (N-1)/4
YValidate (N-1)/2+1 3*(N-1)/4 7 (N-1)/4
XTest 3*(N-1)/4+1 N-1 7 (N-1)/4
YTest 3*(N-1)/4+1 N-1 7 (N-1)/4
The human control team from Earth sent adjustment orders on the trajectory
due to the mission’s numerous science and celestial goals. We use LSTM neural
network layers to better sense the memory property of the trajectory because of
inertia of the Cassini. Figure 5 provide the adopted architecture of the recurrent
neural network.
Figure 5. Architecture of the adopted recurrent neural network.
27
The RNN method conducts a binary trajectory sample classification. The se-
quences of the sampled multidimensional time series will be detected depending on
the trajectory’s extreme events. The orbiter’s automatic adjustments have been
produced to hold the orbiter on the complicated helicoid described in Section 3.
It is common to stack LSTM layers for better modeling capacity, particularly
when a large amount of training data is available based on its ability to manip-
ulate previous computation knowledge. In principle, RNNs should accommodate
arbitrary long-term dependencies in the input series to prevent the gradient issue
where long-term dependencies occur. Our each neural network machine perfor-
mance is a binary feature that demonstrates how the Cassini orbiter trajectory is
highly changed. Each neural network has formation algorithm style ADAM; the
threshold gradient method is L2Norm. Table 4 offers additional criteria for the
used set of neural networks.
Table 4. Training option values of the RNN.
Option Value
GradientDecayFactor 0.9000
SquaredGradientDecayFactor 0.9900
InitialLearnRate 0.0200
GradientThreshold 1.0000
MaxEpochs 100
Number of Classes 2
The number of classes for the tested neural networks is two to detect the trajec-
tory’s complex events. As the CED conditions (see relations 4.5, 4.6) are fulfilled
for any trajectory samples, that sample is classified True, otherwise is classified
False.
5. Experimental Results of the Trajectory Manoeu-
vres Detection
Training and validation of trajectory research data sets are conducted in the last
13.3 years of the Cassini project using a set of twelve separate recurrent neural
networks. Half of them are LSTMs, while the remainders are BiLSTMs. The
changing input parameters (mini-batch scale, number of hidden units, number of
classes on layer three and layer four) and measured performance metrics (subse-
quent learning time and the precision of these networks’ identification) are shown
in Table 5. It should note that for each RNN type we got detection accuracy over
99 %. Big difference is detected between the learning time of LSTM and BiLSTM
network types. It is obvious that having both direction of the signal propagation
the BiLSTM requires extra processing relative to the LSTM structure.
28
Table 5. Detection accuracy of the trajectory modification of dif-
ferent RNNs.
Mini Hidden Detection
RNN Classes# Classes# Learning
Batch Units# Accuracy
Type on L3 on L4 Time [s]
Size [] on L2 [%]
LSTM 2500 10 100 2 654.2 99.86
LSTM 2500 100 100 2 749.1 99.78
LSTM 5000 10 100 2 625.9 98.39
LSTM 5000 100 100 2 748.8 99.98
LSTM 10000 10 100 2 623.2 99.92
LSTM 10000 100 100 2 748.0 99.06
BiLSTM 2500 10 100 2 1089.8 98.76
BiLSTM 2500 100 100 2 1172.0 99.95
BiLSTM 5000 10 100 2 1093.4 99.11
BiLSTM 5000 100 100 2 1174.7 99.19
BiLSTM 10000 10 100 2 1092.4 99.36
BiLSTM 10000 100 100 2 1175.8 98.20
A popular challenge in machine learning is research and building algorithms that
can learn from and render data predictions. These algorithms operate by rendering
data-driven forecasts or decisions by creating a theoretical framework from input
data. The accuracy levels provided in the deep learning-based model’s spacecraft
maneuvering behavior are acquired within the training dataset. The results support
the view that deep models are important in the detection of trajectory modifications
detection of sensory data.
Figure 6 (left) and Figure 6 (right) visualize the deficit during the learning
process. It can be found that L2’s number of secret units affects learning loss. The
fewer the number of hidden units are, the greater the loss are. For 10 hidden units,
the learning loss doubles. The related activity has LSTM and BiLSTM networks,
but the last one is learned on the L2 layer for 100 hidden units.
The ideal learning rate is bound to be exposed to the lack of the results’ learned
behavior, which depends on the dataset and architecture used. The loss value shows
how effectively or adequately the model performs during each learning iteration.
Figure 6a reveals that RNN4 LSTM offers the best loss relative to other versions.
We can see that RNN8 BiLSTM has the strongest loss on the figure’s right hand
relative to other versions. The efficiency of identification is the ratio between
the number of identified trajectory corrections and the number of real trajectory
corrections. In this context we name it accuracy metric like in popular statistical
software tool environments.
Generally defined model accuracy after measuring the parameters of the this
model is explained in percentage. It is called the model accuracy metric that
compares the model forecast with the correct data. Figure 7 represent dependency
of the accuracy on the learning time for each of the analysed RNN. All LSTM
29
networks need lower learning time than for BiLSTM networks.
The model accuracy is identified after calculating the parameters of the used
model with a percentage style; this is clear in the figure above; as an illustration,
RNN4 is hitting an accuracy that exceeds the value of 99.9% with a minimum
learning time with MiniBatch size = 5000, 100 hidden units and is able to learn
the behaviour with 99.98% accuracy of the trajectory in less than 20.5 minutes on
a desktop computer with 64 GB RAM and 12 CPU cores.
(a) Minibatch learning loss (LSTM). (b) Minibatch learning loss (BiLSTM).
Figure 6. Dependence of the minibatch learning loss on the num-
ber of epochs of the RNNs.
Figure 7. Scatter plot of the learning time and accuracy of the
RNNs.
30
6. Conclusions
C-H spacecraft trajectory modifications detection method was conducted using
LSTM/BiLSTM networks; as far as we know, this study is the first to detect
the events of spacecraft trajectory modifications. By the provided results, we show
that our test study clearly identifies that LSTM models with the chosen parameters
have a reasonable option for specifying Cassini’s trajectory modifications. Their
usage and extra stacked layers produce a noticeable boost in increasing detection
process efficiency. It is worth mentioning that the models used can be comfortably
generalized to cover a large scientific field relevant to estimation. With more specific
information, the provided models present a robust processing step in employing
the inner features and time-series representation via LSTM time dependencies for
precise detection. The proposed detection model was capable of identifying 99.98%
of the trajectory modifications of the Cassini orbiter.
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