Satellite orbit prediction based on recurrent neural network using two line elements

Alaa Osama Awad Mahmoud
• Teacher Assistant faculty of Science
Helwan university
• SERG Member
Satellite Orbit Prediction
Based on Recurrent Neural
Network using Two Line
Elements
Advanced Intelligent Systems for Sustainable Development (AISSD 2021) 20-22 August 2021

Agenda
1. Introduction.
2. Problem Statement.
3. Methods of Satellite Prediction.
4. Two Line Element dataset Format.
5. How to use Machine Learning Techniques to Predict the Satellite Orbit?
6. Related Work

Satellite
• a satellite is an object that has been intentionally placed into orbit. These objects are
called artificial satellites to distinguish them from natural satellites such as Earth's Moon.
• satellite used for (observation , Telecommunication , meteorology , …., etc )

Satellites Orbit
• A satellite orbit follows the Kepler orbit, which is explained by the six Keplerian
elements.
• Predictions of satellite orbits is a significant research issue for avoiding collisions in
space.

Satellite Collision
• Satellite collision events have occurred due to incorrect predictions and false alarms.

• The first two satellites
collision occurred in
February 2009
• collision of a U.S.
Iridium communications
satellite and a Russian
Cosmos 2251
communication satellite

Space Debris
also known as ( space junk, space pollution, space waste, space trash,
or space garbage)

Satellite orbit prediction
• Efficient and high-precision orbit
prediction is increasingly crucial to
enhance the awareness of the space
situation.
• collision avoidance, by describing a
method that contributes to achieving
a requisite increase in orbit
prediction accuracy.
• Previously using physics
• now using machine learning

Satellite orbit prediction Methods
1. Laser

2. GPS Satellite

Two Line Elements

3. Two Line Elements

Two-Line Elements
TLE Set Format is a data format used to transmit one coded set of orbital elements
that perfectly describe the satellite’s orbit around Earth.
The method of orbit prediction by combining multiple TLE can achieve the purpose of
improving orbit predication precision
TLE computed by NORAD (North American Aerospace Defense Command) & NASA
(National Aeronautics and Space Administration) using Radar

Ballistic
coefficient
Drag term or
radiation pressure
coefficient
Classification
International Designator
launch year , launch day and the piece of launch
EX:- "A" shows it was the first object resulting from this
launch.
Note:-
• The final two characters in the second
derivative of mean motion and B* indicate an
applicable power of 10. EX:- in B* value the -4
corresponds to 10^-4.
• The second derivative of mean motion, B*,
and eccentricity all have an assumed leading
decimal before the first digit.
Epoch Date
The number of day , hour ,minutes and
seconds passed in a particular year
Ballistic coefficient
Is the daily rate of change in the number of revs
the object completes each day divided by 2 units (
revs / day )
Second Derivative of Mean Motion
Is a second order drag term in the SGP4 predictor
used to model terminal decay units (revs / day ^3)
It measures the second time derivative in daily
mean motion divided by 6
Bstar Drag term
• The parameter is another drag term in the SGP4
predictor units (radii^-1)
• The true value of B* is unknown for objects in orbit;
instead the dynamics model adjusts the B* term as
necessary to account for non-linear changes in mean
anomaly.
• B* has units of inverse Earth radii.

Inclination (degrees)
The angle between the equator and the orbit
plane.( i )
Right Ascension of the Ascending Node (degrees)
The angle between vernal equinox and the point where the
orbit crosses the equatorial plane (going north).( Ω )
Eccentricity
A constant defining the shape of the orbit (0=circular,
Less than 1=elliptical ).(𝑒 )
Argument of Perigee (degrees)
The angle between the ascending node and the orbit's point
of closest approach to the earth (perigee).(𝜔 )
Mean Anomaly (degrees)
• The angle, measured from perigee, of the satellite location in the orbit
referenced to a circular orbit with radius equal to the semi-major axis.(M)
• is the fraction of an elliptical orbit's period that has elapsed since the orbiting
body passed periapsis
Mean Motion ( rev / day )
The value is the mean number of orbits per day the object
completes.(n)
Revolution Number
• The orbit number at Epoch Time.
• The orbit revolution number normally increments each time the object passes the ascending node
in orbit; however, the value occasionally does not increment correctly, erroneously failing to
increment.
Revolution
number at
epoch

Orbital Elements
a – semi-major axis
this element defines the size of the orbit
e – eccentricity
this element gives the shape of the orbit
i – inclination
this element represents the orientation of
the orbit with respect to Earth’s equator
Ω – longitude of the ascending node
this element represents the location of the
ascending and descending orbit locations with
respect to the Earth’s equatorial plane
ω – argument of perigee
this element defines where the low point, called
perigee, of the orbit is with respect to the Earth’s
surface
𝜈 – true anomaly at epoch
• this element notes where the satellite is within the orbit with
respect to the perigee
• The angle define the position of the satellite on the orbit which
continually increases with time

Machine
Learning is
using Data to
Answer the
Question

Artificial
Intelligence
Intelligence
machines that think
and act like human
Machine
Learning
is an application
provides systems the
ability to
automatically learn
and improve from
experience without
being explicitly
programmed.
Deep
Learning
Machine think like
human brains using
artificial neural
networks

• RNNs are a type of ANN architecture that uses iterative function loops to
store information, inspired by the cyclical connectivity of neurons in the
brain.
Recurrent Neural Network(RNN)
• RNNs are particularly useful for dealing with sequential data because they
consider not only the current input but also the previous input, allowing
them to remember what happened previously.
• RNNs learn from training data and are distinguished by their "memory,"
which allows them to affect current input and output by using information
from previous inputs.

Satellite Orbit Prediction Using
Machine Learning
Using Two Line Element Data Format and the core data of the satellite orbit includes six
integral constants, namely six elements of the Kepler orbit:-
1. semi-major orbit axis a
2. the orbital eccentricity e
3. the angle between the orbital plane of the satellite and the equatorial plane i
4. Equatorial longitude Ω
5. Orbital perigee polar angle ω
6. satellite orbital ascending node N

Translate angels to position
𝒂𝑰
𝒂𝑱
𝒂𝑲
= 𝑻𝑴
𝒂𝑷
𝒂𝑸
𝒂𝑾
Where ( TM ) is the transformation matrix
𝑻𝑴 =
𝒄𝒐𝒔𝝎 𝒄𝒐𝒔𝛺 − 𝒔𝒊𝒏𝝎 𝒔𝒊𝒏𝛺 𝒄𝒐𝒔𝑰 −𝒔𝒊𝒏𝝎 𝒄𝒐𝒔𝛺 − 𝒄𝒐𝒔𝝎 𝒔𝒊𝒏𝛺 𝒄𝒐𝒔𝑰 𝒔𝒊𝒏𝛺 𝒔𝒊𝒏𝑰
𝒄𝒐𝒔𝝎 𝒔𝒊𝒏𝛺 + 𝒔𝒊𝒏𝝎 𝒄𝒐𝒔𝛺 𝒄𝒐𝒔𝑰 −𝒔𝒊𝒏𝝎 𝒔𝒊𝒏𝛺 + 𝒄𝒐𝒔𝝎 𝒄𝒐𝒔𝛺 𝒄𝒐𝒔𝑰 −𝒄𝒐𝒔𝛺 𝒔𝒊𝒏𝑰
𝒔𝒊𝒏𝝎 𝒔𝒊𝒏𝑰 𝒄𝒐𝒔𝝎 𝒔𝒊𝒏𝑰 𝒄𝒐𝒔𝑰

𝒓𝑷𝑸𝑾 =
𝒓 𝒄𝒐𝒔 𝜈
𝒓 𝒔𝒊𝒏 𝜈
𝟎
r =
𝒂 𝟏 − 𝒆𝟐
𝟏+𝒆 𝒄𝒐𝒔 𝜈

𝝂 = 𝒎 + (𝟐𝒆 − 𝟏 𝟒 𝒆 𝟑 )𝒔𝒊𝒏(𝒎) + 𝟒 𝟓 𝒆 𝟐 𝒔𝒊
𝒏(𝟐𝒎) + 𝟏𝟑 𝟏𝟐 𝒆 𝟑 𝒔𝒊𝒏(𝟑𝒎)

𝑬 = 𝒎 + ( 𝒆 − 𝟏 𝟖 𝒆 𝟑 ) 𝒔𝒊𝒏(𝒎) +
𝟏 𝟐 𝒆 𝟐 (𝐬𝐢𝐧 𝐦) 𝟐 + 𝟑 𝟖 𝒆 𝟑 𝒔𝒊𝒏(
𝟑𝒎)

Related Work
Research on Satellite Orbit Prediction
Based on Neural Network Algorithm
June 22–24, 2019

• The experiment is based on the Keras library under the TensorFlow
framework and the Sklearn machine learning library.

Data are added to construct a TLE forecast eight
for TLE data prediction. The elements are as
follows:
The LSTM (Long-term and short-term
memory networks )- based prediction model
consists of four parts, as shown in the figure :
(1) Input layer: Eight element data of TLE orbit
prediction.
(2) LSTM layer: Obtain high-dimensional features
of the eight-element data of TLE orbit prediction.
(3) Full-connect layer: Integrate the acquired high-
dimensional features.
(4) Output layer: Calculate the predicted value of
the target element and outputs it.

Research Objective
we will analyze the current progress
of applying satellite orbit prediction
deep learning techniques to enhance
satellite orbit prediction accuracy
and avoid the satellite collision

Satellite Total
Element of
data
Training
data
Testing
data
Semi
major axis
sat
IRIDIUM 7
24793
14755 80% 20% a =7155
km
Data

Acknowledgment

Satellite orbit prediction based on recurrent neural network using two line elements

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