Application of Machine Learning for tracking Orbital Debris

In 2019, the European Space Agency reported the number of orbiting space debris at greater than 1 meter was about 5,400 objects. Approximately 34,000 objects were larger than 10 centimeters (which includes 2,000 active satellites). There were 900,000 objects greater than 1 centimeter and 130 million objects greater than 1 millimeter.

Given Low Earth Orbit objects speed of up to 17,500 mph (more than 10 times the speed of a bullet), collisions of even the smallest objects with any spacecraft could be catastrophic and propagate further debris. The Kessler Syndrome models space pollution that is perpetuated by collisions between orbiting objects, creating more debris and thus creating a domino effect of future collisions.

Current System for Tracking Orbital Debris

Geometrical Diagram of Keplerian Elements in Orbit

The space debris is categorized into five Keplerian elements, which are known as semimajor axis, eccentricity, inclination, argument of perigee, and the right ascension of ascending node.

Inclination is the angle between the equator and the orbit. Eccentricity is the shape of an orbit (how close to a circle it is). Right Ascension of the Ascending Node (RAAN) is the angle between a distant star and were the satellite crosses the equator heading from south to north. The Argument of Perigee is the position of perigee as measured from ascending node. These points can define any single orbit of a space debris and can be used to calculate the orbit of an object.

Demonstration of Extended Kalman Filter

The Extended Kalman Filter (EKF) correctly models the state transition of error dynamics and statistically corrects via error covariance propagation to estimate orbital waypoints for trajectory prediction. The EKF has been considered the standard in the theory of nonlinear state estimation, navigation systems, and GPS. But the problem is astrodynamics of orbiting objects constantly change due to celestial disturbances, leading to frequent manual tuning of EKF parameters necessary for off-track space targets. Without self-learning and training abilities, covariance driven tracker must be adjusted for individual space targets. Before we tackle the challenge of orbital tracking, we first need to understand the organizations behind the job.

Organizational Structure of Space Operations Command (SpOC)

The Combined Force Space Component Command (CFSCC)/SpOC West’s mission is to plan, integrate, conduct, and assess global space operations in order to deliver combat relevant space capabilities to Combatant Commanders, Coalition partners, the Joint Force, and the Nation. As one of its primary roles, CFSCC plans, tasks, directs, monitors, and assess the execution of combined and joint space operations for theater effects on behalf of the Commander of USSPACECOM in order to directly integrate with ongoing operations in other Combatant Commands.

The 18th Space Control Squadron (18 SPCS), falling under Space Delta 2, predicts when and where man-made objects will reenter the Earth’s atmosphere. 18 SPCS includes maintaining the space catalog through space surveillance and tracking data received from the U.S. Space Surveillance Network (SSN), generating spaceflight safety data, and processing high interest events such as launches, reentries, and breakups. 18 SPCS has broken down 3 types of reentries for its reporting.

3 Types of Reentries

There are 3 types of reentries: Deorbit, Normal Decay, and Reentry Assessment objects. Deorbit is a controlled reentry of an object, usually at a known time to a planned location. Normal decays are objects that decay naturally and not deemed survivable. They are uncontrolled, gradual reduction of an object’s orbit and are not expected to survive reentry. They typically have Radar Cross Section of less than 1m².

Ground Trace of OSNSAT by 18 SPCS

Reentry Assessment (RA) Objects may be classified as routine or high-interest, and include payloads, rocket bodies or platforms. And debris have greater than 1m² of Radar Cross Section or historically been expected to survive.

SGP4 Two-line Elements breakdown

Space Defense Operations Center (SPADOC) analysts identify upcoming reentries by propagating every object for a period of time or until decay using Simplified General Perturbations 4 (SGP4) Two-Line Elements (TLEs), which is adequate for the near-earth, circular objects.

Gravity Map of the Earth

A perturbation is a change in the orbit due to a natural force, like mass asymmetry (J effects), drag (all satellites out to 2000 km), radiation pressure (force from sunlight), and third-body effects (Sun and Moon). General Perturbations (GP, SGP, SGP4), takes average of all perturbations over the entire orbit and lumps it together into one variable, and produces smooth curve over time. It is quick to calculate but not very accurate over time.

SPADOC warns of conjunctions that are under 5 km miss distance at GEO or less than 1km miss distance in LEO, and do this within 72 hours of the time of closest approach. Currently, the estimated day-to-day statistical chance of a collision is 1x10–6 (one in a million). SPADOC collects thousands of observations every 24 hours to generate a current average of 30 daily collision warning notifications that provide to global spacecraft owners and operators. The 18 SPCS also utilizes the Astrodynamics Support Workstation’s (ASW) SP propagator, which has more up-to-date earth models and a more accurate dynamic atmosphere model.

The Space Surveillance Network (USSTRATCOM)

The Joint Space Operations Center (JSpOC), located at Vandenberg Space Force Base, California, actively tracks all objects of ‘softball size’ (10cm) or larger in orbit, using the US Space Surveillance Network (SSN) as the primary detection suite of sensors. They are responsible for correctly mapping objects travelling in the Earth’s orbit, charting the present position of space objects and plotting their anticipated orbital paths, detecting new artificial objects in space, and predicting when and where a decaying space object will re-enter the Earth’s atmosphere.

The Joint Space Operations Center (JSpOC), under its current structure, is primarily a space traffic management center today, but some believe it should do more to preserve national security in space. (US Air Force)

SPACETRACK represents a worldwide Space Surveillance Network (SSN) of dedicated, collateral, and contributing electro-optical, passive radio frequency (RF) and radar sensors. The SSN is tasked to provide space object cataloging and identification, satellite attack warning, timely notification to U.S. forces of satellite fly-over, space treaty monitoring, and scientific and intelligence gathering.

Space-Track.org Reentry Tab (Public Data)

The continued increase in satellite and orbital debris populations, as well as the increasing diversity in launch trajectories, non-standard orbits, and geosynchronous altitudes, necessitates continued modernization of the SSN to meet existing and future requirements and ensure their cost-effective supportability. SPACETRACK has developed the systems interfaces necessary for the command and control, targeting, and damage assessment of a potential future U.S. anti-satellite weapon (ASAT) system.

Russian ASAT Test causing orbital debris (DailyMail)

When debris collide, it generates a cloud of orbital debris, as shown with the destruction of the Kosmos 1408 satellite by a Russian ASAT missile on November 15, 2021, with 1500 pieces of debris being tracked and an estimated hundreds of thousands of pieces too small to track. Since the satellite was in a polar orbit, and its debris has spread out between the altitudes of 300km and 1000km, it could potentially collide with any LEO satellite, including the International Space Station and the Chinese Space Station.

Iridium-Cosmos debris 3 hours (left) and 2 years after impact (Secure World Foundation)

With an ever-growing concern for exponential growth of orbital debris, the current organizations responsible for tracking may need to implement a new tracking method. Seer Tracking provides one method for implementing machine learning for tracking orbital debris.

Application of Machine Learning: Seer Tracking

Amber Yang, a Stanford graduate, founded Seer tracking to track and map space debris in Low Earth Orbit for the purposes of reducing space debris collision risk with space missions. There was a study invoked by 2014 Nobel Prize for discovery that the brain can act as an inner Global Positioning System (GPS) due to its ability to recognize geometric patterns. Amber Yang’s research was to question inherent geometrical patterns that can be noticed in the orbits of debris be used for pattern recognition for artificial neural networks over time.

In machine learning, backpropagation is a widely used algorithm for training feedforward neural networks. Backpropagation is a type of artificial neural network in where the input and output data are initially both presented to the neural network. The neural network learns the conductivity and the weights that are related in between the input and the output after each forward pass through a network. The algorithm is used to effectively train a neural network through a method called chain rule.

Orbital Recognition System Schematic Diagram

Her research involved 1,000 space debris samples and analyzed the changes in Keplerian orbits for the debris over time by testing the samples in her artificial neural network. In her research, she noticed that there were geometric patterns that are inherent in every single orbit.

The Target Detection ANN, in red, is the subsystem for identification, classification, and cataloguing space debris. She was eventually able to garner around a 94% identification accuracy for her target detection neural network as it successfully identified and classified after the orbit of the space debris changed.

Trajectory Prediction Backpropagation ANN Schematic Diagram

The Trajectory Prediction ANN, in blue, is the subsystem for monitoring and tracking space debris. This artificial neural network focused mostly on predicting a future orbit of space debris. The ANN works by inputting five past orbits of the space debris sample and looking at the delta changes of the Keplerian elements in between each orbit. The goal for the output layer would produce a future delta change of the space debris sample in terms of the Keplerian elements. Simulation of Trajectory Prediction ANN for space debris showed that ANN system can interpolate the changes of orbital patterns in the waypoints that were never trained before. She discovered the tracking errors for Trajectory Prediction ANN are smaller than those of conventional tracking methods.

Yang’s second part of the research implemented Iterative Closest Points (ICP) algorithm to simplify a large group of debris into just a few data points. The ICP algorithm is used to register a geometric alignment and relationship between two different scans of objects at two different points in time. The ICP algorithm is often used to reconstruct 2D or 3D surfaces from different scans, whether it is localizing robots and achieving optimal path planning (especially when wheel odometry is unreliable due to slippery terrain).

ICP Approach to Mapping Space Debris Clouds

The ICP algorithm utilized a binary KD-tree search to identify a point relationship between each point in the two different clouds via the Singular-Value Decomposition (SVD) algorithm. Then the ICP algorithm converged to the nearest local minimum of mean-square distance at a fast rate of convergence within a few iterations.

Trajectory Prediction ANN for Space Debris Cloud Tracking

The ICP algorithm decides the congruence of different geometric representations and estimates motion and rotation between two point clouds where correspondences are not known and predict future changes of ICP kinematic patterns for space debris cloud tracking. The average total tracking error for the space debris cloud group was 0.87 km (80 arcseconds) while the average tracking error for an individual space debris sample was less than 0.1 km (10–15 arcseconds), smaller than those of conventional tracking methods.

In conclusion, she was able to create a collision avoidance system by projecting the orbits of the debris and give enough time in advance to warn spacecrafts. And this research can be applied to any moving object with an elliptical orbit, e.g. satellites, space cargo, deep space planets, land drones. And for cloud debris samples, she utilized the ICP algorithm for the first time for object-oriented tracking, with effective results. Ultimately, successful experimental applications of an ANN-based Orbital Recognition System confirm the theoretical approach that pattern recognition ANNs can act as an accurate and effective space surveillance system for real space debris tracking.

Machine Learning during Space Traffic Management Conference 2020 Research by Slingshot Aerospace

In December 2019, SACT (Sprint Advanced Concept Training), a week-long commercial-government exercise, in part to showcase advanced Commercial Space Situational Awareness capabilities to the Department of Defense and Department of Commerce, Slingshot Aerospace ingested Resident Space Objects (RSO) state data from LeoLabs, Numerica, U.S. Space Command’s 18th Space Control Squadron (18 SPCS), Spire Global, and MITRE Corporation.

State Comparison Process by Slingshot Aerospace

LeoLabs achieved orbital state estimations via an Unscented Kalman Filter. This class of algorithm pairs the computational efficiency of a Kalman filter with the unscented transform, which attempts to more accurately render covariance evolution in nonlinear systems by propagating a set of sample points using the full physical model. 18 SPCS provided TLEs, while all others provided state vectors (SV), which are cartesian position and velocity.

Numerica collected data with a worldwide network of optical sensors, both fixed arrays and taskable telescopes. Spire satellites perform precise orbit determination by utilizing multiple Global Navigation Satellite System (GNSS) signals simultaneously collected through a zenith-pointing antenna. MITRE Corporation supplied calibration ephemeris data for a large set of GNSS satellites (e.g. GPS, GLONASS, Galileo, etc.).

Machine learning fusion technique results. Position errors associated with Numerica, 18th SPCS, and fused solutions as compared to MITRE calibration states (Slingshot Aerospace)

Because each data source has their own strengths and weaknesses in different settings (orbit regime, global coverage, RSO type, etc.), there was a need to create the most accurate solution for space catalog. To fuse this data into a best solution, a supervised learning regression model using machine learning was developed that processed provider state solutions over a large spread of objects in Geosynchronous orbit (GEO).

Machine learning fusion technique results. RIC errors associated with Numerica, 18th SPCS, and fused solutions as compared to MITRE calibration states (Slingshot Aerospace)

And this model was able to learn how to characterize the uncertainty developed during propagation and applied this to other objects in GEO to improve their solutions when compared to the standalone estimates from the various providers. Slingshot Aerospace was able to properly account for the error introduced in the propagation of a satellite state and produced a fused result of two different providers that reduced the RMS of the original solutions by nearly 50%.

Summary

Machine learning has been utilized for a wide variety of scientific and engineering problems that have high dynamics and uncertainties. By employing artificial neural network models, we can attempt to learn trends in data and make predictions or inferences based on this learning process. The addition of a neural network to the current framework aims to reduce errors in tracking satellite positions and prevent collisions with predictive modeling.

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