The surge in the number of pieces of orbital debris in Earth’s orbit has become an increasing problem ever since humanity started exploring and expanding into space at the start of the space age in 1957 [1], [2], launching commercial operators and large constellations of satellites to provide data about factors such as climate, atmospheric conditions, and navigation on Earth [3]. The accumulation of a large population of debris surrounding the Earth is making it extremely difficult to maintain sustainability in space in the long-run due to the dangers of space debris striking satellites and spacecraft. It is estimated that there are around 34,000 trackable objects that are 10 cm or larger in Earth’s orbit, posing significant challenges to space travel and development in space [2].

Figure 1 illustrates the scale as well as composition of the orbital environment targeted by this innovative study, as reported by the European Space Agency’s 2025 annual report [3]. Figure 1 is a useful graph showing statistics of growth of cataloged objects across all orbital classes over time. These objects are differentiated by object type– such as unidentified objects, rocket mission related objects, rocket debris, rocket fragmentation debris, rocky bodies, payload mission related objects, payload debris, payload fragmentation debris, and payloads – and the trend of the data illuminates that after decades of gradual increase in the number of objects in orbit, the curve steepens dramatically in the last decade as large constellations of satellites and major collisions add active spacecraft and debris, respectively [3]. Fig. 1. Evolution of object counts in all of Earth’s orbits stacked by object class from 1960 to present. Adapted from [3]. The objects are differentiated by object class – unidentified objects (gray), rocket mission related objects (orange), rocket debris (maroon), rocket fragmentation debris (yellow), rocky bodies (red), payload mission related objects (cyan), payload debris (dark gray), payload fragmentation debris (blue), and payloads (navy), respectively – and show a gradual then steep increase in the total number of objects in Earth’s orbit in the last decade.

The rapid increase in all object classes in Earth’s orbit underscores the need for automated, machine learning-assisted predictions since orbit propagations are increasingly necessary for timely and accurate risk assessment in space. Due to orbital debris’ inherent lack of navigational systems, in contrast to satellites and spacecraft, uncertainty arises about the exact trajectories of these objects, adding another level of risk to human-made spacecraft. Several incidents have occurred in history where satellites and spacecraft have collided with objects in space, in turn creating a larger, vast field of debris which continues the cycle of debris in Earth’s orbit and increases the risk level even more [4]. An example of this was the February 10, 2009 collision of the U.S. Iridium 33 communication satellite with the derelict Russian Cosmos 2251 communication satellite both orbiting the Earth at an altitude of around 790 km [5], [6]. Their collision speed was about 11 km/s, and this event resulted in the creation of two new major debris fields that contributed to the dispersal of orbital debris around Low Earth Orbit (LEO) space [5], [6].

Figure 2 illustrates how a large amount of space debris clouds resulting from catastrophic collisions in LEO can spread and diffuse quickly, illustrating how the large amount of debris in Earth's orbit is a sizable risk to human spacecraft and satellites [5]. Therefore, the need for accurate and prompt orbit propagation systems to ensure all spacecraft stay intact is more crucial than ever in the modern age.

Fig. 2. Timestamped projection diagram showing the general pattern of the spread of debris clouds. Adapted from [5]. The debris clouds’ distribution is imaged approximately 9 minutes, 10 days, 6 months, and 3 years (left to right) after a major collision resulting in debris formation.

Obtaining accurate predictions of satellite trajectories through the use of detection algorithms is an essential part of space-situational awareness (SSA), and it ensures spacecraft and satellites are kept safe while in orbit [7]. Recent improvements in the sensor capabilities of space surveillance technologies have even made it possible to track and catalog smaller pieces of debris more than ever before [3], which opens up the opportunity for the orbits of these pieces of debris to be analyzed and predicted using orbit propagation techniques.

The current popular method of propagating and predicting orbital trajectories involves a physics-based method, which can produce volatile predictions due to many factors of space, such as atmospheric drag, solar radiation pressure, and Earth’s gravity [4]. The surveillance equipment required to collect these precise measurements is expensive, and data acquisition is time consuming, making it almost impossible to have necessary, timely orbital predictions [4]. Additionally, the errors from this type of physics-based orbital prediction, which typically uses Simplified General Perturbations-4 (SGP4) propagator systems, increase very rapidly as time goes on since over-simplifications are made by the system, especially when trying to predict the orbit of an object in LEO over extended periods of time or long distances [8], [9]. Therefore, physics-based orbital propagation is a pressing issue in the modern-day fields of aerospace development and satellite tracking since there is a very large potential for error, and a few meters in LEO space could make all the difference between a close-call encounter between pieces of debris or a major collision [8].

The CASSIOPE satellite, fully developed by the University of Calgary and the satellite of study for this project, is a polar-orbiting satellite in an elliptical LEO orbit that provides high-accuracy GPS-based orbit data due to its array of five dual-frequency GPS receivers [12]. These GPS receivers are used to derive the satellite’s position and velocity with extreme accuracy, with up to 100 GPS samples per second, meaning CASSIOPE’s GPS data is very accurate and reliable [12]. Additionally, ESA’s Swarm satellites also use advanced onboard GPS dual-frequency receivers for precise orbit determination with near-continuous coverage, enabling accuracy down to the centimeter level [13]. Swarm’s primary mission objective is to study the dynamics of Earth’s magnetic field and how the magnetic field interacts with the Earth. All four Swarm satellites carry advanced instruments like magnetometers, a tool used to measure the strength and direction, as well as changes to Earth’s magnetic fields [13]. Also, the Swarm satellites are equipped with an accelerometer that is used to derive thermospheric density and winds as a secondary mission objective [13]. Because both of these satellites support scientific objectives of high-value and further scientific development, improving multi-day orbit predictions can reduce the collision risk and increase the safety of these satellites in the increasingly dangerous LEO environment.

Machine learning (ML) methods offer a promising new approach to addressing the issue of increased error growth resulting from SGP4 propagations, as the predictions of orbits will be able to be made without the explicit data points of atmospheric drag, gravitational forces, among other factors [4]. In contrast to physics-based orbital propagation methods, ML algorithms work similar to a human brain’s neural networks by taking in large amounts of data, recognizing patterns, and using this past data to predict future events based on patterns [4]. Specifically, supervised learning is a ML training technique where labelled input data with corresponding known outputs is inserted into a ML model [4], [9]. This method of training is very effective since the algorithm is able to devise patterns and relationships within the data to propagate future orbits [4], [9].

A key data type in the ML process are Two-Line Element (TLE) sets. TLEs are an example of a public, open-source data record for resident space objects (RSOs), encoding an object’s orbit at a specific epoch. However, when TLEs are propagated with SGP4 to predict an object’s future position, the resulting positions will have significant error growth when compared to the true position of the object [8], [10]. TLEs exist for thousands of cataloged objects, always appearing in a consistent format, making them an extremely useful, standardized type of data that can be sorted through easily by a ML algorithm [4]. Leveraging these consistent, widely available records of an object's position, paired with their SGP4 propagated states will offer excellent input data for a ML model since the model will be able to look for patterns and comparisons between an object’s actual position and the position that SGP4 predicted.

Prior work in this field includes utilizing and developing supervised and reinforced ML algorithms as an alternative to physics-based propagation methods [4]. Most of these systems utilize known “truth” data such as its position or velocity in conjunction with ground-based data like solar flux or geomagnetic index measurements [8], [10] to make predictions about the error level of physics-based SGP4-propagated data [4]. Data types historically used for this step have included simulation-based space catalog environments, RSO radar-based observational data, image-based data, among others [4], [10]. The accuracy and usefulness of these ML systems have depended on many factors such as: the type of ML algorithm used, the type of ML style used, the program or development environment used to implement it, the accuracy of the data inputted, and the time range examined [4], [8], [10]. Overall, many experiments have been successful in their ML models, with measurable reductions in orbit-prediction error after the ML-based corrections were implemented, although the magnitude of the improvement varies across different studies [4], [8], [10].

Different ML systems use different classifiers to approach data sets, such as random decision forests, which combine multiple decision “trees” to improve the accuracy and robustness of prediction [8], and support vector machines, which plot points in n-dimensional space based on the number of features in the dataset to come to conclusions [10], [11]. The differences in these methods can translate to the accuracy of the results given. In general, the prediction error of orbital trajectories has decreased due to the general usefulness and accuracy of ML-augmented predictions that help minimize the physics-based prediction errors [4]. Since the ML field and information about the increasing amounts of orbital debris in LEO space is relatively new, many scientists hint that more research needs to be done and more ML algorithms need to be tested for indisputable conclusions to be made on the subject area [4].

As one representative example, Peng and Bai [4] propose a hybrid orbital-prediction method in their 2018 study that uses a physics-based propagator, but also a supervised ML model to learn the prediction error from the historical “truth” data and physics-based propagation values. As part of their study, they applied the ML “learned error” as a correction to the model’s outputs in the hope for more accurate results with less error over time. A performance metric was reported for the percentage of residual error after ML correction relative to the original error in the physics-based propagated states. This metric was reported to have experienced strong reductions, meaning the residual error values after the ML correction were lower than they were before the model’s correction. Overall, the supervised ML model they used could reduce prediction error by more than half across the many generalization tests they conducted, which supports the continued potential of developing ML-based correction approaches especially in the orbital object prediction field [4]. In their analysis, they also wrote that “further studies are required to draw concrete conclusions” about the effectiveness of supervised ML models and the accuracy of their orbital position outputs [4].

This study aims at specifically targeting the error growth of physics-based orbit propagation methods. A supervised ML model (with a neural-network baseline) can learn the error patterns between SGP4 error growth and time since the starting epoch to potentially increase the accuracy of LEO orbit prediction compared to the standard SGP4 algorithm. The ML model characterizes the residual errors between predicted and observed satellite states, thereby enhancing the accuracy of orbit propagation. This approach augments existing physics-based methods, which prove to be inaccurate over long periods of time or distance [14].

A secondary objective is to investigate the sensitivity to the ML model to the specific physical and orbital characteristics of the objects under analysis. Data from the University of Calgary’s CASSIOPE satellite [12] and one of the European Space Agency’s four Swarm satellites is analyzed [13].  In all, the overall, general objective is to determine, by using a systematic and quantitative comparison, whether a supervised ML correction model can meaningfully reduce extended day LEO propagation error relative to the SGP4 propagations that are currently in widespread use in the space industry now [8]. If successful, the results from this study would make space situation awareness more reliable by improving the accuracy of orbital predictions as well as reducing the unnecessary workload from avoidable false alerts due to the inaccuracies of traditional physics-based propagations [9].

The overall, general objective is to determine, by using a systematic and quantitative comparison, whether a supervised ML correction model can meaningfully reduce extended day LEO propagation error relative to the SGP4 propagations that are currently in widespread use in the space industry now [8]. If successful, the results from this study would make space situation awareness more reliable by improving the accuracy of orbital predictions as well as reducing the unnecessary workload from avoidable false alerts due to the inaccuracies of traditional physics-based propagations [9].

1) Data Collection and Organization

This project uses archived 2019 data for the University of Calgary’s CASSIOPE satellite currently in LEO space [2], and combines GPS-derived “truth” ephemerides, TLE data for baseline propagation for the spacecraft and space weather indices used as other ML inputs.

1. Truth Ephemerides: Truth orbit states for the CASSIOPE satellite were obtained using the Orbit Geo SP3 product associated with the CASSIOPE mission data system. These truth states provide specific time-stamped position and velocity data in the International Terrestrial Reference Frame (ITRF) and in GPS time [3]. Truth ephemeris files from CASSIOPE’s Orbit Geo SP3 product were downloaded for a six-month period spanning from January 1, 2019 to June 30, 2019.
2. TLE Data: For the same time period, CASSIOPE TLEs were collected as well as stored as the baseline inputs for SGP4 orbit propagation.
3. Space Weather Data: Space weather indices were included in the ML training since geomagnetic and solar activity have the ability to influence upper-atmosphere and LEO conditions, and affect drag-related prediction errors. The two space weather indices used in this project were 10.7 cm solar radio flux (F10.7), which is an indicator of solar activity. Additionally, the planetary K-index (Kp) was used as an indicator of geomagnetic disturbance level. These indices were joined and time-aligned to the orbit dataset features.

All data used for ML training and evaluation were previously collected and stored in open-source data sets, and the analysis was performed offline using archived data points rather than real-time onboard processing techniques. All data files used were organized by date and processed using Python scripts carried out in Visual Studio (VS) Code. The intermediate tables were stored as Pandas DataFrames to keep the steps reproducible for potential future use for other satellites’ information.

2) Data Preparation, Parsing, and Cleaning

After the collection of all of the data for the CASSIOPE satellite, each data source was converted from raw text files and combined into one large synchronized dataset sorted by time.

1. Parsing: The GPS truth ephemeris files were parsed using Python to programmatically read the files. The time stamps and position/velocity state vectors for CASSIOPE at each recorded epoch were recorded and converted into a structured Pandas DataFrame in Python. Data was stored in this tabular format to ensure that the data could be merged using by consistent timestamps.
2. Data Cleaning: Data points were excluded from the ephemeris if any of the following conditions occurred: (i) missing SP3 truth values at required timestamps, (ii) missing SGP4-propagated state (position and velocity) vectors at a specific timestamp, (iii) invalid timestamps or invalid numerical values in the DataFrame. These exclusion rules were applied consistently throughout the full dataset to ensure that the data was standardized and could be used for computations and ML training easily.
3. Time Standardization: GPS time stamps were converted into a consistent data and time format inside of the Pandas DataFrame so that the SGP4 prediction times could be aligned seamlessly. Additionally, the F10.7 and Kp times were also aligned to this same time standardization format. However, since Kp is reported over intervals or multiple hours where F10.7 data values are typically reported daily, the space weather values were aligned by using the most recent available value so that each epoch had a defined space weather value without any gaps.

3) Baseline Orbit Propagation and Residual Calculations

Once all the data in the dataset was cleaned and time-aligned, the baseline propagations were generated using SGP4 and converted over to a comparable reference frame so that the difference between the propagated states and the GPS truth data states could be computed accurately.

1. SGP4 Propagation: TLEs for CASSIOPE were grouped into weekly “packets” across the study period, producing 26 TLE packet sets. To create each packet, a selected TLE was propagated forward using SGP4 over a fixed two-week propagation window, and the resulting state vectors were generated at the same epochs as the GPS truth samples to allow for easy comparison. This SGP4 output served as the baseline prediction dataset used to calculate residual error, and to build the training inputs for the supervised ML model.
2. Reference-Frame Harmonization: Since the GPS truth states for CASSIOPE were provided in ITRF, the baseline SGP4 outputs were transformed, using Python in VS Code, into the same Earth-centered reference frame before the residual error computation.
3. Residual Error Calculation: Residuals were computed as the difference between the baseline predicted position, using SGP4 propagation, and the GPS truth position, given by the CASSIOPE GPS data files, at each epoch. In order for residual error calculations to be accurate, both the baseline SGP4 propagated states and the CASSIOPE truth data were compared at identical epochs and also were compared in the same coordinate reference frame.

4) Machine-Learning Correction

The ML component of the project was implemented in Python using TensorFlow, which provides a framework for defining, training, and validating neural networks on large, structured datasets [16]. TensorFlow’s system and design and training capabilities are described in [16]. The goal of the project's ML model was not to replace the SGP4 propagations, but to use SGP4 as the baseline propagator and have the ML model produce a “correction factor” output that, when applied to the SGP4 baseline propagations, could yield a propagation result that is hopefully closer to the GPS truth of where CASSIOPE actually was at a specific time. The ML model was utilized like this so that the final propagated states could better match the GPS truth trajectory of CASSIOPE over longer prediction times, which is when large residual errors occur in the baseline SGP4 prediction.

1. Machine Learning Model Inputs: The neural network ML model’s input data set contained the time from the TLE epoch, the baseline position and velocity information at each timestamp, as well as Kp and F10.7 space weather indices.

5) Time-Gated Correction

To reduce the risk of the ML model making the propagations close to the start of the initial epoch more inaccurate and increasing the error in early time periods where the SGP4 propagations were already very accurate, a time-gated correction approach was applied. Therefore, the main incentive for implementing this time-gated approach was to improve longer-horizon prediction accuracy without degrading short-horizon performance. For each propagated epoch, the trained neural network produced a predicted correction vector on top of the baseline SGP4 propagator outputs derived from the learned error patterns using the prepared dataset that included time since epoch, the baseline SGP4 state information of CASSIOPE, and the time-aligned space-weather indices.

The ML-corrected state was defined as the baseline SGP4 state minus the predicted correction term, scaled by a time-dependent gate. Under this rule, the gate function (α(t)) was set to zero for the first seven days following the TLE epoch, and it was set to one after day seven. As a result, the ML-corrected state was identical to the baseline output during the first week to stabilize early predictions, while ML influence was only applied during the later portion of the two-week window (from seven to fourteen days). This design was implemented because early-time predictions tend to be less dominated by residual growth, while later-time predictions show larger divergence from the GPS truth trajectory and they have a larger residual error. The time-gated approach therefore stabilizes the earliest segment of each propagation and targets the correction to the period where error growth is typically most significant at times further from the initial epoch.

6) Machine-Learning Validation and Performance Metrics

1. Machine-Learning Validation Process: The effectiveness of the ML model was evaluated using the six TLE packets that were not used in the ML training process. Specifically, the supervised neural network was tested on these six TLE packets not seen during the training process to validate whether the ML model was able to learn a repeatable error correction factor that could be applied to TLEs it had never encountered before. During the ML validation processes, the baseline SGP4 residual error that was obtained by comparing the SGP4 output to the GPS truth states at matched epochs, was compared on the same plot as the post ML-correction residual error obtained using the time-gated correction model.
2. Statistical Analysis: To quantify performance of the ML model, percentile-based indicators, such as P50, P90, and P99, were used to investigate the residual error distribution in the ML outputs [16]. The P50 metric represents the 50th percentile, or median, residual error magnitude with the ML-correction active, meaning that half of the residual error values fall below this level. The P90 metric represents the 90th percentile, meaning ninety percent of the residual error values from the ML correction fall below this level, and the P99 metric represents the 99th percentile, showing specifically the top one percent of highest residual error values that were predicted by the ML model. This indicator is specifically focused on showing extreme outlier error and how robust the ML model is under worst-case conditions. These indicators were calculated in Python by first compiling all of the residual error magnitude output values that the ML model predicted. The percentage functions were computed using numerical percentile functions in Python, while making specific use of NumPy, a specific Python library that is made for high-level numerical computations [17].
3. Plotting Using Python: Finally, the results of the ML-correction were visualized using Python plotting tools to clearly compare the baseline SGP4 residual error growth against the ML-correction residual error growth. Graphs were created to show how the residuals evolved and increased relative to the ML-correct residual error growth. In addition to a “mean residual error” line for both the SGP4 baseline propagation and the ML-correction, percentile shading was also included to show the extreme outliers in the data.

Residual error growth was first characterized using two-week SGP4 baseline propagations generated from TLEs along with the GPS truth data at each epoch to be used to verify the residual error at each time. After matching the epochs and comparing positions using the same Earth-centered reference frame, namely the International Terrestrial Reference Frame (ITRF), the baseline SGP4 residuals showed a clear increase in error growth over time, progressing from sub-kilometer error levels to tens of kilometers by fourteen days after the initial epoch. When the SGP4 residual error growth was graphed in figure 1, the graph confirms that the multi-day LEO predictions accumulate more residual error over time when using the standard physics-based SGP4 propagation method, and it also provides a clear reason and incentive for why improving LEO prediction is necessary – to reduce residual error, making orbit predictions more accurate and useful to satellites and space objects. Fig. 1. SGP4 Baseline Residual Error Growth. As time since the initial TLE epoch increases in days on the horizontal axis, the 3D residual error (blue line) resulting from this propagation process increases rapidly on the vertical axis, showing a visual representation of the rapid error growth from using SGP4 propagation.

Next, the supervised neural network correction model was evaluated using the project’s time-gated correction approach. This means that the model’s correction influence was not active from day zero to seven, and was only activated during the day seven to fourteen window. The results of this time-gating approach were that the early predictions, given by the baseline SGP4 propagator, remained stabilized and accurate in the time period closest to the initial propagation epoch, but as time increased from after the seven day mark, the ML model was able to generalize to the higher-error data and effectively decrease the error compared to the baseline SGP4 propagations. Specifically, this gating framework was used to isolate whether the ML model could actually reduce the repeatable error patterns that occurred later in the propagation window, without introducing any sort of instability to the short-term propagation interval. In figure 2, it was observed that the ML model was able to reduce the error growth compared to the baseline SGP4 error in the time interval from seven to fourteen days, and this data is also graphically shown by the fact that the ML-correction median error is clearly and fully below the median SGP4 error line, especially around the ten to fourteen day mark. Fig. 2. Training Set Error Growth With ML Correction. A comparison of the residual error values of CASSIOPE’s future trajectory propagations between the standard SGP4 physics-based propagator system and the ML-correction model. The ML corrections are active from the seven to fourteen day mark because of the time-gated corrections. From around the ten to fourteen day mark, the median ML model error (red line) is clearly below the SGP4 baseline error level (blue line).

Performance by the ML model was then quantified by comparing the baseline residual error to ML-corrected residual error on six unseen TLEs that were not included in the twenty TLE training set. Figure 3 shows the ML model’s validation error growth over the fourteen day propagation period, however, it shows some signs of overfitting as well. Overfitting occurs when a model “memorizes” parts of patterns that are specific to the training data, so that the training improvement is larger than the actual validation data. In figure 3, the after-ML median mostly tracks with the baseline SGP4’s error growth, showing only modest improvement after the gate activates, hinting that the model’s learned corrections may have not fully been able to generalize with the training dataset’s patterns. At the same time, the fact that the validation performance by the ML model stays close to, and in some regions, has less error than the SGP4 propagations (shown when the red after-ML correction line is beneath the blue SGP4 median error line), highlights how a positive result was still achieved by the ML model. This is because the data suggests that the correction is not destabilizing the trajectory of the CASSIOPE satellite, and is not worse than the baseline SGP4 propagations. While the validation results show a smaller decrease in error growth compared to the training set data, the small, measurable reductions in error that the ML model is successfully completing is a positive sign that the ML model has potential to make stronger patterns with the error growth data with a larger training set and with a longer period of training data.

Fig. 3. Baseline SGP4 Error Growth Vs. After-ML Validation Error Growth. Over a fourteen day propagation window, the median baseline SGP4 error growth (blue line) is compared to the ML validation outputs (red line) on 6 unseen TLEs not in the original training set.

Additionally, percentile indicators, such as P50, P90, and P99, were used to compute the residual error magnitude distribution in the seven- to fourteen-day ML influence window. The median error (or P50) value improved with the ML-correction active, as the median error reduced from 6.64 km to 6.50 km when the ML-correction model's error was compared to the SGP4 baseline error. The P90 value, which represents the 90th percentile of the output error data (or the value that ninety percent of the error output values are under) also improved with the ML-correction, since the error was reduced from 25.08km to 24.81 km compared to the standard SGP4 error. However, the extreme outlier metric (P99) which represents the value that ninety-nine percent of the residual error output values were under slightly worsened from 29.57 km to 30.02 km with the ML-correction. This indicates that while the model reduced error for most cases, it did not consistently reduce the worse-case events/outliers in the dataset, meaning that outlier-aware ML training will be required in the future.

This innovative project demonstrated that baseline SGP4 propagation for LEO spacecraft exhibits substantial error growth over multi-day propagation prediction windows, due to oversimplifications made by the propagation model and the variability of various drag, geomagnetic, and solar factors in the space environment surrounding the Earth. In the fourteen-day propagation window examined in this project, residual error was seen to increase at an exponential rate as time (in days) went on from sub-kilometer levels to tens of kilometers by the fourteenth day. This error growth reinforces why long-term prediction uncertainty is a real and measurable limitation to spacecraft propagation and overall orbit prediction in the astrophysics field currently. The LEO space environment would be safer and more inviting to more satellites and spacecraft if precise orbit propagation is able to be achieved.

The time-gating correction strategy utilized in the project was able to successfully preserve relatively low propagation prediction error during the early time since initial TLE epoch, and this is because the ML influence was not applied on early-window times when the SGP4 propagation was already giving more accurate results. However, in the active ML-correction window, which was from seven to fourteen days after the initial TLE epoch, the supervised neural network produced a measurable reduction in residual error compared to the baseline SGP4 propagation error, which supported the project’s main research goal of attempting to utilize a supervised ML model to improve multi-day orbit propagation prediction accuracy using a residual-correction approach rather than using the standard SGP4 propagation system.

However, the ML validation results showed a limitation that is important to address before the model is used in any space-safety applications. The P99 value, which represents the top one percent of highest error values, slightly increased under the current ML model setup. While the P50 and P90 indicators improved with the utilization of the ML model, more outlier-aware ML training/outlier-focused ML evaluation will be needed in the future to ensure that the worst-outliers in the output data do not get any worse. Also, the ML validation showed some small signs of overfitting, however the overall predictions given from the ML model were not worse than the SGP4 baseline. A larger dataset in the future for ML training could combat the potential overfitting in the current model.

Overall, though, the findings of the project support the conclusion that ML can be used to learn the repeatable residual patterns that are present in SGP4 propagations to reduce multi-day LEO orbit propagation error, but additional future work will be needed in order to ensure that this supervised ML method can be considered robust enough to use in an operational context in the field of astrophysics.

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Thank you to:

• Andrew Howarth and the University of Calgary’s Department of Physics and Astronomy
• Dr. Garcia-Diaz and Webber Academy for ongoing support and project supervision
• The CASSIOPE/e-POP mission data resources and public catalog/space-weather providers

Use of AI: Generative AI (ChatGPT by OpenAI) was used as a writing/coding assistant (brainstorming and debugging). Project coding and results analysis were performed and verified by the author.