⚡ electrical engineering

Machine Learning-Based Evaluation of Attitude Sensor Characteristics Using Microsatellite Flight Data

This study demonstrates that a machine learning-based approach using a one-dimensional convolutional neural network can significantly improve microsatellite attitude determination accuracy by reducing RMS errors from approximately 7 degrees to 2–3 degrees compared to conventional TRIAD methods, by effectively learning and correcting nonlinear sensor error patterns from actual flight data.

Original authors: Yuji Sakamoto

Published 2026-01-28

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yuji Sakamoto

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: Teaching a Satellite to "Guess" Better

Imagine you are trying to navigate a car in the dark. You have a high-tech GPS and a perfect compass (the "Star Sensor" and "Gyro"), but they sometimes glitch or turn off when the sun is too bright. You also have a cheap, old-school map and a basic magnetic compass (the "Sun Sensor" and "Magnetometer").

Usually, when the high-tech gear fails, pilots rely on the cheap gear using strict math rules. This paper says: "What if we taught a computer to learn from the car's past trips instead of just following the math rules?"

The researchers took data from a small satellite (a "microsatellite") that had already finished its mission. They used the satellite's "perfect" past data as the answer key (Ground Truth) to train a Machine Learning model. Then, they asked the model to look at the "cheap" sensor data and predict where the satellite was pointing.

The Problem: The "Rough" Sensors

The satellite had two types of sensors:

The VIPs: A Star Sensor and a Fiber Optical Gyro. These are like a high-end GPS. They are very accurate but can get confused by sunlight or Earth's glare.
The Workhorses: Sun Sensors and Magnetic Field Sensors. These are like a cheap compass and a light meter. They are always on, but they are "noisy" and often give rough, inaccurate directions (about 7 degrees off).

In the past, engineers used a standard math method called TRIAD to combine these rough sensors. It was like trying to draw a straight line through a messy scribble. It worked okay, but the error was large (about 7 degrees).

The Solution: The "Pattern Recognizer"

Instead of using strict math formulas, the researchers used a Machine Learning tool called a Conv1D (a type of neural network).

Think of this tool as a super-observant student.

The Teacher: The "VIP" sensors (Star Sensor + Gyro) provided the correct answers.
The Homework: The "Workhorse" sensors (Sun + Magnetometer) provided the messy data.
The Lesson: The student looked at thousands of examples of messy data paired with the correct answer. It didn't just learn the rules; it learned the quirks. It learned, "Oh, when the magnetometer reads this specific weird number and the sun sensor reads that, the satellite is actually pointing here, even though the math says otherwise."

The model looked at short sequences of data (like a 5-second video clip of sensor readings) to predict the satellite's angle.

The Results: From "Rough" to "Sharp"

The researchers tested this on five different flight paths (passes). They trained the model on four passes and tested it on the fifth one (which the model had never seen before).

The Old Way (TRIAD Math): The error was about 7 degrees. (Imagine pointing your finger at a door, but missing it by a wide margin).
The New Way (Machine Learning):
- On data it had studied: The error dropped to 0.7 degrees. (You hit the door handle perfectly).
- On new data it hadn't seen: The error was 2 to 3 degrees. (You still missed the handle, but you were much closer than before).

Key Findings & Surprises

Learning from "Messy" Data: The model got better at guessing even when it only had the "cheap" sensors. It learned to ignore the noise and find the hidden patterns.
The "Earth Reflection" Trick: The Sun sensors can see direct sunlight and light bouncing off the Earth (albedo). The old math usually ignored the Earth reflection. The AI realized this "background noise" actually helped it figure out where the satellite was.
One Sensor is Enough (Sometimes): Even if the satellite lost its Sun sensors and only had the Magnetometer (like being in a total eclipse), the AI could still guess the direction with reasonable accuracy (about 2.1 degrees error). This is huge for when satellites are in the dark.
No "Magic" Initialization: The model didn't need to know where the satellite started. It just looked at the flow of the data and figured it out.

The Catch (What the Paper Actually Says)

The paper is very careful to say what this doesn't do:

It needs a "Teacher": The AI learned because it had the "VIP" sensors to show it the correct answers during training. You can't just throw a cheap sensor at a satellite and expect it to work perfectly without ever having seen a "correct" answer first.
It's for "Rough" Stuff: This isn't meant to replace the high-precision GPS for landing a rocket. It's meant to help the satellite get close enough to turn on the high-precision sensors, or to keep working when the expensive sensors are broken or blinded.
It's a "Post-Flight" Study: They used data from a satellite that already finished its job. They are proving the concept works, suggesting that future satellites could use this to save time and money during development.

Summary Analogy

Imagine you are trying to guess the temperature of a room.

The Old Way: You use a formula based on the heater's setting. It's usually off by 10 degrees.
The New Way: You show a computer 1,000 photos of the room's heater settings and the actual temperature (measured by a perfect thermometer). The computer learns that "When the heater is at setting 5 and the window is slightly open, the room is actually 72 degrees, not 65."
The Result: Now, even if you only give the computer the heater setting, it can guess the temperature much better than the old formula ever could.

This paper shows that for small satellites, using AI to learn from past flight data can make "cheap" sensors act like "expensive" ones, saving money and making space operations more reliable.

Technical Summary: Machine Learning-Based Evaluation of Attitude Sensor Characteristics Using Microsatellite Flight Data

Problem Statement
Conventional satellite attitude determination often relies on batch estimation or Kalman filtering based on predefined physical models and white-noise assumptions. While effective for mission requirements, these methods may not fully capture complex, structural, and nonlinear error patterns embedded in real observational data, particularly for coarse attitude sensors like Sun sensors and magnetic field sensors. Traditional approaches often treat these unmodeled effects as random errors. Furthermore, the increasing need for efficient satellite operations, reduced launch costs, and rapid deployment in low-altitude orbits necessitates technologies that can reduce human workload and operational time. This study addresses the challenge of re-evaluating attitude determination performance and sensor error characteristics using actual flight data from a completed microsatellite mission, moving beyond classical filtering to explore machine learning (ML) capabilities.

Methodology
The study utilizes flight data from the RISING-4 microsatellite (a 50-cm-class satellite operated by Tohoku University from 2021 to 2023). The methodology employs a supervised learning approach where high-quality attitude determination results, derived from onboard star sensors and a fiber optical gyro (FOG), serve as "ground truth."

Data Preparation: Five sets of on-orbit observation logs were used. Four passes (P1–P4) were designated for training, and one independent pass (P5) was used for testing. The input data ( $X$ ) consisted of time-series measurements from coarse sensors (Sun sensors and magnetic field sensors), model-derived vectors (Sun, magnetic, and Earth directions in the inertial frame), and gyro angular rates. The output ( $Y$ ) was the attitude quaternion, converted to Modified Rodrigues Parameters (MRP).
Model Architecture: A one-dimensional convolutional neural network (Conv1D) was employed. This architecture processes consecutive time-step sensor measurements (a temporal window of $n=5$ was adopted as the baseline) to regressively predict attitude. The model transforms input vectors through expanded feature dimensions (21 to 64 to 128) and compresses them back to the output (3 elements) using ReLU activation functions and a 1% dropout rate to prevent overfitting.
Training Strategy: The model was trained to minimize the root-mean-square (RMS) rotation angle error between the predicted attitude and the ground truth. To avoid temporal bias, training sets generated from the time-series data were randomly shuffled before training.

Key Contributions

Retroactive ML Application: The study demonstrates the application of machine learning techniques to flight data from a mission that was originally developed and operated without AI, proving that ML can extract structural error patterns from historical data.
Sensor Characterization: By treating star sensor/FOG data as ground truth, the study re-evaluates the error characteristics of Sun and magnetic sensors, identifying that nonlinear biases and alignment errors can be learned and corrected.
Single-Sensor Feasibility: The research investigates the feasibility of attitude determination using single sensor types (e.g., magnetic sensors alone during eclipse) or combinations without explicit physical models, showing that ML can learn the relationship between sensor measurements and attitude even when traditional observability constraints (like the TRIAD method requiring two vectors) are not strictly met in the input features.

Results

Performance Comparison: Conventional attitude determination using the TRIAD method yielded RMS errors on the order of 7.34 deg. In contrast, the proposed ML approach achieved significantly lower errors:
- Training Set: RMS errors of approximately 0.7 deg were achieved for optimal configurations (e.g., Case C1e and C1f, which included both Sun and magnetic sensors along with model vectors and gyro data).
- Test Set: On the independent test pass (P5), the best-performing models achieved RMS errors between 2.1 deg and 3.0 deg, depending on the sensor combination.
Sensor Combinations:
- The combination of Sun sensors, magnetic sensors, and model-derived vectors provided favorable performance.
- When gyro measurements were excluded, the combination of Sun and magnetic sensors remained effective.
- Crucially, the study found that attitude determination using only magnetic field measurements (Case C3f) yielded a test-set RMS of 2.1 deg, suggesting that a certain level of accuracy is achievable during eclipse conditions where Sun sensors are unavailable.
- Using a single sensor type without model vectors (e.g., Sun sensors alone) resulted in significantly higher errors, indicating the importance of supplementary data or learned context.
Generalization: The study noted that the best-performing model on the training set did not always yield the best results on the test set, highlighting the importance of evaluating generalization capabilities. The strong similarity in time-series data profiles between training and testing passes (due to standardized maneuver strategies) contributed to the model's effectiveness.

Significance and Claims
The paper claims that machine learning-based methods are promising candidates for both onboard computation in future satellites and offline analysis of past missions. The study emphasizes that the proposed approach is particularly valuable for:

Initial Acquisition Support: Guiding spacecraft toward optimal attitudes for star sensor acquisition or ground station communication without relying on star sensors.
Redundancy: Providing auxiliary attitude estimation when primary sensors fail or are unavailable.
Operational Efficiency: Reducing the need for complex physical modeling and human intervention in satellite operations.

However, the authors maintain a modest stance regarding the generalizability of these findings. They explicitly state that the results rely on supervised learning where high-quality ground truth (from star sensors/FOG) was available to train the model. The paper does not claim that attitude determination is generally possible using only a single coarse sensor in the absence of such ground truth or simulation data. Instead, it posits that the ML model implicitly embeds nonlinear sensor biases and spacecraft-specific disturbance characteristics present in the actual flight environment. The authors suggest that future work could explore using indirect ground-truth information (such as Earth observation images or fisheye camera data) to train models where direct high-precision attitude data is unavailable, but this remains a proposal for future research rather than a demonstrated result of the current study.