A Learning-based approach for bias elimination in low cost gyroscopes

Technical Summary: A Learning-Based Approach for Bias Elimination in Low-Cost Gyroscopes

Problem Statement
Modern operating platforms, ranging from autonomous vehicles to household appliances, increasingly rely on low-cost inertial sensors. However, these sensors accumulate various error sources upon leaving the factory, degrading their precision and reliability over time. A primary challenge is the presence of bias errors in gyroscopes. While traditional calibration methods exist, they often rely on extensive analytic models and require long averaging times to suppress background noise and estimate the true bias. This averaging process is time-consuming and assumes stationary conditions, which are difficult to maintain in real-time scenarios where platforms face disruptions. Furthermore, existing literature offers limited data-driven solutions for this specific calibration task, despite the proven success of learning-based techniques in other navigation domains.

Methodology
The authors propose a supervised learning framework to estimate ground-truth (GT) biases in low-cost gyroscopes, replacing traditional linear model-based calibration with a non-linear regression approach.

• Data Acquisition and Preparation: The dataset was constructed using five different low-cost inertial sensors (sampled at 200 Hz) via the phyphox application. Ten one-minute measurements were taken from each sensor after varying standby times to ensure a range of fixed biases. The raw data was processed to create sample-label pairs: short-duration segments served as inputs, while the expected value of the full one-minute measurement served as the "ground truth" label. The dataset was augmented by applying additive bias and zero-mean white noise transformations, expanding the sample size to 5,000 to improve generalizability.
• Model Architecture: A two-layer Convolutional Neural Network (CNN) was selected as the approximation function. The architecture consists of an encoder module performing sequential 1D convolutions followed by subsampling (pooling) to generate low-dimensional feature representations. These features are then passed to a fully connected network to perform regression, outputting the predicted bias ($\hat{b}^s_g$).
• Training and Evaluation: The model was trained using a Mean Squared Error (MSE) loss function to minimize the deviation between the predicted bias and the GT labels. The dataset was split 80:20 for training and testing. Performance was evaluated by comparing the Root Mean Square Error (RMSE) of the CNN predictions against a baseline method, which relies on simple time-averaging of the sensor output.

Key Results
The study demonstrates that the learning-based approach can significantly reduce the time required for bias estimation compared to traditional averaging:

• Time Reduction: The CNN model successfully predicted biases using input durations as short as 10 seconds (a division factor of 6 from the 60-second baseline) with an RMSE of 0.588 mrad/s. While the baseline (60-second averaging) achieved an RMSE of 0.439 mrad/s, the model achieved comparable accuracy in a fraction of the time.
• Performance Trade-off: Table I indicates a trade-off between measurement duration and error. For instance, a 1-second input resulted in an error roughly double that of the baseline (208% of baseline error), while a 10-second input reduced this to 133% of the baseline error.
• Noise Handling: Unlike the baseline, which exhibits slow decay and sharp fluctuations in response to noise bursts, the learning-based model demonstrated the ability to "skip" waiting times and predict actual biases based on patterns learned during training, effectively filtering background noise more efficiently than simple averaging.

Significance and Claims
The paper claims that its primary contribution is demonstrating that non-linear estimators, specifically CNNs, can outperform linear model-based calibration for bias elimination in low-cost gyroscopes. The authors highlight three specific achievements:

1. Superiority of Non-Linear Estimators: CNNs provide better performance than traditional linear calibration methods.
2. Efficiency: The well-trained model can reduce the necessary averaging time by approximately one order of magnitude (e.g., achieving useful results in 10 seconds versus 60 seconds).
3. Robustness: The learnable parameters enhance the model's robustness to non-stationary disturbances, offering a time-sparing alternative to the "precious averaging times" required in sterile environments.

The authors conclude that while sufficient data acquisition and training are prerequisites, this data-driven approach offers a viable, faster method for bias determination, removing the strict dependency on long, stationary observation periods.