Neural-Assisted in-Motion Self-Heading Alignment

1. Problem Statement

Accurate initial heading (yaw) estimation is a critical prerequisite for the operation of Strapdown Inertial Navigation Systems (SINS) on autonomous marine platforms (e.g., AUVs, ASVs).

• The Challenge: Traditional model-based approaches (such as Dual-Vector Decomposition and Optimized Attitude Decomposition) rely on analytical formulations that require long alignment times to achieve satisfactory accuracy, especially in low-dynamic or quasi-stationary marine environments where external aiding (like GNSS) is limited or unavailable during the initial phase.
• Limitations of Classical Methods: These methods are highly sensitive to environmental disturbances, sensor noise, and the "richness" of vehicle motion (excitation). They often suffer from significant accuracy degradation when the vehicle is moored or drifting slowly, necessitating prolonged stationary periods before mission deployment.

2. Methodology: HeadingNet

The authors propose HeadingNet, an end-to-end, model-free, neural-assisted framework designed to estimate the initial heading angle rapidly and accurately using only inertial measurements.

Input Data

The network utilizes four specific inputs, mirroring the physical quantities used in classical methods but processed differently:

1. Measured angular velocity ($\tilde{\omega}^b_{ib}$) from the IMU.
2. Measured specific force ($\tilde{f}^b$) from the IMU.
3. Transport rate ($\omega^n_{in}$) derived from GNSS-RTK positioning.
4. Local gravity vector ($g_n$) derived from GNSS-RTK positioning.

Network Architecture

HeadingNet employs a multi-head 2D Convolutional Neural Network (2DCNN) architecture designed to reflect the physical decomposition of the alignment problem:

• Dual-Head Processing: The inputs are split based on their reference frames (Body frame vs. Navigation frame) and processed by two parallel 2DCNN heads (Head 1 and Head 2). These heads extract lower-level spatial and temporal features.
• Feature Fusion: The outputs of the first two heads are concatenated and fed into a third 2DCNN head (Head 3) for finer feature extraction and correlation analysis.
• Regression Block: The extracted features are flattened and passed through a Fully Connected (FC) block consisting of four layers with TanH activation and Dropout regularization to output the estimated heading angle ($\hat{\psi}$).
• Adaptability: The architecture is flexible. Five variations of HeadingNet (HeadingNet10, 30, 60, 90, 120) were developed to accommodate different alignment time windows ($T_{Align}$). As $T_{Align}$ increases, kernel sizes and layer depths are adjusted to handle the larger temporal input dimensions.

Training Strategy

• Loss Function: A Cyclic Mean Square Error (CMSE) loss was used to account for the periodic nature of angles (e.g., distinguishing between $359^\circ$ and $1^\circ$).
• Optimizer: AdamW with weight decay and a StepLR learning rate scheduler.
• Regularization: Dropout layers were applied to prevent overfitting.

3. Key Contributions

1. Neural-Assisted Model-Free Approach: The paper introduces a novel end-to-end framework that replaces traditional analytical observation vector construction with a data-driven neural network, eliminating the need for explicit physical modeling of noise and excitation.
2. Novel Multi-Head CNN Architecture: The design utilizes a specific multi-head 2DCNN structure that mimics the physical separation of body and navigation frame vectors, leveraging the network's ability to learn complex nonlinear relationships and higher-order temporal correlations.
3. Significant Reduction in Alignment Time: The approach demonstrates the ability to achieve high-accuracy heading estimates in significantly shorter timeframes compared to state-of-the-art model-based methods.

4. Experimental Results

The method was validated using a real-world dataset collected from an Autonomous Surface Vehicle (ASV) moored at a pier over five different days under varying sea conditions. The dataset included IMU data (100 Hz) and GNSS-RTK data (5 Hz).

• Baseline Comparison: HeadingNet was compared against four classical methods: I-DVA, A-DVA, I-OBA, and A-OBA.
• Accuracy Improvement:
  • HeadingNet achieved an average absolute error (AE) improvement of 53% over the best-performing model-based baseline across all tested alignment times.
  • At the shortest alignment time (10 seconds), HeadingNet achieved a 97% improvement in accuracy compared to the best baseline (which had an error of ~150° vs. HeadingNet's ~4.3°).
  • Even at the longest alignment time (120 seconds), HeadingNet outperformed the best baseline by 51%.
• Time Efficiency:
  • HeadingNet reduced the required alignment time by up to 67%.
  • Specifically, HeadingNet achieved at 10 seconds an accuracy that the best baseline only reached at 30 seconds (a 66% time reduction).
  • At 30 seconds, HeadingNet matched the accuracy of baselines that required 60 seconds (a 50% time reduction).
• Convergence: The network demonstrated rapid convergence, achieving sub-5° alignment error in just 10 seconds, whereas classical methods often required minutes to reach similar stability.

5. Significance

This work represents a paradigm shift in inertial navigation alignment for autonomous marine systems:

• Operational Efficiency: By drastically reducing the time required for initial heading alignment, autonomous platforms can deploy faster, which is critical for time-sensitive missions like search and rescue or rapid response operations.
• Robustness in Low-Dynamics: The neural approach proves superior in low-dynamic, noisy environments where classical analytical models struggle due to poor observability.
• Data-Driven Potential: It validates that deep learning can effectively learn the implicit mapping from raw sensor data to navigation states, capturing complex temporal patterns that fixed analytical models miss.

In conclusion, HeadingNet offers a robust, model-free alternative to traditional SINS alignment, providing a practical solution for rapid, high-precision initialization of autonomous marine vehicles.