Reliability-aware short-term roll prediction for unmanned surface vehicles via multi-task learning and adaptive centralization

1. Introduction

• Wave-induced high-amplitude roll motions can compromise onboard weapon stability and UAV launch and recovery safety, motivating uncertainty-aware predictions for risk-sensitive decisions.Probabilistic predictive states can inform firing-window selection and UAV contact timing.Source: §1 · p. 1
• Existing prediction-interval methods describe future-state uncertainty but lack confidence assessment for each predicted point across multiple forecasting steps.Deterministic point forecasts likewise do not assess uncertainty, motivating confidence assessment for risk-aware autonomous decisions.Source: §1 · p. 2
• Small USVs’ short-period, nonlinear roll dynamics make conventional adaptation and normalization less effective under rapidly changing short-term disturbances.These approaches typically depend on sufficient historical observations to update parameters or estimate robust statistics.Source: §1 · p. 2
• A shared-backbone multi-task predictor combines roll regression and confidence scoring with consistency learning and adaptive centralization for distribution drift.The confidence head estimates step-wise confidence from discretized roll-angle intervals; adaptive centralization de-means inputs and compensates for mean shifts.Source: §1 · pp. 2–3

2.1. Adaptive Centralization

• Z-Score standardization can be unsuitable for short-horizon online USV prediction because reliable statistics need longer histories, may amplify values when σ approaches zero, and may mismatch online or future-sequence statistics.Roll-motion drift can occur both across voyages and within a prediction window.Source: §2.1 · pp. 3–4
• Adaptive centralization removes input offsets and predicts the mean shift between input and output sequences to reduce sensitivity to drift while preserving motion dynamics.A moving-average filter extracts a local trend from short sequences.Source: §2.1 · pp. 3–4

2.2.1. Feature Extraction Module

• The encoder-decoder Bi-LSTM extracts temporal features using forward and backward sequence context for the subsequent prediction and confidence-estimation tasks.Its backward branch supplements the original LSTM’s unidirectional information flow.Source: §2.2.1 · p. 5

2.2.2. Confidence Assessment Module

• A confidence-assessment module pairs a regression head for roll values with a classification head that assigns probabilities to discretized roll-angle bins.The probability for the bin associated with the regression output serves as its confidence score.Source: §2.2.2 · pp. 5–6

2.3. Loss function and metric

• The method trains the classification branch with KL divergence and the regression branch with MSE, then adds a consistency loss to align their outputs.The reported figure shows improved alignment between the maximum-confidence bin and regression index after adding the consistency loss.Source: §2.3 · p. 6, Figure 4 · p. 7
• The total loss weights the component losses, while evaluation covers point accuracy with RMSE and MAE and interval quality with PICP and AWD.PICP measures coverage relative to the target confidence level; smaller AWD indicates better interval quality.Source: §2.3 · pp. 6–7

3.1. Dataset Analysis

• Based on the measured-data empirical distribution, the confidence-assessment head sets an effective roll-classification range of [−15◦, 15◦]; 40 discrete bins correspond to 0.75◦ resolution, providing navigation-safety granularity while avoiding label sparseness and insufficient forecasting precision.Extreme roll events beyond this range have very low probability and lack statistical representativeness.Source: §3.1 · p. 8
• Dataset #0 is split 8:2 into training and validation sets, while Datasets #1 and #2 are reserved as independent tests.Operating and environmental changes produce both train-to-online drift and input-to-future shifts within a prediction window.Source: §3.1 · p. 8

3.2.1. Sliding Window Method

• Each sample pairs a historical sequence of length d with a future target sequence of length p, and the window advances by one sampling point.Adjacent samples share d−1 historical observations; the measured data were downsampled from 20 Hz to 10 Hz.Source: §3.1 · p. 7, §3.2.1 · pp. 8–9

3.2.2. Label Smoothing

• Dynamic label smoothing distributes target probability between the main bin and an adjacent bin according to the target’s relative position, supporting local continuity and better-calibrated confidence learning.The classification branch is trained with KL divergence; hard one-hot labels can introduce quantization error and unstable gradients near bin boundaries.Source: §3.2.2 · pp. 9, 11

3.3. Hyperparameter Settings

• The final kernel size is k=3, selected from 3, 5, and 7 because it achieved the lowest validation error.Training used learning rate 0.001, batch size 64, 100 epochs, Adam, and random seeds [42, 123, 2026].Source: §3.3 · p. 11

4.1.1. Generalization Test of Adaptive Centralization

• AdaC reduces prediction errors by approximately 13% and 14% on Dataset #1, and 44% and 46% on Dataset #2, versus no-standardization and Z-score under changing conditions.No-standardization and Z-score show large deviations during distribution shifts; AdaC maintains high prediction accuracy.Source: §4.1.1 · pp. 12, 14, Figure 9 · p. 12
• On Dataset #1, AdaC reduces RMSE by approximately 8%-15% and MAE by about 6%-15%; on Dataset #2, it reduces RMSE by 6%–57% and MAE by 3%–59% versus advanced baselines.AdaC achieves the lowest RMSE and MAE among advanced methods on both datasets.Source: Figure 10 · p. 13, §4.1.1 · p. 14, Table 4 · p. 14

4.1.2. Ablation study

• RMSE and MAE increase as the prediction horizon expands across the tested input-output window configurations.The study considers short-horizon predictions of lengths 10–20, approximately one roll cycle.Source: §4.1.1 · p. 11, §4.1.2 · p. 14, Figure 11 · p. 14
• Bi-LSTM achieves the lowest overall RMSE among tested backbones, outperforming Transformer models and CNN models at shorter horizons.The comparison replaces Bi-LSTM with CNN, Transformer, and Informer while holding other components unchanged.Source: §4.1.2 · pp. 14–15, Figure 12 · p. 15

4.2.1. Step-wise confidence Assessment

• Step-wise confidence generally decreases as prediction horizons lengthen, and forecasts below the low-confidence threshold of 0.4 coincide with significant deviations from ground truth.The displayed high-, medium-, and low-confidence ranges are 0.7–1, 0.4–0.7, and 0–0.4; these thresholds were chosen empirically for visualization.Source: §4.2.1 · p. 15, Figure 13 · p. 16
• The confidence head's step-wise scores support identifying when forecasts transition from reliable to unreliable for risk-aware decisions and prediction truncation.The paper presents forecast comparisons and corresponding confidence bars for 20-5, 20-10, 20-15, and 20-20 input-output settings.Source: §4.2.1 · p. 15

4.2.2. Interval Confidence Assessment

• HQ intervals select the most probable discretized roll bins whose cumulative probability reaches the nominal confidence level, then use their minimum and maximum roll values as bounds.The classification head supplies a probability mass for each roll bin at each forecasting step.Source: §4.2.2 · p. 15
• At 80% confidence, HQ achieves 81.5% PICP versus 68.6% for ND and 63.6% for TD, and its AWD of 0.226 is 47.9% and 40.3% lower, respectively.HQ has the closest coverage to the nominal level and the lowest AWD across confidence levels.Source: §4.2.2 · p. 17, Table 5 · p. 17, Figure 15 · p. 18

4.3.1. Confidence Calibration

• Most predicted roll angles cluster around the identity line, agreeing closely with ground truth; PCC is 0.9585 for 10-step predictions and 0.8228 for 20-step predictions, indicating strong linear correlation.Point transparency indicates predicted confidence, with higher opacity denoting higher confidence.Source: §4.3.1 · p. 18, Figure 17 · p. 19
• Prediction error decreases monotonically as confidence increases across the binned error-confidence analysis.Confidence values are divided into ten bins of width 0.1, with mean confidence and absolute error plotted for populated bins.Source: §4.3.1 · pp. 18–19, Figure 18 · p. 19

4.3.2. Effectiveness of the consistency loss

• Adding the consistency loss increases RMSE by 3.97%, 3.53%, and 0.49% for the 20-5, 20-10, and 20-15 horizons, respectively.The authors attribute the marginal point-error increase to the loss encouraging alignment between regression and classification outputs.Source: §4.3.2 · pp. 19–20, Table 6 · p. 20
• With consistency loss, a larger proportion of high-confidence predictions concentrates near the identity line, indicating improved agreement between regression outputs and high-confidence bins.The ablation compares the framework with and without the consistency loss.Source: §4.3.2 · pp. 19–20, Figure 19 · p. 20

4.4. Significance test

• AdaC is significantly better than most normalization methods on RMSE and MAE, except RevIN on MAE (p=0.2529); HQ significantly outperforms ND and TD on PICP and AWD at all tested confidence levels.The reported significant comparisons have p-values below 0.05.Source: §4.4 · p. 20

5.1. Conclusion

• Adaptive centralization addresses non-stationary mean drift in short-term roll sequences, while a confidence-assessment head uses discretized roll bins to provide step-wise scores.The framework augments a regression-based predictor with adaptive feature processing and an auxiliary confidence-assessment branch.Source: §5.1 · p. 20
• The paradigm provides prediction intervals at different nominal confidence levels and actionable reliability information for downstream USV decision-making.Source: §5.1 · p. 21
• Real-sea experiments show adaptive centralization significantly enhances generalization across operating conditions, while estimated confidence is consistent with observed prediction errors.The overall paradigm is also described as model-agnostic and offering a degree of interpretability.Source: §5.1 · p. 21

5.2. Limitations and future work

• The model is designed primarily for short-term prediction; accuracy and confidence reliability may degrade over longer horizons as uncertainty and cumulative error grow.It uses historical roll sequences without external factors such as wind speed and wave height, which may limit capture of sudden roll peaks in rapidly varying seas.Source: §5.2 · p. 21
• Future work may incorporate relationships between roll and variables such as wind speed and wave height, and integrate mechanistic models to improve interpretability and physical consistency.Source: §5.2 · p. 21

• The authors acknowledge support from the National Natural Science Foundation of China (No.62225308) and Shanghai Science and Technology Innovation Project (No.XTCX-KJB002-2025-2-03).Source: Funding · p. 21