Enhancing Maritime Safety: Estimating Collision Probabilities with Trajectory Prediction Boundaries Using Deep Learning Models
Abstract
:1. Introduction
1.1. Significance of the Problem and Contribution
- This research employs several statistical and geometrical methods, including ellipsoidal prediction regions (EPRs), confidence intervals (CIs), prediction intervals (PIs), and conformal prediction regions (CPRs), to quantify uncertainty in vessel trajectory predictions. These methods provide a comparative analysis for determining trajectory prediction boundaries—often called guard zones, which may also be defined as ship domains—enhancing the precision of collision detection.
- The proposed methods are validated using a real-world case study, specifically the 2021 collision between the Scot Carrier and Karin Hoej cargo vessels. This validation demonstrates the practical applicability of the framework and evaluates the effectiveness of different boundary-determination techniques in detecting potential collisions.
- By training multiple models that have the same architecture, this study assesses trajectory prediction uncertainty without relying on traditional bootstrapping methods. This approach enhances the reliability of predictions by capturing variations across models, contributing to more robust boundary determination.
- A unique method is proposed to calculate and evaluate the overlapped trajectory prediction boundaries from each vessel’s perspective. This comprehensive assessment provides a collision risk score based on a Jaccard index measure, which offers a probabilistic measure of collision risk. Unlike traditional methods such as CPA, this approach considers the entire trajectory prediction boundary, holistically capturing collision risks.
1.2. Background and State of the Art
1.3. Introduction to the Workflow
1.4. Aim and Organisation of the Article
2. Related Studies
2.1. Vessel Trajectory Prediction Methods and Uncertainty Estimation
2.2. Collision Risk Assessment and Predictive Frameworks
3. Methods
3.1. Deep Learning Model for Trajectory Prediction
3.2. Confidence and Prediction Intervals
- is the critical value of the student’s distribution (t-score) corresponding to the desired confidence level, , and degrees of freedom, where n is the sample size.
- is the sample’s standard deviation, representing the spread of the data points.
- is the standard error of the estimate, which adjusts the standard deviation for the size of the sample.
- The term accounts for the added uncertainty when predicting a single future observation rather than estimating the population’s mean.
3.3. Ellipsoidal Prediction Regions
Algorithm 1 EPR calculation. |
function CalculateEPR(, ) Input: —array of latitude and longitude points Input: —center point (mean) of the EPR Output: —the calculated ellipsoidal prediction region as a polygon hull←ConvexHull(points) covMatrix←Covariance(hullVertices) [eigValues,eigVectors]←Eigen(covMatrix)) for to 100 do end for return end function |
3.4. Conformal Prediction Regions
4. Experiments
4.1. Data and Experiment Set-Up
4.2. Region Evaluation
4.3. Verification: Collision Between Scot Carrier and Karin Hoej Cargo Ships
4.4. Analysis of Prediction Accuracy and Risk Estimation
5. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
AIS | Automatic Identification System |
CI | Confidence interval |
CPA | Closest Point of Approach |
CPR | Conformal prediction region |
EPR | Ellipsoidal prediction region |
HELCOM | Helsinki Commission |
LSTM | Long Short-Term Memory |
MAEH | Mean Haversine Absolute Error |
MMSI | Maritime Mobile Service Identity |
PI | Prediction interval |
TCPA | Time to Closest Point of Approach |
Appendix A
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Parameter | Value | Note | Parameter | Value | Note |
---|---|---|---|---|---|
Layers | 3 | Total number of encoder and decoder parts | Number of Units | 275 | Cells in each LSTM layer |
Seq. Len. | 50 | 30 input, 20 output | Batch Size | 128 | Examples utilised in one iteration |
Epochs | 100 | - | Models Size | 20 | Models trained on the same data |
Optimiser | 0.001 | Adam (with Learning Rate) | Loss F-ion | MSE | Measures prediction quality |
Regularisation | 0.01 | Dropout layers | Activation F-ion | ReLU | Used in LSTM gates and Dense |
Time Step | EPR | CPR | ||||||
Area A, m2 | Area B, m2 | , m2 | Prob (%) | Area A, m2 | Area B, m2 | , m2 | Prob (%) | |
1 | 11,425.5 | 32,978.4 | 0.0 | 0.00 | 20,812.7 | 20,808.5 | 0.0 | 0.00 |
2 | 35,960.2 | 117,517.0 | 0.0 | 0.00 | 64,937.4 | 64,927.8 | 0.0 | 0.00 |
3 | 72,216.4 | 220,926.0 | 0.0 | 0.00 | 153,537.9 | 153,523.8 | 0.0 | 0.00 |
4 | 132,867.0 | 368,967.0 | 96,986.7 | 23.96 | 302,596.1 | 302,584.9 | 171,576.5 | 39.57 |
5 | 198,320.0 | 536,512.0 | 22,066.5 | 3.10 | 524,334.6 | 524,344.3 | 89,920.4 | 9.38 |
6 | 274,578.0 | 762,444.0 | 0.0 | 0.00 | 826,551.7 | 826,611.9 | 0.0 | 0.00 |
Time Step | PIs | CIs | ||||||
Area A, m2 | Area B, m2 | , m2 | Prob (%) | Area A, m2 | Area B, m2 | , m2 | Prob (%) | |
1 | 4717.5 | 14,151.0 | 0.0 | 0.00 | 224.6 | 673.9 | 0.0 | 0.00 |
2 | 14,568.8 | 53,199.1 | 0.0 | 0.00 | 693.8 | 2533.3 | 0.0 | 0.00 |
3 | 31,642.8 | 112,766.8 | 0.0 | 0.00 | 1506.8 | 5369.8 | 0.0 | 0.00 |
4 | 53,492.5 | 190,868.5 | 8420.9 | 3.57 | 2547.3 | 9089.0 | 0.0 | 0.00 |
5 | 79,293.0 | 288,027.5 | 0.0 | 0.00 | 3775.9 | 13,715.6 | 0.0 | 0.00 |
6 | 107,950.1 | 405,907.8 | 0.0 | 0.00 | 5140.5 | 19,328.9 | 0.0 | 0.00 |
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Jurkus, R.; Venskus, J.; Markevičiūtė, J.; Treigys, P. Enhancing Maritime Safety: Estimating Collision Probabilities with Trajectory Prediction Boundaries Using Deep Learning Models. Sensors 2025, 25, 1365. https://doi.org/10.3390/s25051365
Jurkus R, Venskus J, Markevičiūtė J, Treigys P. Enhancing Maritime Safety: Estimating Collision Probabilities with Trajectory Prediction Boundaries Using Deep Learning Models. Sensors. 2025; 25(5):1365. https://doi.org/10.3390/s25051365
Chicago/Turabian StyleJurkus, Robertas, Julius Venskus, Jurgita Markevičiūtė, and Povilas Treigys. 2025. "Enhancing Maritime Safety: Estimating Collision Probabilities with Trajectory Prediction Boundaries Using Deep Learning Models" Sensors 25, no. 5: 1365. https://doi.org/10.3390/s25051365
APA StyleJurkus, R., Venskus, J., Markevičiūtė, J., & Treigys, P. (2025). Enhancing Maritime Safety: Estimating Collision Probabilities with Trajectory Prediction Boundaries Using Deep Learning Models. Sensors, 25(5), 1365. https://doi.org/10.3390/s25051365