A Novel Copula-Based Multi-Feature CFAR Framework for Radar Target Detection
Abstract
1. Introduction
- Copula-based modeling of feature dependence: We propose a Copula-based feature fusion method to flexibly capture nonlinear dependencies among radar features under complex sea clutter conditions.
- Analytical PFA control: We derive explicit mathematical expressions linking the detection threshold to the PFA using the Copula framework, enabling interpretable FAR control in high-dimensional feature spaces.
- Copula-CFAR detection framework: We design a complete Copula-CFAR detection framework and validate its performance through simulations and real-scene experiments, demonstrating superior robustness and detection accuracy compared to existing methods.
2. Method
2.1. Detection Theorem
2.2. Corollaries for Different Copula Function
2.3. Copula-Based Target Detection Algorithm
- Extract multivariate features from the radar echo signals, and estimate the marginal CDF for each feature .
- For each observed feature value , calculate its cumulative probability
- Construct a Copula structure based on the marginal distributions of the features and estimate the parameters of Copula function.
- For a given , the thresholds are derived by this equation .
- Using the thresholds calculated in Step 1, transform each feature value as follows:
- Define the test statistic as the maximum value of the transformed features:
- If conclude that a target is present.
- If , we fail to reject the null hypothesis , indicating that the observed signal is attributable to sea clutter.
3. Result
3.1. Simulation Validation
3.2. Experimental Validation
4. Discussion
5. Conclusions
- A Copula-CFAR theorem is established to rigorously characterize the nonlinear dependence among multiple features, providing a theoretical foundation for multi-feature target detection with controlled false alarm performance.
- Analytical formulas relating detection thresholds to PFA are derived for various Copula structures, enabling the design of an effective multi-feature Copula-CFAR detection algorithm.
- Extensive real-world data experiments demonstrate that the proposed method achieves a detection rate of 75.20% in a high state at a given PFA of 0.001 using only two features and 512 samples, significantly surpassing advanced multi-feature detectors.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
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Detector | Features | Sample Size | Detection Rate | FAR |
---|---|---|---|---|
Convex Hull [19,21] | RAA, RPH, RVE [21] | 512 | 75.20% | 17.19% |
Concave Hull [20,46] | RAA, RPH, RVE | 512 | 92.77% | 29.69% |
Convex Hull | 12 multi-domain features [14] + PCA [47] | 512 | 67.77% | 13.67% |
Concave Hull | 12 multi-domain features [14] + PCA [47] | 512 | 84.57% | 25.00% |
Proposed Method | Proposed Features | 512 | 75.20% | 0.5% |
Detector | Features | Sample Size | Detection Rate | FAR |
---|---|---|---|---|
Convex Hull | RAA, RPH, RVE | 10,240 | 32.62% | 0.51% |
Concave Hull | RAA, RPH, RVE | 10,240 | 66.99% | 0.61% |
Convex Hull | 12multi-domain features + PCA | 10,240 | 50.78% | 0.23% |
Concave Hull | 12 multi-domain features + PCA | 10,240 | 55.86% | 0.41% |
Proposed Method | Proposed Features | 512 | 75.20% | 0.5% |
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Li, J.; Dong, Y.; Liu, N.; Huang, Y.; Jiang, X.; Sun, J. A Novel Copula-Based Multi-Feature CFAR Framework for Radar Target Detection. Remote Sens. 2025, 17, 2299. https://doi.org/10.3390/rs17132299
Li J, Dong Y, Liu N, Huang Y, Jiang X, Sun J. A Novel Copula-Based Multi-Feature CFAR Framework for Radar Target Detection. Remote Sensing. 2025; 17(13):2299. https://doi.org/10.3390/rs17132299
Chicago/Turabian StyleLi, Juan, Yunlong Dong, Ningbo Liu, Yong Huang, Xingyu Jiang, and Jinping Sun. 2025. "A Novel Copula-Based Multi-Feature CFAR Framework for Radar Target Detection" Remote Sensing 17, no. 13: 2299. https://doi.org/10.3390/rs17132299
APA StyleLi, J., Dong, Y., Liu, N., Huang, Y., Jiang, X., & Sun, J. (2025). A Novel Copula-Based Multi-Feature CFAR Framework for Radar Target Detection. Remote Sensing, 17(13), 2299. https://doi.org/10.3390/rs17132299