Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain
Abstract
1. Introduction
2. Methods
2.1. Theoretical Foundations
- (1)
- Mean absolute value: in radar target detection, the average amplitude of the echo signal serves as a primary indicator of target signal strength.
- (2)
- Aspect ratio: due to fluctuations in the ship’s RCS and observation angle, the TF ridge may appear continuous or intermittent. Additionally, differing radial velocities between the ship and noise cause their energy distributions to occupy separate Doppler frequency bands on the TF plane. Accordingly, the TF ridge aspect ratio is defined to capture this distinguishing characteristic. Let N denote the length of the extracted TF ridge, and W represent the number of Doppler distribution units. The TF ridge aspect ratio can then be expressed as
- (3)
- Kurtosis: kurtosis characterizes the sharpness of the data distribution along the TF ridge [35]. For a normal distribution, the kurtosis value is equal to 3. A high kurtosis indicates a peaked distribution, while a low kurtosis suggests a flatter profile.
- (4)
- Skewness: skewness quantifies the asymmetry of the TF ridge amplitude distribution [36], and its calculation formula is as follows.
- (5)
- Variance: variance reflects the degree of signal energy dispersion, providing a means to distinguish target, clutter, and noise, as shown in the following equation.
- (6)
- Average amplitude change: the average amplitude change is computed as the mean of adjacent-point amplitude differences along the TF ridge, reflecting signal complexity.
- (7)
- Peak factor: the peak factor, defined as the ratio of the peak amplitude to the RMS value, indicates the presence of impulsive components in the signal. The calculation formula is as follows:
- (8)
- Ratio of standard deviations after bisection: the standard deviation of the entire TF ridge, denoted as std1, is first computed. The ridge is then bisected, and the standard deviation of one half, denoted as std2, is calculated. The ratio of the standard deviations is as follows:
- (9)
- Ratio of bisected means: the TF ridge coefficients are split into two groups based on the global mean. The means of the upper and lower subsets are denoted as m22 and m21, respectively. The ratio between the two is as follows:
- (10)
- Absolute standard deviation of the difference: this metric resembles the root mean square but is derived from the standard deviation of differences between adjacent TF amplitudes. Its calculation formula is as follows:
- (11)
- Integral ratio: the integral value represents the total energy of the TF ridge. The integral ratio compares this energy to that of the surrounding TF region, excluding the ridge. The formula is as follows:
- (12)
- Maximum kurtosis: kurtosis, which represents the normalized fourth-order central moment, characterizes the amplitude distribution within the TF region that encompasses the ridge [37]. It is commonly employed to determine whether a random variable follows a normal distribution.
- (13)
- Renyi entropy: Renyi entropy generalizes Shannon entropy and quantifies the TF energy concentration of the target signal for a given order α [38]. The value of Rα indicates the quality of TF concentration: a smaller Rα suggests better TF concentration, while a larger Rα indicates poorer TF concentration, with α set to 2 in this case.
- (14)
- Normalized third-order Renyi entropy [39].
- (15)
- Gradient: in the TF domain, the radar echo is represented as a 2D image, denoted as z = S(t, f). Assuming that z has continuous first-order partial derivatives within S, the gradient at each point (t, f) can be calculated using the following formula.
- (16)
- Image entropy: image entropy quantifies signal uncertainty, with higher entropy indicating greater randomness or complexity in the TF image. The formula for calculating image entropy is as follows.
2.2. TF Ridge Extraction Method
2.3. Cascade Detection Method
3. Results
3.1. Denoising
3.2. Non-CFAR Detection
3.2.1. Ship Target Detection in Noise Regions
3.2.2. Statistical Analysis of Target Detection in Noise Regions
3.2.3. SNR Distribution of Matching Target in Noise Regions
3.3. Statistical Analysis of Matching Targets
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
HFSWR | High-Frequency Surface Wave Radar |
SNR | Signal to Noise |
TF | Time–Frequency |
CFAR | Constant False Alarm Rate |
RCS | Radar Cross Section |
CA | Cell Averaging |
GO | Greatest of |
SO | Smallest of |
OS | Ordered Statistics |
CMLD | Censored Mean Level Detector |
TM | Trimmed-Mean |
S-CFAR | Switching-CFAR |
E-CFAR | Ensemble-CFAR |
GM | Geometric Mean |
VI | Variability Index |
TI | Test Inclusive |
FOD | First-Order Difference |
SOD | Second-Order Difference |
BVI | Bayesian Variability Index |
HF | High Frequency |
RD | Range Doppler |
STFT | Short Time Fourier transform |
DWT | Discrete Wavelet Transform |
PCA | Principal Component Analysis |
TFA | Time–Frequency Analysis |
1D | One-Dimensional |
2D | Two-Dimensional |
SET | Synchronous Extraction Transform |
TF-BI-CFAR | Time–Frequency Binary Integration-CFAR |
SST | Synchrosqueezed Transform |
CIT | Coherent Integration Time |
AIS | Automatic Identification System |
TF-Non-CFAR | Time–Frequency Non-CFAR |
OSMAR | Ocean State Measuring and Analyzing Radar |
SD | S stands for Small, Smart, and Super, and D stands for Digital |
KNN | K-Nearest Neighbor |
DT | Decision Tree |
SVM | Support Vector Machine |
NN | Neural Network |
Pd | Detection Probability |
Pfa | False Alarm Probability |
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Parameter | Value |
---|---|
Carrier frequency (MHz) | 13.15 |
Sweep band (kHz) | 60 |
Range resolution (km) | 2.5 |
Velocity resolution (m/s) | 0.0825 |
Receive antenna | Cross-Loop/Monopole |
Sweep cycle (s) | 0.54 |
Coherent integration time (CIT) (s) | 138.24 |
Method | Date | Detected Number | Matched Number | Matching Rate (%) |
---|---|---|---|---|
Without denoising | 22 September | 145,217 | 15,893 | 10.94 |
6 October | 156,171 | 13,712 | 8.78 | |
15 November | 156,332 | 16,454 | 10.52 | |
Denoising | 22 September | 139,362 | 15,814 | 11.34 |
6 October | 139,520 | 13,675 | 9.80 | |
15 November | 139,556 | 16,405 | 11.75 |
Method | Detected Number of Noise Region | Matched Number of Noise Region | Matching Rate (%) |
---|---|---|---|
CA-CFAR | 9856 | 123 | 1.24 |
OS-CFAR | 9023 | 102 | 1.13 |
TM-CFAR | 9328 | 113 | 1.21 |
CMLD-CFAR | 9265 | 123 | 1.32 |
VI-CFAR | 9653 | 124 | 1.28 |
FOD-CFAR | 8741 | 79 | 0.90 |
SOD-CFAR | 10,344 | 105 | 1.01 |
BVI-CFAR | 9303 | 114 | 1.22 |
TF-BI-CFAR | 4574 | 335 | 7.32 |
TF-Non-CFAR | 743 | 269 | 36.20 |
SNR | Date | CFAR | TF-Non-CFAR |
---|---|---|---|
<10 dB | 22 September | 37 | 107 |
25 September | 37 | 350 | |
6 October | 14 | 78 | |
15 November | 37 | 88 | |
≥10 dB | 22 September | 76 | 124 |
25 September | 49 | 192 | |
6 October | 43 | 128 | |
15 November | 28 | 158 |
Method | Date | Detected Number of Noise Region | Matched Number of Noise Region | Matching Rate (%) |
---|---|---|---|---|
TF-BI-CFAR | 22 September | 4574 | 335 | 7.32 |
25 September | 6036 | 293 | 4.85 | |
6 October | 3946 | 191 | 4.84 | |
15 November | 3661 | 252 | 6.88 | |
TF-Non-CFAR | 22 September | 743 | 269 | 36.20 |
25 September | 2479 | 278 | 11.21 | |
6 October | 647 | 157 | 24.26 | |
15 November | 778 | 203 | 26.09 |
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Yang, Z.; Zhou, H.; Tian, Y.; Liu, G.; Zhang, B.; Qin, Y.; Li, P.; Huang, W. Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain. Remote Sens. 2025, 17, 2580. https://doi.org/10.3390/rs17152580
Yang Z, Zhou H, Tian Y, Liu G, Zhang B, Qin Y, Li P, Huang W. Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain. Remote Sensing. 2025; 17(15):2580. https://doi.org/10.3390/rs17152580
Chicago/Turabian StyleYang, Zhiqing, Hao Zhou, Yingwei Tian, Gan Liu, Bing Zhang, Yao Qin, Peng Li, and Weimin Huang. 2025. "Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain" Remote Sensing 17, no. 15: 2580. https://doi.org/10.3390/rs17152580
APA StyleYang, Z., Zhou, H., Tian, Y., Liu, G., Zhang, B., Qin, Y., Li, P., & Huang, W. (2025). Cascaded Detection Method for Ship Targets Using High-Frequency Surface Wave Radar in the Time–Frequency Domain. Remote Sensing, 17(15), 2580. https://doi.org/10.3390/rs17152580