# Improving Ship Detection in Clutter-Edge and Multi-Target Scenarios for High-Frequency Radar

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{fa}) is calculated by fitting a probability distribution model of sea clutter. The advantage of combining MSST and the Hessian matrix is that the TF ridges of multi-targets can be separated easily. The detection of TF ridges without using reference units can avoid targets from being missed in strong clutter and multi-target scenarios. To validate the proposed method, a dataset collected by the Ocean State Monitoring and Analyzing Radar, type SD (OSMAR-SD) on 5 October 2015 is used along with the ship records from an automatic identification system (AIS) as the ground truth. Results show that the method proposed in this paper outperforms the conventional CFAR and TF-BI-CFAR methods for HFSWR.

## 2. Method

_{fa}, after which the average energy D of the extracted TF ridge is compared with T to determine whether a target exists.

#### 2.1. Signal Representation and Extraction

^{T}denotes transpose operation, ΔP is the variation of P, $\nabla I(P)$ is the gradient of the image at the point of P, and H (P) is the Hessian matrix of P. The Hessian matrix has been widely used to detect and analyze specific shapes [74,75,76]. The curvature of this curved surface C at P can be defined using Hessian matrix [77]

_{ii}(P), I

_{ij}(P), I

_{ji}(P), and I

_{jj}(P) denote the second derivative of image along different directions. λ

_{α,k}, v

_{α,k}(k = 1, 2) are used to denote the eigenvalue and eigenvector of Hessian matrix at scale α, respectively. Assuming |λ

_{1}| < |λ

_{2}|, from the definition of eigenvalue, we have

_{1}and v

_{2}that are parallel and perpendicular to the TF ridge [78], respectively. In order to reduce noise and smooth the original TF image, a 4-by-4 Gaussian filter g(P, α) with a scale α = 0.5 is used in this study and its first and second derivatives are denoted as g

_{i}, g

_{j}, g

_{ii}, g

_{ij}, g

_{ji}and g

_{jj}, respectively. Then, these derivatives of the Gaussian filter are convoluted with each pixel of the TF image to obtain the derivatives of each pixel of the TF image, denoted as I

_{i}(P), I

_{j}(P), I

_{ii}(P), I

_{ij}(P), I

_{ji}(P), and I

_{jj}(P), respectively. The eigenvalue of the Hessian matrix with a larger absolute value λ

_{2}and corresponding eigenvector v

_{2}indicates the normal direction of TF ridge, denoted as (n

_{i}, n

_{j}). The gray level of the adjacent pixels of P can be expressed as

_{2}is smaller than a threshold p (here, p = 0.5), then the pixel is considered as part of the ridge, otherwise, it is not. By checking each pixel, the regions of ridges on a TF image can be identified and marked by the Hessian matrix.

- The marked area where the TF ridge spans more than 20% of coherent integration time (CIT) is kept and the other areas in the TF plane are removed and set to zero;
- Each marked TF ridge area with a length greater than 80% of CIT is selected as a complete TF ridge region and the Doppler frequency ranges of them are recorded;
- For the broken TF ridge regions, the summation is performed in order in the time direction along the Doppler axis, and the Doppler region where the summation value from non-zero to zero is treated as a complete TF ridge region, and the Doppler range of the region is recorded;
- The complete TF ridge is extracted from the recorded Doppler frequency range based on local maximum search.

#### 2.2. Target Detection

_{fa}, the decision threshold can be calculated. The echo signal denoted by x(t) generally consists of two possible components, one from the target, denoted as s(t), and the other from the clutter, denoted as c(t). The absence or presence of s(t) is denoted by H

_{0}and H

_{1}, respectively. The likelihood ratio can be expressed as

_{1}) is the PDF of x(t) with the presence of s(t), and f(x|H

_{0}) is the PDF of x(t) if s(t) does not exist. According to the Bayesian criterion [80], it can be expressed as

_{0}and H

_{1}assumptions, T(x) can be represented by T

_{0}(x) and T

_{1}(x), respectively.

_{T0}(x) of c(t) can be obtained by fitting the real measured data. Due to

_{d}and T is given by

_{T1}(x) is not known, therefore, the P

_{d}of targets cannot be analyzed quantitatively. However, the PDF of sea clutter can be obtained in advance from measured data. The relationship between P

_{fa}and T can be determined and shown in Figure 4.

## 3. Results

#### 3.1. Comparison of TF-BI-CFAR and TF-CFAR

#### 3.2. Target Matching

_{fa}(see Figure 9a,b). Therefore, to compare the detection performance of the seven CFAR detectors in a reasonable way, match rate (the ratio of the number of matched targets over the number of detected targets) is used as a measure for comparison. As can be seen from Figure 9c, the match rates of the seven CFAR detectors are different under various P

_{fa}, but under the approximately same number of detected targets, the match rate of TF-CFAR is 7–12% higher than that of the five conventional CFAR methods (see Figure 9d). At the same time, the match rate of TF-CFAR is 2–4% higher than that of TF-BI-CFAR (see Figure 9d), which proves the superiority of TF-CFAR for target detection.

#### 3.3. Comparison of Conventional CFAR and TF-CFAR

#### 3.4. Impact of Strong Interference

#### 3.5. Statistical Analysis of Matched Targets

## 4. Discussion

#### 4.1. Length of TF Ridges

#### 4.2. Number of SST

#### 4.3. Strong Interference

#### 4.4. Target Detection Strategies

#### 4.5. The Pros and Cons of Different Methods

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Power spectrum, TF image, and ridge extraction of radar signal at 18th range bin at 01:11 on 5 October 2015. (

**a**) power spectrum; (

**b**) the regions of ridges marked by Hessian matrix; (

**c**) the extracted discontinuous TF ridges; (

**d**) the extracted continuous TF ridges.

**Figure 6.**Comparison of multi-target by TF-BI-CFAR and TF-CFAR at 07:36 on 5 October 2015 and (

**c**–

**h**) are from TF-BI-CFAR and TF-CFAR, respectively. (

**a**) target matching map on RD; (

**b**) power spectrum at the 6th range bin; (

**c**) SST image at the 6th range bin; (

**d**) binary grayscale image of (

**c**); (

**e**) vertical projection of (

**d**); (

**f**) TF ridges extracted from (

**c**); (

**g**) TF ridges marked by Hessian matrix; (

**h**) TF ridges extracted from (

**g**).

**Figure 7.**Comparison of clutter edge by TF-BI-CFAR and TF-CFAR at 20:00 on 5 October 2015 and (

**c**–

**h**) are from TF-BI-CFAR and TF-CFAR, respectively. (

**a**) target matching map on RD; (

**b**) power spectrum at the 9th range bin; (

**c**) SST image at the 9th range bin; (

**d**) binary grayscale image of (

**c**); (

**e**) vertical projection of (

**d**); (

**f**) TF ridges extracted from (

**c**); (

**g**) TF ridges marked by Hessian matrix; (

**h**) TF ridges extracted from (

**g**).

**Figure 8.**Comparison of clutter edge by TF-BI-CFAR and TF-CFAR at 16:15 on 5 October 2015 and (

**c**–

**f**) are from TF-BI-CFAR and TF-CFAR, respectively. (

**a**) target matching map on RD; (

**b**) power spectrum at the 5th range bin; (

**c**) SST image at the 5th range bin; (

**d**) binary grayscale image of (

**c**); (

**e**) TF ridges marked by Hessian matrix; (

**f**) TF ridges extracted from (

**e**).

**Figure 9.**Number of detected and matched targets by seven CFAR detectors under different P

_{fa}on 5 October 2015. (

**a**) number of detected targets under different P

_{fa}; (

**b**) the number of matched targets under different P

_{fa}; (

**c**) match rates under different P

_{fa}; (

**d**) match rates under the same number of detected targets.

**Figure 10.**Target detection by ACMLD-CFAR and TF-CFAR at the edge of Bragg region at 00:07 on 5 October 2015 and (

**b**–

**e**) are from ACMLD-CFAR and TF-CFAR, respectively. (

**a**) target matching map on RD; (

**b**) power spectrum at the 12th range bin; (

**c**) TF image at the 12th range bin; (

**d**) power spectrum at the 5th range bin; (

**e**) TF image at the 5th range bin.

**Figure 11.**Multi-target detection by ACMLD-CFAR and TF-CFAR at 04:02 and 02:32 on 5 October 2015 and (

**b**,

**c**,

**e**,

**f**) are from ACMLD-CFAR and TF-CFAR, respectively. (

**a**) target matching map on RD; (

**b**) power spectrum at the 5th range bin; (

**c**) TF image at the 5th range bin; (

**d**) target matching map on RD; (

**e**) power spectrum at the 6th range bin; (

**f**) TF image at the 6th range bin.

**Figure 12.**Target detection in the presence of strong interference. (

**a**) time sequence of average noise intensity; (

**b**) time sequence of the number of detected targets by ACMLD-CFAR, TF-BI-CFAR, and TF-CFAR; (

**c**) time sequence of the number of matched targets by ACMLD-CFAR, TF-BI-CFAR, and TF-CFAR; (

**d**) RD map contaminated by strong interference.

Clutter Data | Weibull | Gamma | Log-Normal |
---|---|---|---|

Test value | 0.0679 | 0.1006 | 0.0165 |

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 |

**Table 3.**Comparison of matched targets by seven CFAR detectors under the same number of detected targets on 5 October 2015.

CFAR Method | Detected Number | Matched Number | Match Rate (%) |
---|---|---|---|

OS-CFAR | 30,000 | 5031 | 16.77 |

ACMLD-CFAR | 5133 | 17.11 | |

VI-CFAR | 4841 | 16.13 | |

FOD-CFAR | 4984 | 16.61 | |

SOD-CFAR | 4679 | 15.59 | |

TF-BI-CFAR | 7737 | 25.79 | |

TF-CFAR | 8463 | 28.21 |

**Table 4.**Comparison of match rates by seven CFAR detectors under the same number of detected targets in three days.

Time (Month/Day) | 09/29 | 10/04 | 10/05 | |
---|---|---|---|---|

CFAR Method | Detected Number | Match Rate (%) | ||

OS-CFAR | 30,000 | 22.39 | 18.07 | 16.77 |

ACMLD-CFAR | 22.71 | 18.21 | 17.11 | |

VI-CFAR | 21.28 | 17.68 | 16.13 | |

FOD-CFAR | 21.95 | 17.40 | 16.61 | |

SOD-CFAR | 20.88 | 16.67 | 15.59 | |

TF-BI-CFAR | 33.67 | 29.55 | 25.79 | |

TF-CFAR | 35.55 | 32.47 | 28.21 |

**Table 5.**Comparison of matched targets by TF-CFAR and other six CFAR detectors at the edge of Bragg peaks.

Time (Month/Day) | 09/29 | 10/04 | 10/05 |
---|---|---|---|

AIS total | 26,861 | 24,483 | 24,435 |

AIS (clutter edge) | 5877 | 4989 | 4216 |

OS-CFAR | 574 | 464 | 468 |

ACMLD-CFAR | 595 | 458 | 465 |

VI-CFAR | 515 | 425 | 441 |

FOD-CFAR | 625 | 503 | 496 |

SOD-CFAR | 542 | 425 | 440 |

TF-BI-CFAR | 2350 | 1923 | 1824 |

TF-CFAR | 2628 | 2481 | 2279 |

Time (Month/Day) | 09/29 | 10/04 | 10/05 |
---|---|---|---|

AIS (multi-target) | 2085 | 2341 | 1593 |

OS-CFAR | 311 | 204 | 201 |

ACMLD-CFAR | 308 | 206 | 199 |

VI-CFAR | 271 | 189 | 188 |

FOD-CFAR | 294 | 216 | 205 |

SOD-CFAR | 202 | 186 | 140 |

TF-BI-CFAR | 677 | 559 | 333 |

TF-CFAR | 884 | 701 | 469 |

SNR | <0 dB | 0–10 dB | ≥10 dB | Total | |
---|---|---|---|---|---|

Number of AIS Targets | 2169 | 5364 | 6964 | 14,497 | |

OS-CFAR | Matched number | 44 | 912 | 6037 | 6993 |

Percentage (%) | 0.63 | 13.04 | 86.33 | 100 | |

VI-CFAR | Matched number | 34 | 729 | 5330 | 6093 |

Percentage (%) | 0.56 | 11.97 | 87.47 | 100 | |

FOD-CFAR | Matched number | 25 | 664 | 5875 | 6564 |

Percentage (%) | 0.38 | 10.12 | 89.50 | 100 | |

TF-BI-CFAR | Matched number | 66 | 1427 | 6939 | 8432 |

Percentage (%) | 0.78 | 16.92 | 82.30 | 100 | |

TF-CFAR (proposed) | Matched number | 335 | 2928 | 6853 | 10,116 |

Percentage (%) | 3.31 | 28.94 | 67.75 | 100 |

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## Share and Cite

**MDPI and ACS Style**

Yang, Z.; Zhou, H.; Tian, Y.; Huang, W.; Shen, W.
Improving Ship Detection in Clutter-Edge and Multi-Target Scenarios for High-Frequency Radar. *Remote Sens.* **2021**, *13*, 4305.
https://doi.org/10.3390/rs13214305

**AMA Style**

Yang Z, Zhou H, Tian Y, Huang W, Shen W.
Improving Ship Detection in Clutter-Edge and Multi-Target Scenarios for High-Frequency Radar. *Remote Sensing*. 2021; 13(21):4305.
https://doi.org/10.3390/rs13214305

**Chicago/Turabian Style**

Yang, Zhiqing, Hao Zhou, Yingwei Tian, Weimin Huang, and Wei Shen.
2021. "Improving Ship Detection in Clutter-Edge and Multi-Target Scenarios for High-Frequency Radar" *Remote Sensing* 13, no. 21: 4305.
https://doi.org/10.3390/rs13214305