# Low Observable Radar Target Detection Method within Sea Clutter Based on Correlation Estimation

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## Abstract

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## 1. Introduction

- (1)
- A correlation estimation method of sea clutter based on correlation time is proposed. The correlation of sea clutter is evaluated by calculating the correlation time in both time and space domains. According to the estimation results, the sea clutter in different range bins is suppressed.
- (2)
- A selective whitening filter is proposed. In the selective whitening filter, the processing bins are selected adaptively according to the sea clutter correlation estimation results, which can facilitate the suppression of the sea clutter in the target echo components and reduce the computational load.
- (3)
- The FRFT-PAR is presented to distinguish between the sea clutter and target, which is adopted to make better use of the energy accumulation characteristics and further suppress the interference of sea clutter.

## 2. Material and Methods

#### 2.1. Sea Clutter Suppression Stage

#### 2.1.1. Correlation Time of Sea Clutter in Time and Space Domains

#### 2.1.2. Sea Clutter Suppression Method Based on Correlation Time Estimation

- (1)
- Suppose the estimation result of a particular range bin satisfies ${s}_{xy}(u)=1$. In that case, it is regarded that the auto-correlation between the echoes of this range bin is strong, and the cross-correlation between the echoes in the adjacent range bin is weak. It is considered an interested bin.
- (2)
- Suppose the estimation result of a certain range bin satisfies ${s}_{xy}(u)=0$. In that case, it is regarded that the auto-correlation between the echoes of this range bin is weak, or the cross-correlation between the echoes in the adjacent range bin is strong. It is considered a sea clutter bin.

#### 2.1.3. Selective Whitening Filter Based on Correlation Estimation

#### 2.2. Target Decision Stage

## 3. Results

#### 3.1. Dataset Description

#### 3.2. Comparison with the Existing Algorithms

#### 3.2.1. Detection Results on IPIX-1993 Dataset

#### 3.2.2. Detection Results on IPIX-1998 Dataset

#### 3.3. Comprehensive Experimental Results

## 4. Discussion

#### 4.1. Validation of the Sea Clutter Suppression Method

#### 4.2. Validation of the Sea Clutter Suppression Stage

#### 4.3. Comparison of the Computational Complexity

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Flow chart of the proposed sea clutter suppression stage. (

**a**) Sea clutter suppression method based on correlation time estimation. (

**b**) Selective whitening filter.

**Figure 7.**Comparison results of whitening filter on IPIX-#1. (

**a**) Raw data (5.70 dB). (

**b**) Traditional whitening (4.08 dB). (

**c**) Selective whitening (12.32 dB).

**Figure 8.**Comparison results of whitening filter on IPIX-#11. (

**a**) Raw data (6.70 dB). (

**b**) Traditional whitening (10.24 dB). (

**c**) Selective whitening(17.04dB).

**Figure 11.**Statistical results of the FRFT-PAR. (

**a**) FRFT-PAR of IPIX-1993. (

**b**) FRFT-PAR of IPIX-1998.

**Figure 15.**Target detection probability (observation time 2.048 s). (

**a**) Detection rates of different algorithms. (

**b**) ROC curves of different algorithms.

**Figure 16.**Quantitative indicators of the proposed correlation estimation method. (

**a**) perception rate. (

**b**) suppression rate.

**Figure 17.**Target detection probability (observation time 2.048 s). (

**a**) Detection rates of different algorithms. (

**b**) ROC curves of different algorithms.

Label | File Name |
WS (km/h) |
SWH (m) |
Angle (Degree) | Primary |
---|---|---|---|---|---|

1 | 19931107_135603_starea17 | 9 | 2.2 | 9 | 8 |

2 | 19931107_145028_starea19 | - | - | - | 5 |

3 | 19931108_220902_starea26 | 9 | 1.1 | 97 | 6 |

4 | 19931109_191449_starea30 | 19 | 0.9 | 98 | 6 |

5 | 19931111_163625_starea54 | 20 | 0.7 | 8 | 7 |

6 | 19931118_023604_stareC0000280 | 10 | 1.6 | 130 | 7 |

7 | 19931118_035737_stareC0000283 | - | - | - | 8 |

8 | 19931118_162155_stareC0000310 | 33 | 0.9 | 30 | 6 |

9 | 19931118_162658_stareC0000311 | 33 | 0.9 | 40 | 6 |

10 | 19931118_174259_stareC0000320 | 28 | 0.9 | 30 | 6 |

11 | 19980204_163113_ANTSTEP6 | - | - | 165 | 23 |

12 | 19980204_202225_ANTSTEP21 | - | - | 165 | 23 |

13 | 19980204_202525_ANTSTEP22 | - | - | 180 | 6 |

14 | 19980205_171437_ANTSTEP41 | - | - | 180 | 6 |

15 | 19980205_180558_ANTSTEP46 | - | - | 180 | 6 |

16 | 19980212_195704_ANTSTEP65 | - | - | 180 | 6 |

17 | 19980223_164055_ANTSTEP82 | - | - | 165 | 30 |

18 | 19980223_173317_ANTSTEP91 | - | - | 165 | 31 |

19 | 19980223_173950_ANTSTEP92 | - | - | 165 | 28 |

20 | 19980304_184537_ANTSTEP204 | - | - | - | 21 |

Interval Number | SNR Interval/dB | Data Label | Interval Number | SNR Interval/dB | Data Label |
---|---|---|---|---|---|

1 | [−1, 2.02] | 4 | 9 | [11.3, 11.9] | 2, 7, 10 |

2 | [2.54, 3.05] | 8 | 10 | [11.9, 12.4] | 1 |

3 | [5.12, 5.64] | 3 | 11 | [12.4, 12.9] | 9 |

4 | [5.64, 6.16] | 6 | 12 | [14.4, 15] | 5, 13 |

5 | [6.68, 7.19] | 18 | 13 | [15, 15.5] | 15 |

6 | [7.19, 7.71] | 19 | 14 | [16, 16.5] | 12 |

7 | [9.26, 9.78] | 11, 17, 20 | 15 | [16.5, 17] | 16 |

8 | [10.3, 10.8] | 14 |

Observation Time(s) | 0.512 s | 1.024 s | ||||||

Polarizations | HH | HV | VH | VV | HH | HV | VH | VV |

CSM detector | 0.743 | 0.726 | 0.819 | 0.837 | 0.793 | 0.779 | 0.846 | 0.861 |

CF detector | 0.672 | 0.604 | 0.840 | 0.854 | 0.762 | 0.700 | 0.891 | 0.906 |

CANMF detector | 0.843 | 0.784 | 0.894 | 0.884 | 0.873 | 0.820 | 0.907 | 0.905 |

Proposed detector | 0.940 | 0.807 | 0.990 | 1.000 | 0.834 | 0.894 | 0.986 | 0.989 |

Observation Time(s) | 2.048 s | 4.096 s | ||||||

Polarizations | HH | HV | VH | VV | HH | HV | VH | VV |

CSM detector | 0.855 | 0.866 | 0.881 | 0.900 | 0.929 | 0.904 | 0.896 | 0.903 |

CF detector | 0.838 | 0.799 | 0.940 | 0.941 | 0.883 | 0.858 | 0.966 | 0.973 |

CANMF detector | 0.895 | 0.854 | 0.926 | 0.925 | 0.932 | 0.896 | 0.945 | 0.947 |

Proposed detector | 0.991 | 0.926 | 0.986 | 0.986 | 0.962 | 0.908 | 0.992 | 0.994 |

Observation Time(s) | 0.512 s | 1.024 s | ||||||

Polarizations | HH | HV | VH | VV | HH | HV | VH | VV |

RFT detector | 0.522 | 0.476 | 0.773 | 0.795 | 0.534 | 0.491 | 0.815 | 0.833 |

FRFT-FD detector | 0.694 | 0.688 | 0.779 | 0.848 | 0.846 | 0.852 | 0.893 | 0.913 |

FRFT-PAR detector | 0.651 | 0.584 | 0.809 | 0.826 | 0.667 | 0.605 | 0.832 | 0.843 |

Proposed detector | 0.940 | 0.807 | 0.990 | 1.000 | 0.834 | 0.894 | 0.986 | 0.989 |

Observation Time(s) | 2.048 s | 4.096 s | ||||||

Polarizations | HH | HV | VH | VV | HH | HV | VH | VV |

RFT detector | 0.570 | 0.538 | 0.852 | 0.863 | 0.626 | 0.593 | 0.896 | 0.897 |

FD detector | 0.489 | 0.413 | 0.623 | 0.591 | 0.232 | 0.156 | 0.278 | 0.245 |

FRFT-PAR detector | 0.702 | 0.638 | 0.859 | 0.866 | 0.725 | 0.654 | 0.879 | 0.888 |

Proposed detector | 0.991 | 0.926 | 0.986 | 0.986 | 0.962 | 0.908 | 0.992 | 0.994 |

Method | Computation Complexity |
---|---|

CSM | $O(M(N{\mathrm{log}}_{2}N+{N}^{2}\mathrm{log}N+{N}^{3}))$ |

CF | $O(MN{\mathrm{log}}_{2}N)$ |

CANMF | $O(M{N}_{1}{N}_{2}{N}^{2}+M{N}_{1}{N}^{2})$ |

RFT | $O(NM\mathrm{log}M+NM\mathrm{log}N)$ |

FD | $O(M{N}_{3}N\mathrm{log}N+MN)$ |

FRFT-PAR | $O(M{N}_{3}N\mathrm{log}N+MN)$ |

Proposed method | $O(M{N}_{1}(N{\mathrm{log}}_{2}N+{N}_{2}N\mathrm{log}N)+(1-{N}_{4})M({N}_{2}{N}^{2}+{N}^{2}+{N}_{3}N{\mathrm{log}}_{2}N))$ |

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## Share and Cite

**MDPI and ACS Style**

Luo, Z.; Li, Z.; Zhang, C.; Deng, J.; Qin, T.
Low Observable Radar Target Detection Method within Sea Clutter Based on Correlation Estimation. *Remote Sens.* **2022**, *14*, 2233.
https://doi.org/10.3390/rs14092233

**AMA Style**

Luo Z, Li Z, Zhang C, Deng J, Qin T.
Low Observable Radar Target Detection Method within Sea Clutter Based on Correlation Estimation. *Remote Sensing*. 2022; 14(9):2233.
https://doi.org/10.3390/rs14092233

**Chicago/Turabian Style**

Luo, Zefeng, Zhengzhou Li, Chao Zhang, Jiaqi Deng, and Tianqi Qin.
2022. "Low Observable Radar Target Detection Method within Sea Clutter Based on Correlation Estimation" *Remote Sensing* 14, no. 9: 2233.
https://doi.org/10.3390/rs14092233