# Robust Automatic Target Recognition via HRRP Sequence Based on Scatterer Matching

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## Abstract

**:**

## 1. Introduction

## 2. HRRP Sequence Model for Recognition

## 3. The Proposed HRRP Sequence Matching Method

#### 3.1. Singular Value Decomposition of the HRRP Sequence

**V**span the orthogonal basis space in the range domain, while the LSVs in

**U**span the basis space in the angle domain [38]. Given the Eckhart and Young theorem [44], the top singular vectors with the largest SVs can well approximate the signal, called the signal subspace, while the tail vectors with smallest SVs span the noise subspace. By reconstructing the signal with the top singular vectors, background interference can be reduced as it corresponds to the tail singular vectors. The energy threshold is set as $\eta $, defined by $\eta ={\displaystyle {\sum}_{i=1}^{{Q}_{S}}{\lambda}_{i}}/{\displaystyle {\sum}_{i=1}^{N}{\lambda}_{i}}$. Thus ${Q}_{S}$, the number of SVs to be chosen, can be determined by $\eta $.

**V**are utilized for ATR while the LSVs are ignored [36,37,38]. However, the information in

**U**is also useful in our HRRP sequence based recognition. Thus, we exploit the SVD-based feature extraction method by jointly using RSVs and LSVs, called the SSM-ANM method which will be discussed in detail in the following part.

#### 3.2. The Process of the SSM-ANM Method for Recognition

#### 3.3. Implemantation of the Key Procedures in SSM-ANM

#### 3.3.1. Dominant Scatterer Extraction by Atomic Norm Minimization

#### 3.3.2. Scatterer Matching for the Dominant RSVs by Dominant-Scatterers’ Hausdorff Distance

#### 3.3.3. Angle Space Correlation by the LSVs

#### 3.4. Some Remarks on the Proposed SSM-ANM Method

**Remark 1.**

**Remark 2.**

**Remark 3.**

## 4. Numerical and Outfield Experiments

#### 4.1. Effectiveness of ANM in Dominant Scatterer Extraction

**A**to

**F**. The relative radial range of the six scatterers as well as their intensities are listed in Table 2, where

**C**and

**D**have the largest and stable intensity and the other smaller ones have fluctuate intensity following Rayleigh distribution. The signal is modeled as (8)–(11), and the system parameters are listed as Table 3.

**A**,

**B**,

**E**and

**F**have fluctuate intensity, their profiles vary seriously. After SVD, the SVs are plotted in Figure 6a, where most energy falls on the first three largest ones, and the smaller SVs only contain the noise. Figure 6b–d give the RSVs corresponding to the 1st, 2nd, 3rd largest SVs. It can be seen that the 1st RSV is consisted by the most stable components of the HRRP sequence, thus the scatterer

**C**and

**D**have more energy in it. The 2nd singular value contains more fluctuate components where scatterer

**F**,

**E**,

**B**and

**A**are more prominent than

**C**and

**D**. As to the 3rd singular value,

**C**and

**D**are even weaker than the others, nearly submerged by the noise.

#### 4.2. Performance of the SSM-ANM Method for Recognition

#### 4.2.1. The Effectiveness of the LSVs for Target Recognition

#### 4.2.2. Recognition Performance Comparisons

#### 4.2.3. Outfield Real Data Experiment

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**SVs and dominant RSVs of the HRRP sequence. (

**a**) Singular values of HRRPs; (

**b**) RSV corresponding to the 1st singular value; (

**c**) RSV corresponding to the 2nd singular value; (

**d**) RSV corresponding to the 3rd singular value.

**Figure 7.**The scatterer extraction comparison for ANM, OMP and BP. (

**a**) The scatterer extraction result via ANM; (

**b**) The scatterer extraction result via OMP; (

**c**) The scatterer extraction result via BP.

**Figure 8.**Recognition performance comparison in different SNRs. (

**a**) Type A; (

**b**) Type B; (

**c**) Type C; (

**d**) Type D.

**Figure 9.**Recognition performance comparison in different SNRs (CPI = 20). (

**a**) Type A; (

**b**) Type B; (

**c**) Type C; (

**d**) Type D.

**Figure 10.**Typical HRRP sequences for the four types of vehicles (CPI = 10). (

**a**) Type A; (

**b**) Type B; (

**c**) Type C; (

**d**) Type D.

Algorithmic Recap of the SSM-ANM Method |

Input: The training data ${\left\{{\mathbf{X}}_{N\times {M}_{d,g}}^{d.g}\right\}}_{d=1,g=1}^{{D}_{g}G}$ with G types of targets and ${D}_{g}$ aspect-frames for $g\mathrm{th}$ target. The test data ${\mathbf{Y}}_{N\times M}$.
- Get the SVD result for ${\mathbf{Y}}_{N\times M}$, denoted by ${\mathbf{Y}}_{N\times M}={\mathbf{U}}^{0}{\mathbf{\Lambda}}^{0}{\mathbf{V}}^{0}$.
- Choose the t dominant singular values and singular vectors, represented as $\left\{{\lambda}_{1}^{0},{\lambda}_{2}^{0},\cdots ,{\lambda}_{t}^{0}\right\}$, $\left\{{\mathit{u}}_{1}^{0},\cdots ,{\mathit{u}}_{t}^{0}\right\}$ and $\left\{{\mathit{v}}_{1}^{0},\cdots ,{\mathit{v}}_{t}^{0}\right\}$.
- Extract the location and intensity information of the dominant scatterers for ${\mathit{v}}_{i}^{0}\left(i=1,\cdots ,t\right)$.
- Calculate the matching score ${o}^{d.g}$ for each training data ${\mathbf{X}}_{N\times {M}_{d,g}}^{d.g}$.
For d = 1 to ${D}_{g}$ - Get the SVD result for ${\mathbf{X}}_{N\times {M}_{d,g}}^{d.g}$, denoted by ${\mathbf{X}}_{N\times {M}_{d,g}}^{d.g}={\mathbf{U}}^{d,g}{\mathbf{\Lambda}}^{d,g}{\mathbf{V}}^{d,g}$.
- Choose the s dominant singular values and singular vectors, represented as $\left\{{\lambda}_{1}^{d,g},{\lambda}_{2}^{d,g},\cdots ,{\lambda}_{s}^{d,g}\right\}$, $\left\{{\mathit{u}}_{1}^{d,g},\cdots ,{\mathit{u}}_{s}^{d,g}\right\}$ and $\left\{{\mathit{v}}_{1}^{d,g},\cdots ,{\mathit{v}}_{s}^{d,g}\right\}$.
- Extract the location and intensity information of the dominant scatterers by ANM for ${\mathit{v}}_{j}^{d,g}\left(j=1,\cdots ,s\right)$, as represented by $\text{\mathbb{P}}$.
- Calculate the ds-HD for ${\mathit{v}}_{i}^{0}$ and ${\mathit{v}}_{j}^{d,g}$ for each $i=1,\cdots ,t$ and $j=1,\cdots ,s$, and form the matching matrix ${\mathbf{M}}_{s\times t}^{d,g}$.
- Calculate the correlation for ${\mathit{u}}_{i}^{0}$ and ${\mathit{u}}_{j}^{d,g}$ for each $i=1,\cdots ,t$ and $j=1,\cdots ,s$, and denoted by a correlation matrix ${\mathbf{Z}}_{s\times t}^{d.g}$.
- Get the matching score ${o}^{d.g}$ according to the following definition (15)
EndEnd- Find the largest score ${o}^{{d}_{0}.{g}_{0}}$ corresponding to the type ${g}_{0}$ with aspect-frame ${d}_{0}$.
Output: The recognition result ${g}_{0}$ for the test data ${\mathbf{Y}}_{N\times M}$. |

Scatterer Number | A | B | C | D | E | F |
---|---|---|---|---|---|---|

Radial range/m | 3.28 | 2.05 | 0.41 | −0.82 | −2.05 | −3.27 |

Intensity | 0.3 | 0.3 | 1 | 1 | 0.2 | 0.2 |

Parameter | Value |
---|---|

Carrier frequency ${f}_{0}$ | X-band |

Waveform | Chirp |

Bandwidth B | 1 GHz |

Pulse repetition frequency | 50 Hz |

Pulse width ${T}_{p}$ | 2 ms |

CPI | 10 pulses |

Training HRRPs | Test HRRPs | ||||

Type A | Type B | Type C | Type D | ||

Type A | 1.00/1.00 | 0.58/0.24 | 0.17/0.04 | 0.43/0.05 | |

Type B | 0.59/0.47 | 1.00/1.00 | 0.41/0.18 | 0.75/0.30 | |

Type C | 0.16/0.13 | 0.53/0.27 | 1.00/1.00 | 0.52/0.19 | |

Type D | 0.35/0.10 | 0.81/0.14 | 0.29/0.04 | 1.00/1.00 |

Methods | Computational Complexity |
---|---|

SSM-ANM | O(MN^{2}) + O(M^{3}) + O(N^{3}) |

SSM-OMP | O(MN^{2}) + O(MK^{2}) + O(N^{3}) |

HSM-OMP | O(MK^{2}) |

RSM-ANM | O(N^{2}M) + O(M^{3}) |

Target 1 | Target 2 | Target 3 | Target 4 | |
---|---|---|---|---|

Target 1 | 0.81 | 0.04 | 0.06 | 0.09 |

Target 2 | 0.01 | 0.87 | 0.05 | 0.07 |

Target 3 | 0.04 | 0.02 | 0.83 | 0.11 |

Target 4 | 0.13 | 0.01 | 0.01 | 0.85 |

Average recognition rate: 0.84 |

Target 1 | Target 2 | Target 3 | Target 4 | |
---|---|---|---|---|

Target 1 | 0.72 | 0.06 | 0.09 | 0.13 |

Target 2 | 0.03 | 0.81 | 0.05 | 0.11 |

Target 3 | 0.08 | 0.04 | 0.76 | 0.12 |

Target 4 | 0.16 | 0.03 | 0.07 | 0.74 |

Average recognition rate: 0.76 |

Target 1 | Target 2 | Target 3 | Target 4 | |
---|---|---|---|---|

Target 1 | 0.76 | 0.04 | 0.07 | 0.13 |

Target 2 | 0.01 | 0.83 | 0.06 | 0.10 |

Target 3 | 0.06 | 0.05 | 0.75 | 0.14 |

Target 4 | 0.12 | 0.07 | 0.03 | 0.78 |

Average recognition rate: 0.78 |

Target 1 | Target 2 | Target 3 | Target 4 | |
---|---|---|---|---|

Target 1 | 0.68 | 0.08 | 0.11 | 0.13 |

Target 2 | 0.06 | 0.72 | 0.10 | 0.12 |

Target 3 | 0.08 | 0.07 | 0.70 | 0.15 |

Target 4 | 0.21 | 0.06 | 0.08 | 0.65 |

Average recognition rate: 0.69 |

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## Share and Cite

**MDPI and ACS Style**

Jiang, Y.; Li, Y.; Cai, J.; Wang, Y.; Xu, J.
Robust Automatic Target Recognition via HRRP Sequence Based on Scatterer Matching. *Sensors* **2018**, *18*, 593.
https://doi.org/10.3390/s18020593

**AMA Style**

Jiang Y, Li Y, Cai J, Wang Y, Xu J.
Robust Automatic Target Recognition via HRRP Sequence Based on Scatterer Matching. *Sensors*. 2018; 18(2):593.
https://doi.org/10.3390/s18020593

**Chicago/Turabian Style**

Jiang, Yuan, Yang Li, Jinjian Cai, Yanhua Wang, and Jia Xu.
2018. "Robust Automatic Target Recognition via HRRP Sequence Based on Scatterer Matching" *Sensors* 18, no. 2: 593.
https://doi.org/10.3390/s18020593