# Railway Track Recognition Based on Radar Cross-Section Statistical Characterization Using mmWave Radar

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## Abstract

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## 1. Introduction

- The RCS data set of track settlement detection under the actual scenario is constructed. The statistical feature extraction and analysis method based on RCS data set is proposed, and the multi-class DAG-SVM based recognition algorithm is applied to achieve accurate track recognition in a dynamic and static mixed multi-object scene.
- The ACZT algorithm is adopted to achieve the high-precision distance estimation between the track and radar for complex multi-target scenarios under the requirement of lower bandwidth 1.5 GHz, realizing the distance estimation accuracy of 0.5 mm.
- A complete and feasible high-precision detection method for track settlement is designed, and the practical experiment platform is established to verify the proposed method by using the common commercial-grade millimeter-wave radar. Simultaneously, the influence of different track condition on the detection performance has been investigated thoroughly.

## 2. Relatred Work

## 3. System Framework and Problem Formulation

## 4. Track Recognition Based on RCS Statistical Feature Data Set and Classifier

#### 4.1. Definition and Influencing Factors of RCS

#### 4.2. RCS Data Set Construction and Statistical Feature Extraction

#### 4.3. Track Recognition Based on DAG-SVM and Decision Tree

## 5. Track Settlement Measurement Based on FMCW Technology with High Precision Target Distance Estimation

#### 5.1. Basics of FMCW Radar Operation and Range Estimation

#### 5.2. High Precision Distance Estimation Based on ACZT Algorithm

## 6. Experiment

#### 6.1. Performance Evaluation of Railway Track Recognition Method

#### 6.2. Performance Evaluation of Railway Track Settlement Measurement Method

#### 6.2.1. Impact of the Distance between Radar and Track on Settlement Measurement

#### 6.2.2. Impact of the SNR on Settlement Measurement

#### 6.2.3. Impact of the Vibration on Settlement Measurement

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

FMCW | frequency-modulated continuous wave |

RCS | radar cross section |

DAG-SVM | directed acyclic graph-support vector machine |

FFT | fast Fourier transform |

SNR | signal to noise rate |

CRLB | Cramér–Rao lower bound |

ACZT | adaptive chirp-z-transform |

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**Figure 3.**Overlapping areas between two statistical features. (

**a**) x- mean y- skewness, (

**b**) x- variance y- skewness, (

**c**) x- variance y- kurtosis, (

**d**) x- kurtosis y- skewness.

**Figure 8.**Photograph and range doppler heat map of the experimental environment for track settlement measurement. (

**a**) photograph of the experimental environment; (

**b**) range doppler heat map.

**Figure 9.**Confusion matrix of track recognition by DAG-SVM and decision tree at a radar height of 1.0157 m (SNR = 15 dB). (

**a**) Confusion matrix of DAG-SVM; (

**b**) Confusion matrix of decision tree.

**Figure 10.**Confusion matrix of track recognition by DAG-SVM and decision tree at a radar height of 2.1235 m (SNR = 15 dB). (

**a**) Confusion matrix of DAG-SVM; (

**b**) Confusion matrix of decision tree.

**Figure 11.**Confusion matrix of track recognition by DAG-SVM and decision tree at a radar height of 2.1235 m. (SNR = 7.5 dB). (

**a**) Confusion matrix of DAG-SVM; (

**b**) Confusion matrix of decision tree.

**Figure 12.**The experiment results by three different algorithms when the distance between the radar and the center of the track 1 is different. The height of (

**a**) is 1.0157 m; The height of (

**b**) is 2.1235 m.

**Figure 13.**The distance error of three different algorithms. (

**a**) is distance error of the ACZT; (

**b**) is distance error of the RootMUSIC; (

**c**) is distance error of the ZoomFFT; (

**d**) is the comparison of distance error for three algorithms.

Algorithms | ACZT | RootMUSIC | ZoomFFT |
---|---|---|---|

Computation amounts | $O(3N{log}_{2}\left(2N\right)+6N)$ | $O\left({N}^{3}\right)$ | $O({\displaystyle \frac{N}{2}}{log}_{2}\left(N\right)+2N+DNQ)$ |

Parameters | Value |
---|---|

Starting frequency (GHz) | 77 |

Bandwidth (GHz) | 1.5 |

TX Antenna Gain (dB) | 36 |

RX Antenna Gain (dB) | 42 |

SNR (dB) | 15 |

Number of TX Antennas used | 1 |

Number of RX Antennas used | 1 |

Vehicle speed(m/s) | 3.3 |

Number of mmwave radar ADC bits | 16-bits |

ADC sampling frequency | 5 MHz |

number of ADC samples collected during “ADC Sampling Time” | 512 |

Chirp number in a frame | 500 |

Total Chirp time(chirp time+idle time) (us) | 660 (100 + 560) |

Trainning Time | Prediction Speed | |
---|---|---|

DAG-SVM | 2.6799 s | 57,000 obs/s |

Decision Tree | 0.84401 s | 270,000 obs/s |

List | Problems and Possible Solutions |
---|---|

1 | P:Selection of base points and observation points |

S: Refer to manual measurement method | |

2 | P:Power supply |

S: Utilize solar energy and batteries | |

3 | P:Calibration of millimeter-wave radar |

S: Combination of automatic calibration and regular manual calibration | |

4 | P:Transfer of Settlement Detection Data |

S: Integration of Radar and Communication |

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**MDPI and ACS Style**

Li, S.; Ding, J.; Liu, W.; Li, H.; Zhou, F.; Zhu, Z.
Railway Track Recognition Based on Radar Cross-Section Statistical Characterization Using mmWave Radar. *Remote Sens.* **2022**, *14*, 294.
https://doi.org/10.3390/rs14020294

**AMA Style**

Li S, Ding J, Liu W, Li H, Zhou F, Zhu Z.
Railway Track Recognition Based on Radar Cross-Section Statistical Characterization Using mmWave Radar. *Remote Sensing*. 2022; 14(2):294.
https://doi.org/10.3390/rs14020294

**Chicago/Turabian Style**

Li, Shuo, Jieqiong Ding, Weirong Liu, Heng Li, Feng Zhou, and Zhengfa Zhu.
2022. "Railway Track Recognition Based on Radar Cross-Section Statistical Characterization Using mmWave Radar" *Remote Sensing* 14, no. 2: 294.
https://doi.org/10.3390/rs14020294