# A Fast Motion Parameters Estimation Method Based on Cross-Correlation of Adjacent Echoes for Wideband LFM Radars

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## Abstract

**:**

## 1. Introduction

## 2. Signal Model

## 3. Estimation of Motion Parameters Based on the CCAE Method

#### 3.1. “Stretching” Idea of the Proposed CCAE Method

#### 3.2. Proposed CCAE Algorithm

#### 3.2.1. Estimation of Velocity

#### 3.2.2. Estimation of Higher Order Parameters

#### 3.3. Implementation of the Proposed CCAE Method

- The first UR or stretched signal is multiplied with the conjugate of the second UR or stretched signal. For acceleration estimation, the second echo signal is also multiplied with the third echo signal.
- The FFT operation is performed on the multiplication results for energy accumulation.
- Estimate the frequencies of the above FFT results.

#### 3.4. Performance Analysis

## 4. Simulations and Real Data Processing

#### 4.1. Evaluation of the Proposed CCAE Method

#### 4.2. Comparison with the ACCF Method

^{2}. Three pulses are used for velocity and acceleration estimation, the other parameters being the same as those of the previous experiments. The estimated acceleration results are shown in Figure 7, from which we can see that the RMSE performance of CCAE on UR signals is better than that of ACCF on UR signals. It can also be seen that the threshold SNR of CCAE on UR signals is smaller than that of ACCF on UR signals, i.e., −16 dB versus −8 dB. As has already been analyzed in Section 3.4, SNR decreases after cross-correlation. To estimate the acceleration, the conjugate multiplication has to be used twice in the ACCF method, but only once in the CCAE method. Therefore, the performance loss is more in the ACCF method than in the CCAE method. In addition, the performance of CCAE on stretched signals is better than that of CCAE on UR signals, due to the higher SNR of stretched signals.

#### 4.3. Verification with Real Data

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 6.**RMSE comparison of velocity estimation by using CCAE on stretched signals, CCAE on uncompressed received (UR) signals and adjacent cross-correlation function (ACCF) on UR signals (without acceleration).

**Figure 7.**RMSE comparison of acceleration estimation by using CCAE on stretched signals, CCAE on UR signals and ACCF on UR signals (with acceleration).

**Figure 8.**RMSE comparison of velocity estimation by using CCAE on stretched signals, CCAE on UR signals and ACCF on UR signals (with acceleration).

**Figure 9.**The spectrums of the cross-correlation results. (

**a**) The spectrum of the cross-correlation result of radar Dataset 1. (

**b**) The spectrum of the cross-correlation result of radar Dataset 2.

**Figure 10.**Estimation results of Dataset 1. (

**a**) The estimated velocity and the target’s real velocity (due to the high speed of the target and the high precision of the estimated velocity, the two lines overlap). (

**b**) The absolute values of differences between the estimated velocities and the target’s real velocities.

**Figure 11.**Estimation results of Dataset 2. (

**a**) The estimated velocity and real velocity of the target (due to the high speed of the target and the high precision of the estimated velocity, the two lines overlap). (

**b**) The absolute values of differences between the estimated velocities and the target’s real velocities.

**Figure 12.**The range profiles of the target. (

**a**) The range profiles with the range migration (RM) effect. (

**b**) The range profiles after range alignment by the proposed CCAE method.

Notation | Type | Meaning |
---|---|---|

$ur$ | Subscript | The received signal is uncompressed. |

$st$ | Subscript | The signal is stretched. |

$ac$ | Subscript | The signal is obtained by multiplying a echo signal with the conjugate of another echo signal. |

$se$ | Subscript | The signal is the multiplication result of the different echo signal from the same scatterers. |

$cr$ | Subscript | The signal is the multiplication result of the different echo signal from the different scatterers. |

${s}_{tr}\left(t\right)$ | Signal | The transmitted signal. |

${s}_{LO}\left(t\right)$ | Signal | The local reference signal. |

${s}_{ur}(t,{t}_{m})$ | Signal | The uncompressed received signal. |

${s}_{st}(t,{t}_{m})$ | Signal | The stretched signal. |

${R}_{p}\left({t}_{m}\right)$ | Signal | The distance from radar to the p-th scatterer. |

Center Frequency (GHz) | Bandwidth (MHz) | Pulse Width (μs) | Sampling Frequency (MHz) | PRI (ms) |
---|---|---|---|---|

9 | 200 | 100 | 10 | 5 |

**Table 3.**Simulation parameters of the comparison with the adjacent cross-correlation function (ACCF) method.

Center Frequency (GHz) | Bandwidth (GHz) | Pulse Width (μs) | Sampling Frequency (MHz) | PRI (ms) |
---|---|---|---|---|

9 | 1 | 100 | 10 | 10 |

**Table 4.**Comparison of the time cost between CCAE on stretched signals, CCAE on UR signals and ACCF on UR signals.

Time Cost (s) | CCAE_Stretched | CCAE_UR | ACCF_UR |
---|---|---|---|

Estimation without acceleration | 81.6 | 2545.1 | 5282.1 |

Estimation with acceleration | 156.5 | 4869.7 | 10175.3 |

Parameters | Radar 1 | Radar 2 |
---|---|---|

Center Frequency (GHz) | 9 | 3.2 |

Bandwidth (MHz) | 2000 | 300 |

Sampling Frequency (MHz) | 10 | 10 |

Pulse Width (μs) | 400 | 200 |

PRI (ms) | 40 | 100 |

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**MDPI and ACS Style**

Zhang, Y.-X.; Hong, R.-J.; Yang, C.-F.; Zhang, Y.-J.; Deng, Z.-M.; Jin, S.
A Fast Motion Parameters Estimation Method Based on Cross-Correlation of Adjacent Echoes for Wideband LFM Radars. *Appl. Sci.* **2017**, *7*, 500.
https://doi.org/10.3390/app7050500

**AMA Style**

Zhang Y-X, Hong R-J, Yang C-F, Zhang Y-J, Deng Z-M, Jin S.
A Fast Motion Parameters Estimation Method Based on Cross-Correlation of Adjacent Echoes for Wideband LFM Radars. *Applied Sciences*. 2017; 7(5):500.
https://doi.org/10.3390/app7050500

**Chicago/Turabian Style**

Zhang, Yi-Xiong, Ru-Jia Hong, Cheng-Fu Yang, Yun-Jian Zhang, Zhen-Miao Deng, and Sheng Jin.
2017. "A Fast Motion Parameters Estimation Method Based on Cross-Correlation of Adjacent Echoes for Wideband LFM Radars" *Applied Sciences* 7, no. 5: 500.
https://doi.org/10.3390/app7050500