# PBR Clutter Suppression Algorithm Based on Dilation Morphology of Non-Uniform Grid

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## Abstract

**:**

## 1. Introduction

- The space synchronization accuracy is not as good as the traditional radar, resulting in the decreased SNR (signal noise ration) and the poor location precision.
- Simultaneous multi-beam forming leads to the redundant data being increased.
- The reference channel is not ideally compatible to the echo channel due to the multipath and the minor difference of antenna performance. The performance of the following pulse compression degrades.
- Due to the agility of the illuminator parameters, the number of the pulses utilized for detection is less. Besides, the scattered wave of the target depends on the opportunity of the beam steering. Thus, the valid data rate is decreased.
- Since the illuminator parameters are agile pulse by pulse, it is hard to adopt coherent integration to suppress clutter like traditional radar.
- Low SNR calls for low threshold during CFAR (constant false alarm), that is to increase the detection rate, whereas the false-alarm rate increases correspondingly.

## 2. Non-Uniform Polar Grid Construction for PBR

## 3. Separate False Alarm Clutter from Data

#### 3.1. Mark the Point on Grid

#### 3.2. Separate False Alarm Clutter from Data Based on the Dilation Morphology

#### 3.3. Iteratively Calculation Frame by Frame

## 4. Experiment result and Analysis

#### 4.1. Testing by Simulated Data

#### 4.1.1. Scenario for Simulation

#### 4.1.2. The Clutter Suppression Performance Analysis

#### 4.1.3. Computation Analysis

#### 4.1.4. Test the Performance Combining with Tracking Algorithm

^{2}respectively. In Kalman filtering process, the maximum time period of blind prediction is set as 15 s.

#### 4.2. Testing by the Field Data

^{−2}. After CFAR detection, we adopt the multi-beam amplitude comparison direction measurements. Figure 13a illustrates the final detection point map of the field data with 390 s duration. Two directions of jamming are located at 144° and 148°. Suppress the jamming in two directions and adopt the proposed clutter suppression algorithm. The structural element size is 5 × 5. The half number of the reference frames is set as 2. The suppression result is shown in Figure 13b. It is obvious that most of points are filtered out. Instead, points in three suspected track areas are retained. Referring to the ADS-B dataset, we plot the real-time civil flight information in Figure 13c, which is selected with the same duration and detection scope as the field data. The line with different colors stands for different flight track. There are three flights in the detection scope. Comparing with the ADS-B data, we can find that the proposed algorithm can effectively suppress the clutters and retain most of the target information.

^{2}. In Kalman filtering process, the maximum time period of blind prediction is set as 15 s. Each frame consists of the clustered point data with 0.5 s period. Figure 14 and Table 7 illustrates the tracing results and the performance indexes of NN-MHT and MCSNG-NN. Figure 15 and Table 8 illustrates the tracing results and the performance indexes of SNN-Kalman and MCSNG-SNN-K. Comparing with the ADS-B dataset, we marked the true tracks by the ellipses with dotted line. It is obvious that MCSNG-NN reduces the occurrence probability of false tracks relative to NN-MHT. In addition its time-consumption drops to 28.16% of the original NN-MHT time-consumption. Besides, similar conclusions are suitable to SNN-Kalman and MCSNG-SNN-K. We can find that MCSNG-SNN-K reduces the occurrence probability of false tracks and saves time relative to traditional SNN-Kalman.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**The sketch map of processing progress: (

**a**) general view; (

**b**) structural element B; (

**c**) reference mark-matrix ${\Gamma}_{\mathrm{n}}$; (

**d**) dilation result; (

**e**) object mark-matrix ${A}_{\mathrm{n}}$; (

**f**) screened data for ${A}_{\mathrm{n}}$.

**Figure 7.**Production of the simulated data: (

**a**) true tracks of five targets; (

**b**) target tracks with measurement error; (

**c**) target tracks detected; (

**d**) detection results from CFAR.

**Figure 9.**Contrast of before and after the suppression: (

**a**) simulated data before suppression; (

**b**) clutter suppression result.

**Figure 11.**Tracing results comparison of both algorithms: (

**a**) NN-MHT tracing result; (

**b**) MCSNG-NN tracing result.

**Figure 12.**Valid tracing results comparison of both algorithms: (

**a**) SNN-Kalman tracing result; (

**b**) MCSNG-SNN-K tracing result.

**Figure 13.**The contrast of before and after the suppression and the comparison with ADS-B dataset: (

**a**) field data before suppression; (

**b**) clutter suppression result; (

**c**) real-time fights information from ADS-B dataset.

**Figure 14.**Tracing results of NN-MHT and MCSNG-NN: (

**a**) NN-MHT tracing result; (

**b**) MCSNG-NN tracing result.

**Figure 15.**Tracing results of SNN-Kalman and MCSNG-SNN-K: (

**a**) SNN-Kalman tracing result; (

**b**) MCSNG-SNN-K tracing result.

1. Calculate angular coordinate |

The angular coordinate set is $\Theta =\left\{{\mathsf{\theta}}_{\mathrm{k}}|{\mathsf{\theta}}_{\mathrm{k}+1}-{\mathsf{\theta}}_{\mathrm{k}}=3{\mathsf{\sigma}}_{\mathsf{\theta}},k=0\dots N,N=\left[\frac{{\theta}_{max}-{\mathsf{\theta}}_{0}}{3{\mathsf{\sigma}}_{\mathsf{\theta}}}\right]\right\}$. Where $[\xb7]$ is the symbol of round down, and N is the mesh counts in angular dimension. |

2. Aiming at each angular coordinate ${\mathsf{\theta}}_{\mathbf{k}}$ in Θ, iteratively calculate the grid division in range dimension. |

For ${\mathsf{\theta}}_{\mathrm{k}}$, $\mathrm{k}=0\dots \mathrm{N}$ Initialization: $\mathrm{i}=0$, ${\mathrm{R}}_{\mathrm{i}}$ = ${\mathrm{r}}_{0}$; Iteration: ${\mathrm{Rs}}_{\mathrm{i}}={\mathrm{R}}_{\mathrm{i}}+\sqrt{{\mathrm{R}}_{\mathrm{i}}^{2}+{L}^{2}+2{R}_{i}Lcos({\theta}_{k})}$; ${\rho}_{1}({R}_{si},{\theta}_{k})=\frac{{R}_{si}^{2}+{L}^{2}+2{R}_{si}Lcos({\theta}_{k})}{2{({R}_{si}+Lcos({\theta}_{k}))}^{2}}$, ${\rho}_{2}({R}_{si},{\theta}_{k})=\frac{({R}_{si}^{2}-{L}^{2})Lsin({\theta}_{k})}{2{({R}_{si}+Lcos({\theta}_{k}))}^{2}}$. ${\mathrm{R}}_{\mathrm{i}+1}={\mathrm{R}}_{\mathrm{i}}+3\sqrt{{\rho}_{1}^{2}({R}_{si},{\theta}_{k}){\mathsf{\sigma}}_{\mathrm{r}}^{2}+{\rho}_{2}^{2}({R}_{si},{\theta}_{k}){\mathsf{\sigma}}_{\mathsf{\theta}}^{2}}$; $\mathrm{i}=\mathrm{i}+1;$ Terminate when ${\mathrm{R}}_{\mathrm{i}}>{\mathrm{r}}_{max}$. ${\mathrm{N}}_{\mathrm{k}}=i$. ${\mathrm{N}}_{\mathrm{k}}$ is the mesh counts in range dimension for ${\mathsf{\theta}}_{\mathrm{k}}$. The range coordinate set is $\Lambda ={\{\mathrm{R}}_{\mathrm{i},{\theta}_{k}}|\mathrm{i}=0\dots {\mathrm{N}}_{\mathrm{k}},{\mathsf{\theta}}_{\mathrm{k}}\in \Theta \}$. |

Start Position (km, degree) in Polar Coordinates | Start Position (km) in Cartesian Coordinates | Track Slope | Track Intercept (km) | |
---|---|---|---|---|

Target 1 | (86.023,144.5) | (−70, 50) | 5 | 60 |

Target 2 | (70.456,96.5) | (−8, 70) | 10 | 100 |

Target 3 | (80.623,82.9) | (10, 80) | −3 | 10 |

Target 4 | (76.158,113.2) | (−30, 70) | −10 | 80 |

Target 5 | (70.711,135) | (−50, 50) | 30 | 55 |

Detection Accuracy Rate | False Alarm Decline Rate | Miss Detection Rate |
---|---|---|

97.45% | 10.24% | 2.55% |

Total Number of Traces | Mean Trace Length | Max Trace Length | Time Consuming (s) | |
---|---|---|---|---|

NN-MHT | 22 | 39.13 | 89 | 2.99 |

MCSNG-NN | 6 | 78.83 | 89 | 0.7 |

Mean Trace Error (m) | Velocity (m/s) | ||||
---|---|---|---|---|---|

Track NO. | SNN-Kalman | MCSNG-SNN-K | SNN-Kalman | MCSNG-SNN-K | True Value |

1 | 548.87 | 434.56 | 823.5 | 821.7 | 800 |

2 | 1596.55 | 389.63 | 873.6 | 809.4 | 750 |

3 | 644.06 | 141.85 | 614.7 | 612.0 | 600 |

4 | 1286.59 | 283.97 | 395.1 | 415.2 | 400 |

5 | 2721.07 | 1840.33 | 543.5 | 604.0 | 600 |

Total Number of Traces | Mean Trace Length | Max Trace Length | Time Consuming (s) | |
---|---|---|---|---|

SNN-Kalman | 104 | 64.89 | 654 | 0.6715 |

MCSNG-SNN-K | 23 | 124.47 | 474 | 0.6081 |

Total Number of Traces | Mean Trace Length | Max Trace Length | Time Consuming (s) | |
---|---|---|---|---|

NN-MHT | 31 | 38.7 | 135 | 4.83 |

MCSNG-NN | 9 | 39.3 | 120 | 1.36 |

Total Number of Traces | Mean Trace Length | Max Trace Length | Time Consuming (s) | |
---|---|---|---|---|

SNN-Kalman | 23 | 254.5 | 734 | 0.8536 |

MCSNG-SNN-K | 13 | 196.6 | 424 | 0.6467 |

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**MDPI and ACS Style**

Zhu, Q.; Li, T.; Pan, J.; Bao, Q.
PBR Clutter Suppression Algorithm Based on Dilation Morphology of Non-Uniform Grid. *Electronics* **2019**, *8*, 708.
https://doi.org/10.3390/electronics8060708

**AMA Style**

Zhu Q, Li T, Pan J, Bao Q.
PBR Clutter Suppression Algorithm Based on Dilation Morphology of Non-Uniform Grid. *Electronics*. 2019; 8(6):708.
https://doi.org/10.3390/electronics8060708

**Chicago/Turabian Style**

Zhu, Qian, Tao Li, Jiameng Pan, and Qinglong Bao.
2019. "PBR Clutter Suppression Algorithm Based on Dilation Morphology of Non-Uniform Grid" *Electronics* 8, no. 6: 708.
https://doi.org/10.3390/electronics8060708