# A Novel Flickering Multi-Target Joint Detection Method Based on a Biological Memory Model

^{*}

## Abstract

**:**

## 1. Introduction

- Detection of the target with flickering characteristics under low SCR. This paper proposes a memory weight DP merit function integral operator. The theory of biological memory is introduced into DP integration to study the appearance and blanking state of targets with flickering characteristics in sea clutter. The merit function effectively integrates the correlation of flickering characteristic targets’ states among different frames. Therefore, the method achieves accurate detection for flickering characteristic targets with a low SCR.
- Multi-target detection is employed without pre-target number information, and the computational cost is reduced. Usually, when using DP to solve multi-target detection problems, the target’s high-dimensional state is difficult to calculate due to the uncertain number of targets. However, the target number being known is inconsistent with practical applications. Therefore, we choose a simple and effective way to achieve the suboptimal solution of multi-target detection. We use a lower global threshold in the DP process and discretize the areas with candidate targets to simplify the high-dimensional maximization to multiple low-dimensional maximization, meaning that the computational cost is reduced.

## 2. DP Model

#### 2.1. Target Motion Model

#### 2.2. Multi-Frame Joint Target Detection

#### 2.2.1. Initialization

#### 2.2.2. Multi-Frame Joint Integration

#### 2.2.3. Target Detection

## 3. Biological Memory Model Based Multi-Target Joint Detection Method

#### 3.1. Biological Memory Theory for the Flickering Characteristics Target

#### 3.1.1. Definition of Memory and Forgetting

- Memory

**Figure 1.**The schematic diagram for the memory stimulus and responses. (

**a**) Responses of two long-interval stimuli; (

**b**) responses of two short-interval stimuli; (

**c**) responses of three consecutive stimuli [40].

- Forgetting

#### 3.1.2. The Memory Model for the Flickering Characteristics Target

#### 3.2. Process of BM-DP-MJD Method

#### 3.2.1. Pre-Filter Operator

#### 3.2.2. Multi-Target Joint Integration

- 1.
- Initialization

- 2.
- Multi-frame joint accumulation

- 3.
- Progressive loop integration

#### 3.2.3. Two-Stage Joint Threshold Criterion

#### 3.3. Assumptions for Special Situations of Flickering Characteristics Multi-Target Detection

## 4. Results and Discussion

#### 4.1. Simulation Data Results

#### 4.1.1. Demonstration of Simulation Data Detection Results

#### 4.1.2. Simulation Data Detection Performance of BMM-DP-MJD

- Detection performance of three types of target

- Detection performance in special assumed situations

- Comparison of the detection performance of three algorithms on simulation data

#### 4.2. Experimental Data Detection Performance of BMM-DP-MJD

#### 4.3. Detection Performance Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Assumptions for special situations of flickering characteristic multi-target detection. (

**a**) Assumption 1; (

**b**) assumption 2; (

**c**) assumption3.

**Figure 5.**Simulation data scenario of five targets. (

**a**) The target generation model; (

**b**) the first frame imaging; (

**c**) the third frame imaging; (

**d**) the fourth frame imaging; (

**e**) the tenth frame imaging.

**Figure 6.**Simulation data detection results of BMM-DP-MJD. (

**a**) Decision program of detection threshold; (

**b**) detection results of BMM-DP-MJD in 2-D; (

**c**) detection results of BMM-DP-MJD in 3-D.

**Figure 7.**The detailed detection performance of 6 separate targets. (

**a**) Simulation scene of the of 6 separated targets; (

**b**) the P

_{d}of 6 separate targets; (

**c**) the RMSE of 6 separate targets; (

**d**) the ${P}_{fa}$ of 6 separate targets.

**Figure 8.**The detection performance in assumed special situations. (

**a**) Simulation scene of assumed situations; (

**b**) the P

_{d}of assumed situations; (

**c**) the RMSE of assumed situations; (

**d**) the ${P}_{fa}$ of assumed situations.

**Figure 9.**Performance curves of the three methods. (

**a**) The P

_{d}of the uniform distribution target; (

**b**) the ${P}_{d}$ of the binomial distribution target; (

**c**) the ${P}_{d}$ of the Swerling I distribution target; (

**d**) the RMSE of the uniform distribution target; (

**e**) the RMSE of the binomial distribution target; (

**f**) the RMSE of the Swerling I distribution target; (

**g**) the ${P}_{fa}$ of the uniform distribution target; (

**h**) the ${P}_{fa}$ of the binomial distribution target; (

**i**) the ${P}_{fa}$ of the Swerling I distribution target.

**Figure 10.**The detection performance curve of the three methods for the target with different binomial probability distributions under SCR = 8 dB. (

**a**) The ${P}_{d}$ of targets under different binomial probability distributions; (

**b**) the RMSE of targets under different binomial probability distributions; (

**c**) the ${P}_{fa}$ of targets under different binomial probability distributions.

**Figure 11.**Experimental data of navigation radar. (

**a**) Experimental scene of the measured data; (

**b**) the 1st-frame imaging; (

**c**) the 3rd-frame imaging; (

**d**) optical scene of the measured data; (

**e**) the 7th-frame imaging; (

**f**) the 9th-frame imaging.

**Figure 12.**The experimental results of the methods mentioned. (

**a**) Merit function results of DP-TBD; (

**b**) merit function results of two-Stage DP-TBD; (

**c**) merit function results of BMM-DP-MJD; (

**d**) results of DP-TBD; (

**e**) results of two-Stage DP-TBD; (

**f**) results of BMM-DP-MJD.

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

K distribution scale parameter | ${\alpha}^{\prime}=2$$,\text{}{\beta}^{\prime}=1$ |

Number of frames | 10 |

False alarm probability | 0.02 |

Target appearance’s probability of binomial distribution | 0.7 |

The size of simulation data | $60\times 60$ |

Target position random noise | ${\sigma}^{2}=1$$,\text{}E=0.001cell$ |

Target Number | SCR | Distribution |
---|---|---|

Target 1 | 5 dB | Swerling I distribution |

Target 2 | 10 dB | Uniform distribution |

Target 3 | 10 dB | Uniform distribution |

Target 4 | 5 dB | Swerling I distribution |

Target 5 | 10 dB | Uniform distribution |

Target Number | Distribution |
---|---|

Target 1, Target 4 | Binomial distribution |

Target 2, Target 5 | Swerling I distribution |

Target 3, Target 6 | Uniform distribution targets |

Target Number | Distribution |
---|---|

Target 1 | The target disappearance probability is 0.2 |

Target 2 | Binomial distribution |

Target 3 | The target disappearance probability is 0.3 |

Target 4 | Binomial distribution |

Target 5 | Binomial distribution |

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

Wave band | X band | Main lobe of the azimuth | 5.1° |

Scanning speed | 72°/s | Bandwidth | 75 MHz |

PRF | 200 Hz | Image size | $1500\times 256$ |

Method | ${\mathit{P}}_{\mathit{d}}$ | ${\mathit{P}}_{\mathit{f}\mathit{a}}$ | RMSE (Cell) |
---|---|---|---|

DP-TBD | 0.4 | 0 | 11.3 of $1500\times 256$ |

Two stage DP-TBD | 0.8 | 0.4 | 14.3 of $1500\times 256$ |

BMM-DP-MJD | 1 | 0 | 1.7 of $1500\times 256$ |

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**MDPI and ACS Style**

Zhang, Q.; Huo, W.; Pei, J.; Zhang, Y.; Yang, J.; Huang, Y.
A Novel Flickering Multi-Target Joint Detection Method Based on a Biological Memory Model. *Remote Sens.* **2022**, *14*, 39.
https://doi.org/10.3390/rs14010039

**AMA Style**

Zhang Q, Huo W, Pei J, Zhang Y, Yang J, Huang Y.
A Novel Flickering Multi-Target Joint Detection Method Based on a Biological Memory Model. *Remote Sensing*. 2022; 14(1):39.
https://doi.org/10.3390/rs14010039

**Chicago/Turabian Style**

Zhang, Qian, Weibo Huo, Jifang Pei, Yongchao Zhang, Jianyu Yang, and Yulin Huang.
2022. "A Novel Flickering Multi-Target Joint Detection Method Based on a Biological Memory Model" *Remote Sensing* 14, no. 1: 39.
https://doi.org/10.3390/rs14010039