# Passive Sonar Target Detection Using Statistical Classifier and Adaptive Threshold

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Target Detection in Passive Sonar

#### 2.1. Ambient Noise

#### 2.2. Radiated Noise

## 3. Statistical Classifier and Adaptive Threshold

#### 3.1. Detection Point in Time Domain

^{ih}iteration $(k\ge 0)$.Convergence condition is $|{\omega}_{{\theta}_{i}}^{(k+1)}-{\omega}_{{\theta}_{i}}^{(k)}|<\epsilon $.

_{Mt}, and the whole number of members is n

_{t}. Since the input signal is added with ambient noise (with same size and in K-means Algorithm K = 2, to correct the error clustering of signals without any noise, equation is multiplied by 2. In the other hands in ideal condition, n

_{Mt}= 0.5n

_{t}. In summary, Figure 5 shows how to calculate detection point in time domain.

#### 3.2. Detection Point in Frequency Domain

#### 3.3. Target Detection

^{th}sequence in m sequences in time domain, ${\overrightarrow{A}}_{ftp}$ is detection point in m sequence of test input signals in frequency domain, ${A}_{ft{p}_{i}}$ is the detection point for i

^{th}sequence in m sequences in frequency domain, w and W are the Wiener filter coefficients, and Detection Point (DP) is detection point after fusion. In this case, the condition (8) changes to condition (10).

## 4. Experimental and Simulation Results

#### 4.1. Simulation Steps

#### 4.2. Database

#### 4.3. The Simulation Results

#### 4.4. Calculation of Detection Points in the Time Domain

#### 4.5. Calculation of Detection Points in the Frequency Domain

#### 4.6. Fusion

## 5. Discussion and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Center of noise and target cluster. (

**a**) Large center is selected as detection point and (

**b**) large center is selected as detection point incorrectly.

**Figure 11.**Bayesian classifier output, in sample of 50 thousand and 100 thousand real target is present (red ellipse).

**Figure 13.**Results of K-means (K = 2), dots shown elements of the first cluster, crosses shown elements of the second cluster and the hollow circles are the cluster center.

**Figure 14.**Vector ${\overrightarrow{a}}_{ttp}$ for two target signals (13 and 14) and two ambient noise signals (15 and 16) in the time domain.

**Figure 16.**Vector ${\overrightarrow{A}}_{ftp}$ for two target signals (13 and 14) and two ambient noise (15 and 16).

**Figure 17.**Average of 20 (m = 20) sequences for 19 test signals (1 to 14 are target signals and 15 to 19 are ambient noise signals).

**Figure 19.**DP for 19 test signals (1 to 14 are the target signals and 15 to 17 are only ambient noise).

**Figure 20.**Receiving Operating Characteristics (ROC) Experimental results for target detection. TPSW NN: Two-Pass Split-Windows Neural Network; DEMON: Detection Envelope Modulation on Noise Neural Network.

No. | Type | ${\mathit{a}}_{\mathit{t}\mathit{t}\mathit{p}}$ |
---|---|---|

1 | Ship Engine 1 | 0.83 |

2 | Ship Propeller 1 | 0.62 |

3 | Ship 1 | 0.39 |

4 | Ship Engine 2 | 0.61 |

5 | Ship 2 | 0.59 |

6 | Ship Engine 3 | 0.6 |

7 | Ship Engine 4 | 0.5 |

8 | Ship Engine 5 | 0.68 |

9 | Ship Engine 6 | 0.82 |

10 | Ship Propeller 2 | 0.21 |

11 | Ship Engine 7 | 0.46 |

12 | Ship Engine 8 | 0.53 |

13 | Ship Engine 9 | 0.7 |

14 | Ship Engine 10 | 0.58 |

15 | Ambient Noise 1 | 0.43 |

16 | Ambient Noise 2 | 0.39 |

17 | Ambient Noise 3 | 0.37 |

18 | Ambient Noise 4 | 0.38 |

19 | Ambient Noise 5 | 0.26 |

No. | Type | ${\mathit{A}}_{\mathit{f}\mathit{t}\mathit{p}}$ |
---|---|---|

1 | Ship Engine 1 | 0.46 |

2 | Ship Propeller 1 | 0.63 |

3 | Ship 1 | 0.65 |

4 | Ship Engine 2 | 0.47 |

5 | Ship 2 | 0.63 |

6 | Ship Engine 3 | 0.83 |

7 | Ship Engine 4 | 0.43 |

8 | Ship Engine 5 | 0.48 |

9 | Ship Engine 6 | 0.49 |

10 | Ship Propeller 2 | 0.57 |

11 | Ship Engine 7 | 0.53 |

12 | Ship Engine 8 | 0.61 |

13 | Ship Engine 9 | 0.43 |

14 | Ship Engine 10 | 0.38 |

15 | Ambient Noise 1 | 0.37 |

16 | Ambient Noise 2 | 0.36 |

17 | Ambient Noise 3 | 0.21 |

18 | Ambient Noise 4 | 0.32 |

19 | Ambient Noise 5 | 0.02 |

**Table 3.**Value of parameters of sonar equation in the Persian Gulf. DI: directivity index; NL: noise level; TL: transmission loss; SL: source level.

Parameter | DI | NL | TL | SL |
---|---|---|---|---|

Value (dB) | 200 | 19.02 | 90 | 31.9 |

**Table 4.**True detection rate. TPSW NN: Two-Pass Split-Windows Neural Network; DEMON: Detection Envelope Modulation on Noise.

Detection Method | Proposed Method (Adaptive Fusion) | The Method Described in [4] (TPSW NN) | The Method Described in [14] (DEMON) | The Method Described in [20] (Sonar Equation) |
---|---|---|---|---|

Database | ||||

First category | 81.20% | 60.35% | 51.12% | 25.36% |

Second category | 73.41% | 44.26% | 48.20% | 23.85% |

Third category | 94.32% | 63.57% | 69.12% | 46.35% |

Total | 85.40% | 58.75% | 61.27% | 35.71% |

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**MDPI and ACS Style**

Komari Alaie, H.; Farsi, H.
Passive Sonar Target Detection Using Statistical Classifier and Adaptive Threshold. *Appl. Sci.* **2018**, *8*, 61.
https://doi.org/10.3390/app8010061

**AMA Style**

Komari Alaie H, Farsi H.
Passive Sonar Target Detection Using Statistical Classifier and Adaptive Threshold. *Applied Sciences*. 2018; 8(1):61.
https://doi.org/10.3390/app8010061

**Chicago/Turabian Style**

Komari Alaie, Hamed, and Hassan Farsi.
2018. "Passive Sonar Target Detection Using Statistical Classifier and Adaptive Threshold" *Applied Sciences* 8, no. 1: 61.
https://doi.org/10.3390/app8010061