# Optimizing Matching Area for Underwater Gravity-Aided Inertial Navigation Based on the Convolution Slop Parameter-Support Vector Machine Combined Method

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Image Convolution

#### 2.2. Convolution Slope Parameter

#### 2.3. Other Characteristic Parameters

#### 2.3.1. Difference between Convolution Rows and Columns Parameter

#### 2.3.2. Convolution Variance

#### 2.3.3. Pooling Difference

#### 2.3.4. Range

#### 2.4. Principle of Support Vector Machine Algorithm

## 3. Results

#### 3.1. Verification

^{−3}m/s

^{2}, the simulated speed was 7 m/s, and the initial position error was set to 700 m. The number of sampling points was 60, and the sampling period was 10 s. The random error of the sampling value with the standard deviation of 1 mGal was used as the real-time measurement data of the gravimeter, and the Tercom algorithm was used for trajectory matching. The effect is shown in Figure 4.

#### 3.2. Appliction

## 4. Conclusions

- (1)
- The Sobel operator was used for convolution of the gravity anomaly map, and the convolution slope parameter was constructed. The difference between convolution rows and columns, convolution variance of the feature map, pooling difference, and range parameter of gravity anomaly map was calculated. SVM algorithm was used to fuse these five parameters, and a convolution slope parameter-support vector machine combined method is proposed.
- (2)
- The samples of the target area were divided into the training set and test set. The training set data were used to calculate the classification model, which separates the test-set samples and compares them with the pre-calibration results. In the experimental results, the classification accuracy of the test set is over 92%.
- (3)
- To verify the effectiveness of the classification results, the classification model was applied to another region, and the suitable areas and unsuitable areas were divided. The navigation experiment was carried out in the suitable areas. The results show that the positioning error is better than 100 m, and the accuracy can be more than 91%. It is proven that this method can effectively divide the matching area of GAINS.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The Sobel Operator: (

**a**) horizontal edge-detection operator; (

**b**) vertical edge-detection operator; (

**c**) 45° edge-detection operator; (

**d**) 135° edge-detection operator.

**Figure 2.**Coverage area of diagonal heading route in target area: (

**a**) Northeast direction; (

**b**) Northwest direction.

**Figure 4.**Matching result: (

**a**) routes distribution of suitable area-matching result; (

**b**) gravity anomaly sequence of simulated route and matching route in (

**a**); (

**c**) routes distribution of unsuitable area-matching result; (

**d**) gravity anomaly sequence of simulated route and matching route in (

**c**).

**Figure 6.**Comparison for pre-calibration and classification results of suitable areas: (

**a**) pre-calibration results of suitable areas for east-west direction; (

**b**) classification results of suitable areas for east-west direction; (

**c**) pre-calibration results of suitable areas for north-south direction; (

**d**) classification results of suitable areas for north-south direction; (

**e**) pre-calibration results of suitable areas for northeast direction; (

**f**) classification results of suitable areas for northeast direction; (

**g**) pre-calibration results of suitable areas for northwest direction; (

**h**) classification results of suitable areas for northwest direction.

**Figure 8.**Distribution of suitable areas in application area: (

**a**) suitable areas for east-west direction; (

**b**) suitable areas for north-south direction; (

**c**) suitable areas for northeast direction; (

**d**) suitable areas for northwest direction.

**Figure 9.**Positioning error of suitable areas: (

**a**) east-west direction suitable areas; (

**b**) north-south direction suitable area; (

**c**) northeast direction suitable areas; (

**d**) northwest direction suitable areas.

Area | Convolution Slop | Difference between Convolution Rows and Columns | Convolution Variance | Pooling Difference | Range |
---|---|---|---|---|---|

A | 1.3939 | 1.2144 | 1.2828 | 0.0212 | 1.5310 |

B | −1.0599 | −0.9096 | −0.5548 | −0.6817 | −0.8296 |

C | −0.4586 | −0.7998 | −0.4899 | −0.5950 | −0.6989 |

D | 2.8311 | 3.9503 | 4.5418 | 2.8409 | 4.1681 |

Area | Average Positioning Error/m | The Standard Deviation of Positioning Error/m |
---|---|---|

A | 60.98 | 36.36 |

B | 911.34 | 617.71 |

C | 234.42 | 141.95 |

D | 59.67 | 49.76 |

Direction | Number of the Suitable Area | Number of Unsuitable Areas |
---|---|---|

East-west | 126 | 799 |

North-south | 136 | 789 |

Northeast | 138 | 787 |

Northwest | 124 | 801 |

Direction | Classification Accuracy of the Test Set | Recall Rate of the Single Category | Classification Accuracy of All Samples | |
---|---|---|---|---|

Recall Rate of the Suitable Area | Recall Rate of the Unsuitable Area | |||

East-west | 93.00% | 75.00% | 96.43% | 92.43% |

North-south | 92.00% | 70.00% | 94.44% | 93.19% |

Northeast | 93.00% | 72.73% | 95.51% | 94.92% |

Northwest | 95.00% | 80.00% | 96.67% | 93.19% |

Direction | Average Positioning Error/m | The Standard Deviation of Positioning Error/m | Correct Rate |
---|---|---|---|

East-west | 65.20 | 56.31 | 91% |

North-south | 63.17 | 60.14 | 92% |

Northeast | 71.75 | 57.26 | 91% |

Northwest | 72.35 | 83.37 | 93% |

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**MDPI and ACS Style**

Wang, S.; Zheng, W.; Li, Z.
Optimizing Matching Area for Underwater Gravity-Aided Inertial Navigation Based on the Convolution Slop Parameter-Support Vector Machine Combined Method. *Remote Sens.* **2021**, *13*, 3940.
https://doi.org/10.3390/rs13193940

**AMA Style**

Wang S, Zheng W, Li Z.
Optimizing Matching Area for Underwater Gravity-Aided Inertial Navigation Based on the Convolution Slop Parameter-Support Vector Machine Combined Method. *Remote Sensing*. 2021; 13(19):3940.
https://doi.org/10.3390/rs13193940

**Chicago/Turabian Style**

Wang, Shuoqi, Wei Zheng, and Zhaowei Li.
2021. "Optimizing Matching Area for Underwater Gravity-Aided Inertial Navigation Based on the Convolution Slop Parameter-Support Vector Machine Combined Method" *Remote Sensing* 13, no. 19: 3940.
https://doi.org/10.3390/rs13193940