# Wavelet Feature Outdoor Fingerprint Localization Based on ResNet and Deep Convolution GAN

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## Abstract

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## 1. Introduction

- (1)
- A fingerprint database is constructed by converting the collected signal data into wavelet feature maps, which visualizes the collected signal features.
- (2)
- To enhance the richness of the fingerprint database, a DCGAN-based model is used to generate symmetric wavelet feature maps of the sampling areas, which can help to reduce the labor required to collect data.
- (3)
- Considering the large amount of data in the fingerprint database, Resnet, with satisfactory learning ability, is proposed for positioning. Furthermore, several data enhancement methods are proposed to improve the robustness of the positioning system.
- (4)
- To verify the superiority of the positioning system, extensive experiments are conducted in a real outdoor environment. Our experimental results show that the proposed positioning system can achieve better performance than other schemes.

## 2. Related Works

## 3. Proposed Positioning System Architecture

#### 3.1. LTE Signal Wavelet Transform

^{2}(R) and its Fourier transform $\widehat{\phi}\left(\omega \right)$ meet the following condition:

^{2}(R) is the Square integrable complex function space. The corresponding wavelet family contains a set of sub-wavelets, which are generated by the expansion and translation of the wavelet function φ(t), as shown below:

^{2}norm Hilbert space, as shown below:

_{m}, let t = mδt and b = nδt, where m,n = 0, 1, 2,…, N–1, N is the sampling point number and δt is the sampling interval. The CWT of x

_{m}is defined as follows:

#### 3.2. Fingerprint Database Construction

_{data}(x) is the real data, z is a uniformly distributed signal, P

_{z}(z) is the fake data, and G(z) and D(x) are the output of generator and discriminator, respectively.

- (1)
- Cancel the pooling layer and use deconvolution for upsampling in G, while using strided convolutions in D to replace the pooling layer;
- (2)
- The data in G and D are batch normalized to solve the problem of poor initialization;
- (3)
- Remove the fully connected layer from G, thus making it a fully convolutional network;
- (4)
- The activation function in the G network uses the ReLU function, while the last layer uses the Tanh function;
- (5)
- The activation function of all layers in the D network uses the LeakyReLU function.

#### 3.3. Resnet Training and Matching

#### Resnet Model Introduction

#### 3.4. Resnet Training and Matching

## 4. Experiments and Results

#### 4.1. Influence of Different Learning Rate on Positioning Performance

#### 4.2. Influence of Different Batch Size on Positioning Accuracy

#### 4.3. Influence of Different Number of Fingerprints on Positioning Accuracy

#### 4.4. Performance Comparation

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Structure diagram of the DCGAN generator. φ denotes the symmetric feature maps generated by the generator; ϕ are feature maps from the training set.

**Figure 6.**(

**a**) Overall diagram of the experimental area and (

**b**,

**c**) experimental scenes of the outdoor area.

**Figure 10.**Positioning comparation with different algorithms: (

**a**) Positioning accuracy with original fingerprint database; and (

**b**) Positioning accuracy with expanded fingerprint database.

MLP | Configuration | Settings and Values |

Number of Hidden layers | 3 | |

Number of Neurons in Each Layer | 200 | |

Activation Function | Leaky ReLU | |

Loss | Cross-entropy | |

Learning Rate | 0.001 |

CNN | Convolution Layer $\to $ Batch Normalization Layer $\to $ Max Pooling Layer $\to $ Convolution Layer $\to $ Batch Normalization Layer $\to $ Max Pooling Layer $\to $ Fully Connected Layer $\to $ Output Layer | |

Configuration | Settings and Values | |

Activation Function | Leaky ReLU | |

Loss | Cross-entropy | |

Learning Rate | 0.001 |

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**MDPI and ACS Style**

Lei, Y.; Li, D.; Zhang, H.; Li, X.
Wavelet Feature Outdoor Fingerprint Localization Based on ResNet and Deep Convolution GAN. *Symmetry* **2020**, *12*, 1565.
https://doi.org/10.3390/sym12091565

**AMA Style**

Lei Y, Li D, Zhang H, Li X.
Wavelet Feature Outdoor Fingerprint Localization Based on ResNet and Deep Convolution GAN. *Symmetry*. 2020; 12(9):1565.
https://doi.org/10.3390/sym12091565

**Chicago/Turabian Style**

Lei, Yingke, Da Li, Haichuan Zhang, and Xin Li.
2020. "Wavelet Feature Outdoor Fingerprint Localization Based on ResNet and Deep Convolution GAN" *Symmetry* 12, no. 9: 1565.
https://doi.org/10.3390/sym12091565