# A Mobile Positioning Method Based on Deep Learning Techniques

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Mobile Positioning System and Method

#### 3.1. Mobile Positioning System

#### 3.1.1. Mobile Stations

#### 3.1.2. Mobile Positioning Server

#### 3.1.3. Database Server

#### 3.1.4. Model Server

#### 3.2. Mobile Positioning Method

#### 3.2.1. Collection and Normalization

_{1}different base stations, and n

_{2}different Wi-Fi APs detected in the experiments. If the RSSIs of base stations or Wi-Fi APs cannot be detected, the values of these RSSIs can be encoded as null. For instance, the mobile station cannot detect the RSSI of Wi-Fi AP2 at time ${t}_{i}$ in Figure 3, so the value of ${r}_{w,2,i}$ is encoded as null.

#### 3.2.2. Mobile Positioning Method Based on Recurrent Neural Network

#### Recurrent Neural Networks with One Timestamp

_{1}base stations (i.e., $\left\{{c}_{1,i},{c}_{2,i},\dots ,{c}_{{n}_{1},i}\right\}$) and n

_{2}Wi-Fi APs (i.e., $\left\{{w}_{1,i},{w}_{2,i},\dots ,{w}_{{n}_{2},i}\right\}$), and the output layer includes the estimated normalized longitude and latitude (i.e., ${\tilde{x}}_{i}$ and ${\tilde{y}}_{i}$). The recurrent hidden layer includes a neuron, and the initial value of the neuron in the recurrent hidden layer is defined as h

_{0}. The value of the neuron in the recurrent hidden layer can be updated as h

_{1}after calculating the RSSIs in the first timestamp. The weights of c

_{j}

_{,i}, w

_{k}

_{,i}, and h

_{0}are ${\alpha}_{j}$, ${\beta}_{k}$, and v, respectively; the weights of h

_{1}for the outputs ${\tilde{x}}_{i}$ and ${\tilde{y}}_{i}$ are ${\gamma}_{1}$ and ${\gamma}_{2}$, respectively. The biases of neurons in the hidden layer and the output layer are defined as b

_{1,1}, b

_{2,1}, and b

_{3,1}. The sigmoid function is elected as the activation function of each neuron, so the values of h

_{0}, h

_{1}, ${\tilde{x}}_{i}$, and ${\tilde{y}}_{i}$ can be calculated by Equations (9)–(12), respectively. Furthermore, the loss function is defined as Equation (13) in accordance with squared errors.

#### Two Timestamps for Recurrent Neural Network

_{1}+ n

_{2}) normalized RSSIs (i.e., $\left\{{c}_{1,i},{c}_{2,i},\dots ,{c}_{{n}_{1},i}\right\}$ and $\left\{{w}_{1,i},{w}_{2,i},\dots ,{w}_{{n}_{2},i}\right\}$) in the first timestamp and (n

_{1}+ n

_{2}) normalized RSSIs (i.e., $\left\{{c}_{1,i+1},{c}_{2,i+1},\dots ,{c}_{{n}_{1},i+1}\right\}$ and $\left\{{w}_{1,i+1},{w}_{2,i+1},\dots ,{w}_{{n}_{2},i+1}\right\}$) in the second timestamp; the output layer includes the estimated normalized longitude and latitude (i.e., ${\tilde{x}}_{i+1}$ and ${\tilde{y}}_{i+1}$) in the second timestamp. The recurrent hidden layer includes a neuron, and the initial value of the neuron in the recurrent hidden layer is defined as h

_{0}(shown in Equation (9)). The value of the neuron in the recurrent hidden layer can be updated as h

_{1}in the first timestamp and as h

_{2}in the second timestamp. The weights of base station j, Wi-Fi AP k in each timestamp are ${\alpha}_{j}$ and ${\beta}_{k}$; the weights of h

_{2}for the outputs ${\tilde{x}}_{i+1}$ and ${\tilde{y}}_{i+1}$ are ${\gamma}_{1}$ and ${\gamma}_{2}$, respectively. Furthermore, the weight of the neurons in the recurrent hidden layer in the least timestamp is defined as v. In the case, the biases of neurons in the hidden layer and the output layer are defined as b

_{1,1}, b

_{2,1}, and b

_{3,1}. The sigmoid function is elected as the activation function of each neuron, so the values of h

_{1}, h

_{2}, ${\tilde{x}}_{i}$, and ${\tilde{y}}_{i}$ can be calculated by Equations (22)–(25), respectively. Furthermore, the loss function is defined as Equation (26) in accordance with squared errors.

#### 3.2.3. De-Normalization and Estimation

## 4. Practical Experimental Results and Discussion

#### 4.1. Practical Experimental Environments

_{1}= 59) in long term evolution (LTE) networks, and 582 different Wi-Fi APs (i.e., n

_{2}= 582) detected in the experiments. The availability of position method based on cellular networks was 100%, but the availability of position method based on Wi-Fi networks was about 96%. Some road segments in experimental environments were not covered by Wi-Fi networks. Therefore, the proposed method based Wi-Fi network signals for outdoor, but in range of a nearby Wi-Fi networks. This study selected 2263 records including GPS coordinates and RSSIs as training data, and other 2262 records were selected as testing data. The mean and median of distances between each of the two measurement locations along the test route were 2.8 and 2.6 m, respectively.

#### 4.2. Practical Experimental Results

#### 4.3. Discussions

#### 4.3.1. The Structure of Neural Networks

_{1}= 59) and Wi-Fi networks (i.e., n

_{2}= 582) were considered as the neurons in the input layer of neural networks. One hidden layer was constructed in neural networks, and the output layer of neural networks included two neurons (i.e., longitude and latitude). When the hidden layer included 10 neurons, the structure of neural network was expressed as 641-10-2. This study considered four structures of hidden layers in neural networks, which included 10, 20, 30, and 40 neurons. Table 2 shows that the average location errors were lower in the case of 641-30-2. Therefore, this study adopted the structure of 641-30-2 for the proposed mobile positioning method.

#### 4.3.2. The Loss Function of Deep Learning Models

#### 4.3.3. Computation Time

#### 4.3.4. Power Consumption

## 5. Conclusions and Future Work

#### 5.1. Conclusions

#### 5.2. Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 7.**The estimated locations by the proposed mobile positioning method with different mobile networks. G: GPS (a red point); C: cellular networks (a green point); W: Wi-Fi networks (a blue point); CW: cellular and Wi-Fi networks (a yellow point).

**Figure 8.**The cumulative distribution function (CDF) of location errors by the proposed mobile positioning method with one timestamp.

**Figure 9.**The cumulative distribution function of location errors by the proposed mobile positioning method with two timestamps.

**Figure 10.**The cumulative distribution function of location errors by the proposed mobile positioning method with three timestamps.

**Table 1.**The average errors of estimated locations by the proposed mobile positioning method (unit: meters).

Number of Timestamps | Only Cellular Networks | Only Wi-Fi Networks | Cellular and Wi-Fi Networks |
---|---|---|---|

1 timestamp | 39.88 | 18.88 | 16.21 |

2 timestamps | 36.51 | 18.69 | 9.19 |

3 timestamps | 34.57 | 17.83 | 9.26 |

**Table 2.**The average errors of estimated locations by different structures of neural networks (unit: meters).

Number of Timestamps | 641-10-2 | 641-20-2 | 641-30-2 | 641-40-2 |
---|---|---|---|---|

1 timestamp | 16.23 | 16.30 | 16.21 | 16.27 |

2 timestamps | 12.07 | 10.87 | 9.19 | 12.09 |

3 timestamps | 11.60 | 10.56 | 9.26 | 11.55 |

**Table 3.**The average errors of estimated locations by the proposed mobile positioning method (unit: meters).

Number of Timestamps | Only Cellular Networks | Only Wi-Fi Networks | Cellular and Wi-Fi Networks |
---|---|---|---|

1 | 34.61 | 16.46 | 14.39 |

2 | 259.44 | 255.87 | 252.53 |

3 | 254.85 | 256.61 | 253.85 |

**Table 4.**The computation time of estimated locations by the proposed mobile positioning method in training stage (unit: seconds).

Number of Timestamps | Only Cellular Networks | Only Wi-Fi Networks | Cellular and Wi-Fi Networks |
---|---|---|---|

1 | 3022 | 6928 | 7302 |

2 | 5383 | 13,513 | 14,533 |

3 | 6156 | 17,938 | 20,485 |

**Table 5.**The computation time of estimated locations by the proposed mobile positioning method in performing stage (unit: seconds).

Number of Timestamps | Only Cellular Networks | Only Wi-Fi Networks | Cellular and Wi-Fi Networks |
---|---|---|---|

1 | 0.15 | 0.35 | 0.37 |

2 | 0.27 | 0.68 | 0.73 |

3 | 0.31 | 0.90 | 1.02 |

Enable Modules | Sampling Period | Lifetime (Seconds) |
---|---|---|

Cellular | Continuous (1/s) | 254,500 |

Cellular and Wi-Fi | Continuous (1/s) | 175,450 |

Cellular and GPS | Continuous (1/s) | 81,000 |

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**MDPI and ACS Style**

Wu, L.; Chen, C.-H.; Zhang, Q. A Mobile Positioning Method Based on Deep Learning Techniques. *Electronics* **2019**, *8*, 59.
https://doi.org/10.3390/electronics8010059

**AMA Style**

Wu L, Chen C-H, Zhang Q. A Mobile Positioning Method Based on Deep Learning Techniques. *Electronics*. 2019; 8(1):59.
https://doi.org/10.3390/electronics8010059

**Chicago/Turabian Style**

Wu, Ling, Chi-Hua Chen, and Qishan Zhang. 2019. "A Mobile Positioning Method Based on Deep Learning Techniques" *Electronics* 8, no. 1: 59.
https://doi.org/10.3390/electronics8010059