# Compound Positioning Method for Connected Electric Vehicles Based on Multi-Source Data Fusion

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## Abstract

**:**

## 1. Introduction

- In the research of roadside-based traffic perception, the current studies mainly focus on the dynamic detection of vehicles with single sensors on the roadside;
- In the compound positioning research of vehicles, the current studies mainly focus on the multiple sensors of a single vehicle, and there is a gap in the cooperative compound positioning of multiple vehicles based on vehicle-infrastructure information fusion.

- A comprehensive system concept is provided based on the positioning accuracy requirements of CEVs.
- A reliable compound positioning approach is developed to achieve higher positioning accuracy among the data obtained from multiple roadside sensors and V2X units.
- Theoretical analysis and extensive experiment results, including the Dempster-Shafer (D-S) evidence theory-based multi-source data fusion method and hybrid neural networks, are provided to validate the proposed concept.

## 2. Multi-Source Data Fusion Based on D-S Evidence Theory

#### 2.1. The Scenario of Multi-Source Data Fusion

#### 2.2. Data Fusion Rules of D-S Evidence Theory

- For ${m}_{1\oplus 2}$ fusion, the normalized coefficient 1-K value is obtained using the D-S evidence fusion rule, which is shown in Equation (6).

- The values of the mass function for each hypothesis are obtained as follows:

- The confidence intervals are obtained as follows:

- Therefore, the credibility of ${m}_{1\oplus 2}$ fusion is ${m}_{1\oplus 2}=\left[\begin{array}{l}m\left({A}_{1}\right)\hfill \\ m\left({A}_{2}\right)\hfill \\ m(\Theta )\hfill \end{array}\right]$
- According to D-S evidence theory, ${m}_{1\oplus 2}$ and ${m}_{3}$ are fused, which represent the combined credibility of camera, lidar, and radar is obtained: ${m}_{1\oplus 2\oplus 3}$.
- In the same way, the credibility of four sensors fusion is finally obtained, which is ${m}_{1\oplus 2\oplus 3\oplus 4}$.

## 3. The Perception Model of Compound Positioning Information

_{1}, P

_{2},…, P

_{n}} denotes the set of track points of the CEV within n time steps, P

_{i}= (lat

_{i}, lon

_{i}, t

_{i}) denotes the i-th positioning point of CEV, lat

_{i}denotes the latitude, lon

_{i}denotes the longitude, and t

_{i}denotes the time. These inputs are passed through the data preprocessing layer, CNN layer, LSTM layer, self-attention layer, dropout layer, and dense layers. The final output of the model is vehicular compound positioning information (lat

_{i}, lon

_{i}, t

_{i}) in real time.

#### 3.1. Date Preprocessing Layer

#### 3.2. CNN Layer

- Input layer

- 2.
- Convolution layer

_{i,j}represents the input two-dimensional data at i-th row and j-th column; w

_{m,n}represents weight value at m-th row and n-th column of the filter matrix; w

_{b}represents the filter bias value; f is the activation function; a

_{i,j}represents the i-th row and j-th column of the feature map.

- 3.
- Pooling layer

- 4.
- Fully connected layer and output layer

#### 3.3. LSTM Layer

_{t}, and the output value h

_{t}

_{−1}and c

_{t}

_{−1}in the previous hidden layer. The output of the LSTM network is the real-time compound positioning data of the CEV. The status of the input gate, forget gate, and output gate in the LSTM network are i

_{t}, f

_{t}, and o

_{t}, which are from 0 to 1. The calculation process can be summarized as follows:

_{t}is the compound positioning data; ${W}_{hf}$,${W}_{hi}$,${W}_{ho}$,${W}_{hc}$ represent the weight matrices of hidden layer ${h}_{t}$ respectively; ${b}_{f}$, ${b}_{i}$, ${b}_{o}$, ${b}_{c}$ represent the bias vector, respectively; $\sigma $ and tanh represent the sigmoid function and hyperbolic tangent function, which are defined in Equations (16) and (17).

#### 3.4. Self-Attention Layer

_{t}and h

_{t’}represent the hidden state of the LSTM layer in current time step t and the previous time step t′, respectively; $\sigma $ represents the sigmoid function; W

_{g}and W

_{g′}represent the weight matrices corresponding to h

_{t}and h

_{t’}; W

_{a}represents the weight matrix corresponding to its nonlinear combination; b

_{g}and b

_{a}represent deviation vectors.

_{t}at the time step t is the weighted sum of all previously hidden states h

_{t’}, which is weighted by a

_{t,t′}. Additionally, a

_{t,t′}represents the similarity or dependence between h

_{t}and h

_{t′}, where the similarity is the relationship between the current position at time t and the previous position at t’ in the input trajectory.

#### 3.5. Dropout Layer

## 4. Field Experiment and Analysis

#### 4.1. Test Field and Datasets

_{1}, C

_{2}, and C

_{3}, respectively. In addition, CEVs were within the detection range of roadside sensors during the whole driving process. In Figure 7, the origin and destination of the driving route are marked. The CEV first passes through the straight road section at a uniform speed from the left-most lane, then makes a U-turn at the intersection, and finally runs at a uniform speed.

#### 4.2. Parameter Setting and Evaluation Index

_{i}is the output of the network; label

_{i}is the label of supervised training.

#### 4.3. Uncertainty Analysis of Multi-Source Data Fusion

#### 4.4. Analysis of Compound Positioning Model

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Uncertainty distribution of detection results. (

**a**) Radar sensor; (

**b**) camera sensor; (

**c**) lidar sensor; (

**d**) V2X unit.

**Figure 11.**Distribution of CEV compound positioning under different methods and different speeds. (

**a**) The position distribution of LSTM model at 15 km/h; (

**b**) the position distribution of LSTM model at 30 km/h; (

**c**) the position distribution of LSTM model at 45 km/h; (

**d**) the position distribution of MV3D at 15 km/h; (

**e**) the position distribution of MV3D at 30 km/h; (

**f**) the position distribution of MV3D at 45 km/h; (

**g**) the position distribution of RoarNet model at 15 km/h; (

**h**) the position distribution of RoarNet model at 30 km/h; (

**i**) the position distribution of RoarNet model at 45 km/h; (

**j**) the position distribution of hybrid LSTM model at 15 km/h; (

**k**) the position distribution of hybrid LSTM model at 30 km/h; (

**l**) the position distribution of hybrid LSTM model at 45 km/h.

**Figure 15.**Comparison results of four models. (

**a**) RMSE values of four models in X and Y direction; (

**b**) MAE values of four models in X and Y direction.

Sensor State | Detected (A) | Undetected (B) | Uncertain (C) | |
---|---|---|---|---|

Sensor Type | ||||

Camera sensor (1) | m_{1} (A) | m_{1} (B) | m_{1} (C) | |

Lidar sensor (2) | m_{2} (A) | m_{2} (B) | m_{2} (C) | |

Radar sensor (3) | m_{3} (A) | m_{3} (B) | m_{3} (C) | |

V2X unit (4) | m_{4} (A) | m_{4} (B) | m_{4} (C) |

**Table 2.**The combination of the detection results for four sensors. “Yes” represents that a vehicle is detected at the position. “No” represents that there is no vehicle at the position.

Combination Forms | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Sensors | |||||||||||||||||

Camera | Yes | Yes | Yes | Yes | No | Yes | Yes | No | Yes | No | No | No | No | No | No | No | |

Lidar | Yes | Yes | Yes | No | Yes | Yes | No | No | No | Yes | Yes | Yes | Yes | No | No | No | |

Radar | Yes | Yes | No | Yes | Yes | No | No | Yes | Yes | No | Yes | No | No | Yes | No | No | |

V2X unit | Yes | No | Yes | Yes | Yes | No | Yes | Yes | No | Yes | No | Yes | No | No | Yes | No |

Combination Form | Sensor Number | m(A) | m(B) | m(Θ) | Fusion Result |
---|---|---|---|---|---|

1 | 4 | 0.949350 | 0.050634 | 0.000016 | A |

2 | 3 | 0.777015 | 0.222413 | 0.000572 | A |

3 | 3 | 0.798684 | 0.200929 | 0.00387 | A |

4 | 2 | 0.419643 | 0.571429 | 0.008929 | B |

5 | 3 | 0.981207 | 0.018715 | 0.000078 | A |

6 | 2 | 0.906375 | 0.090504 | 0.003121 | A |

7 | 2 | 0.901087 | 0.098755 | 0.00159 | A |

8 | 1 | 0.65 | 0.28 | 0.07 | A |

9 | 3 | 0.901087 | 0.098755 | 0.000159 | A |

10 | 2 | 0.627191 | 0.36803 | 0.00478 | A |

11 | 2 | 0.657519 | 0.339188 | 0.003293 | A |

12 | 1 | 0.22 | 0.72 | 0.06 | B |

13 | 2 | 0.962065 | 0.037144 | 0.00079 | A |

14 | 1 | 0.82 | 0.15 | 0.03 | A |

15 | 1 | 0.84 | 0.14 | 0.02 | A |

16 | 0 | —— | —— | —— | Θ |

ID | V2X | Longitude | Latitude | Steering Angle (°) | Speed (m/s) | Acceleration (m/s ^{2}) | Horizontal Distance (m) | Heading Angle (°) |
---|---|---|---|---|---|---|---|---|

76 | Yes | 116.2138743 | 39.9306605 | 2.3 | 0.16 | −0.16 | 7.82 | 88.22 |

77 | No | 116.2139375 | 39.9306708 | —— | 2.11 | —— | 12.14 | 82.92 |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

95 | No | 116.2127606 | 39.9306348 | —— | 2.14 | 0.20 | 17.17 | 154.52 |

96 | No | 116.2120122 | 39.9306519 | —— | 5.58 | —— | 15.17 | 82.59 |

Parameters | Value | |
---|---|---|

CNN | Input layer size | 256 × 256 |

Convolution layer size | 16 × 16 | |

Pooling layer size | 8 × 8 | |

LSTM | Number of hidden layers | 2 |

Number of hidden layer nodes | 200 | |

Epoch | 20 | |

Batch Size | 100 | |

Loss Function | MSE | |

Learning Rate | 0.001 | |

Optimizer | Adam |

Sensor Category | Camera | Lidar | Radar | V2X Unit | |
---|---|---|---|---|---|

Error | |||||

Maximum (m) | 18.4623 | 0.8268 | 2.0168 | 20.9980 | |

Minimum (m) | 0.1917 | 0.0082 | 0.0607 | 0.0488 | |

Average (m) | 3.5881 | 0.2111 | 0.7138 | 8.1386 | |

MAPE | 19.26% | 0.70% | 23.72% | 26.87% |

Model | Anchor 2 | Anchor 3 | Anchor 4 |
---|---|---|---|

LSTM | 0.1179 | 0.0821 | 0.0630 |

MV3D | 0.1475 | 0.1322 | 0.1071 |

RoarNet | 0.1121 | 0.0690 | 0.0610 |

Hybrid LSTM | 0.0910 | 0.0609 | 0.0399 |

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## Share and Cite

**MDPI and ACS Style**

Wang, L.; Li, Z.; Fan, Q.
Compound Positioning Method for Connected Electric Vehicles Based on Multi-Source Data Fusion. *Sustainability* **2022**, *14*, 8323.
https://doi.org/10.3390/su14148323

**AMA Style**

Wang L, Li Z, Fan Q.
Compound Positioning Method for Connected Electric Vehicles Based on Multi-Source Data Fusion. *Sustainability*. 2022; 14(14):8323.
https://doi.org/10.3390/su14148323

**Chicago/Turabian Style**

Wang, Lin, Zhenhua Li, and Qinglan Fan.
2022. "Compound Positioning Method for Connected Electric Vehicles Based on Multi-Source Data Fusion" *Sustainability* 14, no. 14: 8323.
https://doi.org/10.3390/su14148323