# Slope Estimation Method of Electric Vehicles Based on Improved Sage–Husa Adaptive Kalman Filter

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## Abstract

**:**

## 1. Introduction

## 2. Modeling

#### 2.1. Modeling Based on Electric Vehicle Longitudinal Dynamics

#### 2.2. Prediction Equation and Observation Equation

## 3. Adaptive Kalman Filtering

#### 3.1. Flow Chart of Basic Kalman Filter

#### 3.2. Prediction Equations

#### 3.3. The Update Equation

#### 3.4. Sage–Husa Adaptive Kalman Filter

#### 3.5. Improved Sage–Husa Adaptive Kalman Filter

## 4. Experiment

#### 4.1. Experiment Plan

#### 4.2. Experiment Equipment and Parameters

#### 4.3. Experiment Section

#### 4.4. Error Analysis

## 5. Conclusions

- (1)
- In this paper, the improved adaptive Kalman filtering algorithm draws on the valuable experience of predecessors and changes the traditional adaptive Kalman filtering algorithm. It removes the calculation of ${q}_{k}$ and ${r}_{k}$, which may lead to a sharp increase in the subsequent deviation, and reasonably improves the update of ${Q}_{k}$ and ${R}_{k}$ by using double forgetting factors ${b}_{1}$ and ${b}_{2}$.
- (2)
- The algorithm proposed in this paper has a wide range of application. Under the experimental data of multiple 30 s micro slope model and gentle slope model, RMSE can always be maintained within 0.04%, MAE can always be maintained within 0.03%, and short-term effect is relatively good. The RMSE and MAE can always be kept within 0.19% and 0.15%, respectively, under the demonstration of multiple groups of 100 s gentle slope model test data. Generally speaking, the algorithm is applicable to a wide range of slope and has a good general effect.
- (3)
- After a comprehensive comparison of the results of the two algorithms above, it can be found that, compared with the results of the original adaptive Kalman filter slope estimation method, the RMSE and MAE of the improved algorithm are significantly reduced. The RMSE of the micro slope model is reduced by 0.01%, which is 20.8% lower than the original algorithm. The MAE of the micro-slope model is reduced by 0.006%, which is 17.1% lower than the original algorithm. The RMSE of the gentle slope model R1 is reduced by 0.031%, which is 47% lower than the original algorithm. The MAE of the gentle slope model R1 is reduced by 0.018%, which is 38.3% lower than the original algorithm. The RMSE of the gentle slope model R2 is reduced by 0.041%, which is 50.6% lower than the original algorithm. The MAE of the gentle slope model R2 is reduced by 0.034%, which is 53.1% lower than the original algorithm. The error of the 100 s filtering result of the algorithm proposed in this paper increases to some extent compared with the previous 30 s filtering result. However, the error is still reasonable. In conclusion, the improved adaptive Kalman filter slope estimation method is superior.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**GPS images of the test sections. (

**a**) Micro slope model, (

**b**) Gentle slope model R1, (

**c**) Gentle slope model R2.

**Figure 7.**Contrast diagram of test effect. (

**a**) Micro slope model, (

**b**) part of micro slope model, (

**c**) gentle slope model R1, (

**d**) part of gentle slope model R1, (

**e**) gentle slope model R2, (

**f**) part of gentle slope model R2.

**Figure 8.**Comparison diagram of RMSE and MAE for two algorithms. (

**a**) Comparison diagram of RMSE, (

**b**) comparison diagram of MAE.

**Figure 9.**Contrast diagram of long-term test effect. (

**a**) Micro slope model, (

**b**) part of micro slope model, (

**c**) gentle slope model R1, (

**d**) part of gentle slope model R1, (

**e**) gentle slope model R2, (

**f**) part of gentle slope model R2.

Parameter | VALUE |
---|---|

Vehicle type | BAIC EX360 |

Maximum motor power | 80 kW |

Maximum motor torque | 230 N·m |

Transmission type | fixed gear ratio |

Curb weight | 1480 kg |

Size | 4110 mm × 1750 mm × 1543 mm |

Transmission efficiency | 97% |

Tire type | 205/50 R16 |

Parameter | VALUE |
---|---|

r | 0.3 m |

m | 1715 kg |

δ | 1.1 |

Algorithm | AKF2 | QUKF | |||
---|---|---|---|---|---|

Experiment | Test 1 | Test 2 | Test 3 | Test 1 | Test 2 |

RMSE | 1.3% | 0.8% | 1.9% | 7.8% | 7.8% |

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**MDPI and ACS Style**

Guo, J.; He, C.; Li, J.; Wei, H.
Slope Estimation Method of Electric Vehicles Based on Improved Sage–Husa Adaptive Kalman Filter. *Energies* **2022**, *15*, 4126.
https://doi.org/10.3390/en15114126

**AMA Style**

Guo J, He C, Li J, Wei H.
Slope Estimation Method of Electric Vehicles Based on Improved Sage–Husa Adaptive Kalman Filter. *Energies*. 2022; 15(11):4126.
https://doi.org/10.3390/en15114126

**Chicago/Turabian Style**

Guo, Jiawei, Chao He, Jiaqiang Li, and Heng Wei.
2022. "Slope Estimation Method of Electric Vehicles Based on Improved Sage–Husa Adaptive Kalman Filter" *Energies* 15, no. 11: 4126.
https://doi.org/10.3390/en15114126