# Joint Estimation of Mass and Center of Gravity Position for Distributed Drive Electric Vehicles Using Dual Robust Embedded Cubature Kalman Filter

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## Abstract

**:**

## 1. Introduction

## 2. Vehicle Model and Problem Formulation

## 3. Methodology

#### 3.1. The RECKF

- (1)
- Initialization:

_{i}are given by.

- (2)
- Time prediction:

- (3)
- Measurement prediction:

#### 3.2. The Flowchart of Joint Estimation

## 4. Results and Discussion

#### 4.1. Acceleration Test

#### 4.2. Deceleration Test

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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Symbol | Description |
---|---|

$m$ | vehicle mass |

$a$ | distance from the center of gravity to the front axle |

$b$ | distance from the center of gravity to the rear axle |

${v}_{x}$ | longitudinal velocity |

${T}_{r}$ | driving moments of the rear wheels |

${T}_{f}$ | driving moments of the front wheels |

${F}_{xf}$ | longitudinal forces at the front wheels |

${F}_{xr}$ | longitudinal forces at the rear wheels |

${F}_{zf}$ | vertical forces at the front wheels |

${F}_{sr}$ | vertical forces at the rear wheels |

$h$ | height of the CG |

$J$ | wheel inertia |

${\omega}_{r}$ | rear wheel speeds |

${\omega}_{f}$ | front wheel speeds |

$R$ | tire radius |

${C}_{D}$ | air drag influence coefficient |

$\rho $ | air density |

$A$ | windward area |

$g$ | weight acceleration |

${f}_{roll}$ | rolling resistance coefficient |

${a}_{x}$ | longitudinal acceleration |

Symbol | Variables |
---|---|

$z$ | measurement vector |

$f$ | state transition function |

$u$ | input vector |

$w$ | process noise |

$h$ | output function |

$v$ | measurement noise |

Symbol | Values |
---|---|

$m$ | $1270\mathrm{kg}$ |

$a$ | $1.015\mathrm{m}$ |

$A$ | $2.2\mathrm{m}$ |

${I}_{z}$ | $1536.7\mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{2}$ |

$b$ | $1.895\mathrm{m}$ |

${C}_{xf}$ | $28$ |

Symbol | CKF | RECKF |
---|---|---|

m | 111.20 | 76.76 |

a | 0.3691 | 0.3586 |

Symbol | CKF | RECKF |
---|---|---|

m | 242.33 | 224.44 |

a | 0.5330 | 0.4663 |

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**MDPI and ACS Style**

Zhang, Z.; Yin, G.; Wu, Z.
Joint Estimation of Mass and Center of Gravity Position for Distributed Drive Electric Vehicles Using Dual Robust Embedded Cubature Kalman Filter. *Sensors* **2022**, *22*, 10018.
https://doi.org/10.3390/s222410018

**AMA Style**

Zhang Z, Yin G, Wu Z.
Joint Estimation of Mass and Center of Gravity Position for Distributed Drive Electric Vehicles Using Dual Robust Embedded Cubature Kalman Filter. *Sensors*. 2022; 22(24):10018.
https://doi.org/10.3390/s222410018

**Chicago/Turabian Style**

Zhang, Zhiguo, Guodong Yin, and Zhixin Wu.
2022. "Joint Estimation of Mass and Center of Gravity Position for Distributed Drive Electric Vehicles Using Dual Robust Embedded Cubature Kalman Filter" *Sensors* 22, no. 24: 10018.
https://doi.org/10.3390/s222410018