# An Accurate and Generic Testing Approach to Vehicle Stability Parameters Based on GPS and INS

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Objective Fuzzy Logic System and Subtractive Clustering Method

#### 3.1. Objective Fuzzy Logic System

#### 3.2. Fuzzy Logic Subtractive Cluster Approach

_{a}defines the cluster’s neighborhood range in data space, and it is a positive constant. The additional values are: accepted ratio $\overline{\in}$, squash factor η, and rejected ratio $\underset{\_}{\in}$. A parameter investigation is implemented in the cluster values to discover the optimal n-rule modeling.

- $R{u}_{1}$: If x is A
_{1}then ${w}_{1}(\mu )={p}_{10}+{p}_{11}\mu $ - $R{u}_{2}$: If x is A
_{2}then ${w}_{2}(\mu )={p}_{20}+{p}_{21}\mu $

## 4. Models of Vehicle Testing

#### 4.1. Dynamical Model of Vehicle

- (1)
- Automobile vertical and pitch motions are ignored;
- (2)
- The dynamic characteristics of the four tires are same;
- (3)
- The influence of air resistance is ignored;
- (4)
- The effect of sprung mass is ignored [37].

#### 4.2. Model of Two-Stage Kalman Filter

#### 4.3. Vehicle Stability Parameters Calculation

#### 4.3.1. Vehicle Heading Angle Calculation

#### 4.3.2. Vehicle Vertical and Horizontal Velocity Calculation

#### 4.3.3. Vehicle Sideslip Angle Calculation

## 5. Simulation and Application

Symbols | Meaning | Values | Symbols | Meaning | Values |
---|---|---|---|---|---|

$m$ | Vehicle mass | 1704.7 kg | ${k}_{\varphi F}$ | Front suspension stiffness | 47,298 N·m/Rad |

${m}_{s}$ | Suspended mass | 152.6 kg | ${k}_{\varphi R}$ | Rear suspension stiffness | 37,311 N·m/Rad |

${D}_{f}$ | Front axle to centroid distance | 1.035 m | ${c}_{\varphi F}$ | Front suspension damp | 2823 (N·m)/(rad/s) |

${l}_{r}$ | Distance from centroid to rear axle | 1.655 m | ${c}_{\varphi R}$ | Rear suspension roll damp | 2653 (N·m)/(rad/s) |

${t}_{f}$ | Distance between front wheels | 1.535 m | ${I}_{wi}$ | Wheel inertia | 0.99 kg·m^{2} |

${t}_{r}$ | Distance between rear wheels | 1.535 m | ${R}_{w}$ | Wheel radius | 0.313 m |

${h}_{c}$ | Centroid height | 0.542 m | ${k}_{f}$ | Front wheel cornering stiffness | 55,095 N/rad |

${I}_{x}$ | Roll inertia | 744.0 kg·m^{2} | ${k}_{r}$ | Rear wheel cornering stiffness | 55,095 N/rad |

${I}_{z}$ | Yaw inertia | 3048.1 kg·m^{2} | $A$ | Front windward area | 1.8 m^{2} |

#### 5.1. Simulation

#### 5.2. Experimental Apparatus

Band | 1.575 GHz |
---|---|

Type of Receiver | Carrier phase smoothing function, L1, C/A code. |

Maximum data update rate | Heading and position are 20 Hz |

Horizontal positioning accuracy | single machine: <2.5 m (95%, No SA); E-Dif: <1.0 m (95%, 30 min). DGPS: <0.5 m (95%); L-Dif: <0.2 m (95%) |

Heading accuracy | <0.25° RMS, baseline is 0.5 m; <0.15° RMS, 1.0 m baseline; <0.10° RMS, 2.0 m baseline |

Pitch/roll | <1° RMS |

Angular rate | 90°/s (max) |

Maximum speed | 515 m/s |

Maximum elevation | 18.288 m |

Speed and accuracy | 0.05 m/s |

#### 5.3. Measurement Experiment

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Miao, Z.; Zhang, H.; Zhang, J. An Accurate and Generic Testing Approach to Vehicle Stability Parameters Based on GPS and INS. *Sensors* **2015**, *15*, 30469-30486.
https://doi.org/10.3390/s151229812

**AMA Style**

Miao Z, Zhang H, Zhang J. An Accurate and Generic Testing Approach to Vehicle Stability Parameters Based on GPS and INS. *Sensors*. 2015; 15(12):30469-30486.
https://doi.org/10.3390/s151229812

**Chicago/Turabian Style**

Miao, Zhibin, Hongtian Zhang, and Jinzhu Zhang. 2015. "An Accurate and Generic Testing Approach to Vehicle Stability Parameters Based on GPS and INS" *Sensors* 15, no. 12: 30469-30486.
https://doi.org/10.3390/s151229812