# Sensitivity to Time Delays in VDM-Based Navigation

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Proposed Approach

## 2. VDM-Based Navigation

#### 2.1. Frames Definition

#### 2.2. Vehicle Dynamic Model (VDM)

#### 2.3. Navigation System

## 3. Methodology

#### 3.1. Reference and Flight Simulation

#### 3.2. Time-Tagging Errors

#### 3.3. VDM-Based Navigation

## 4. Results and Discussion

#### 4.1. Motor Data Time-Tagging Errors

#### 4.2. Servos Data Time-Tagging Errors

## 5. Conclusions and Perspectives

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

EKF | Extended Kalman filter |

GNSS | Global Navigation Satellite System |

IMU | Inertial Measurment Unit |

INS | Inertial Navigation System |

PVA | Position, Velocity and Attitude |

RPM | Rotations Per Minute |

PPK | Post-Processed Kinematic |

PVT | Position, Velocity, and Time |

UAV | Unmanned Aerial Vehicle |

VDM | Vehicle Dynamic Model |

## References

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**Figure 1.**Local level, body, and wind frames with airspeed $\mathbf{V}$, wind velocity $\mathbf{w}$, and unmanned aerial vehicle (UAV) velocity $\mathbf{v}$ [1].

**Figure 2.**Vehicle dynamic model (VDM)-based navigation filter architecture (${\tilde{\mathbf{X}}}_{k}\equiv {\widehat{\mathbf{X}}}_{k|k-1}$).

Sensor | Error Type | Parameter | Value | Unit |
---|---|---|---|---|

Accelero-meters | Bias | $\sigma $ | 8 | mg |

White Noise | $\sigma $ | 67 | $\mathsf{\mu}$g/$\sqrt{\mathrm{Hz}}$ | |

1st order Gauss–Markov | $\sigma $ | 0.15 | mg | |

T | 200 | s | ||

Gyro-scopes | Bias | $\sigma $ | 720 | ${}^{\circ}$/h |

White Noise | $\sigma $ | 0.005 | ${}^{\circ}/\mathrm{s}/\sqrt{\mathrm{Hz}}$ | |

1st order Gauss–Markov | $\sigma $ | 31 | ${}^{\circ}$/h | |

T | 200 | s |

Fixed Delays [ms] | Random Delays [ms] |
---|---|

0 | 0 |

10 | 10 |

50 | 20 |

100 | 50 |

200 | 100 |

300 | ∅ |

Fixed Delays [ms] | Random Delays [ms] |
---|---|

0 | 0 |

5 | 5 |

10 | 10 |

15 | 15 |

20 | 20 |

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## Share and Cite

**MDPI and ACS Style**

Laupré, G.; Khaghani, M.; Skaloud, J. Sensitivity to Time Delays in VDM-Based Navigation. *Drones* **2019**, *3*, 11.
https://doi.org/10.3390/drones3010011

**AMA Style**

Laupré G, Khaghani M, Skaloud J. Sensitivity to Time Delays in VDM-Based Navigation. *Drones*. 2019; 3(1):11.
https://doi.org/10.3390/drones3010011

**Chicago/Turabian Style**

Laupré, Gabriel, Mehran Khaghani, and Jan Skaloud. 2019. "Sensitivity to Time Delays in VDM-Based Navigation" *Drones* 3, no. 1: 11.
https://doi.org/10.3390/drones3010011