# Gimbal Influence on the Stability of Exterior Orientation Parameters of UAV Acquired Images

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Technology

## 3. Methodology

#### 3.1. Photogrammetric Mathematical Models

_{0}in reference to the coordinate system. Point P (vector X), located on object, can be derived based on vector X

_{0}and vector X″, according to Equation (3). Vector X″ is defined with the point on the object and the center of projection.

_{0}′, y

_{0}′ are the Principal Point of Autocollimation (PPA) image coordinates, c′ is the camera constant, r

_{ij}is the spatial rotational matrix parameter, X, Y, Z are point P coordinates in reference to the coordinate system, X

_{0}, Y

_{0}, Z

_{0}are the projection center coordinates in reference to the coordinate system, and ∆x′, ∆y′ are the distortion parameters.

_{0}′, y

_{0}′, c′, ∆x′, ∆y′) and the exterior orientation (X

_{0}, Y

_{0}, Z

_{0}, $\phi ,\omega ,\kappa $) parameters of a single image. Bundle Block Adjustment (BBA) is applied when adjusting interior and exterior orientation parameters for an arbitrary number of images, which are connected in a single 3D model. Within BBA, observations (image coordinates), classic survey measurements (GCP), and the referent coordinates of the object are adjusted simultaneously. Equation (5) represents the indirect measurements function model.

_{0}′, y

_{0}′, c′, ∆x′, ∆y′), exterior orientation (X

_{0j}, Y

_{0j}, Z

_{0j}, ${\phi}_{j},{\omega}_{j},{\kappa}_{j}$), and object points (X

_{i}, Y

_{i}, Z

_{i}) in reference to the coordinate system are determined in a single adjustment. The statements above indicate that BBA is mathematically the most acceptable method of image orientation in the domain of photogrammetry.

#### 3.2. IMU Data Integration

## 4. Experimental Approach

- Flight simulation,
- Indoor flight,
- Outdoor flight.

#### 4.1. Flight Simulation

#### 4.2. Indoor Flight

#### 4.3. Outdoor Flight

## 5. Results

#### 5.1. Flight Simulation

#### 5.2. Indoor Flight

#### 5.3. Outdoor Flight

## 6. Discussion

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**A Xiaomi Yi action camera; (

**a**) in improving phase; (

**b**) on a 3-axes gimbal on an Unmanned Aerial Vehicle (UAV).

**Figure 5.**(

**a**) Used gimbal; (

**b**) gimbal controller (Storm32) board and primary Inertial Measurement Unit (IMU) (MPU6050).

**Figure 7.**Exterior orientation parameters acquired photogrammetrically and by the Inertial Measurement Unit (IMU) for pitch parameter.

**Figure 8.**Exterior orientation parameters acquired photogrammetrically and by the Inertial Measurement Unit (IMU) for roll parameter.

**Figure 11.**Display of statistical data of indoor flight for: (

**a**) pitch parameter and (

**b**) roll parameter.

**Figure 12.**Display of statistical data of outdoor flight for: (

**a**) pitch parameter and (

**b**) roll parameter.

Processor | Ambarella A7LS |
---|---|

Focal length | 4.35 mm (distortion < 1%) |

Aperture | F2.8 |

FOV ^{1} (diagonal) | 86° |

Sensor | Sony Exmor R BSI CMOS 16 MP |

Size | 6 × 2.1 × 4.2 cm/2.36 × 0.83 × 1.65 inches |

Battery | 1010 mAh |

Weight | 72 g |

Video | Up to 1080 p 60 fps |

Memory | Up to 64 GB SD card |

Connectivity | Wi-Fi, Bluetooth 4.0 v, USB, micro HDMI |

Raw data | Yes |

^{1}FOV—Field of View.

**Table 2.**Statistics of the Inertial Measurement Unit (IMU) and photogrammetry data for the flight simulation.

Pitch (°) | Roll (°) | IMU Pitch (°) | IMU Roll (°) | |
---|---|---|---|---|

Average | 91.13797 | 2.71445 | 2.72 | −0.71 |

St. dev. | 0.46591 | 0.36282 | 13.36 | 10.94 |

Min | 90.03401 | 1.75086 | −32.17 | −41.34 |

Max | 92.59373 | 3.71907 | 37.73 | 51.84 |

1st Session | 2nd Session | 3rd Session | ||||
---|---|---|---|---|---|---|

Pitch (°) | Roll (°) | Pitch (°) | Roll (°) | Pitch (°) | Roll (°) | |

Average | 91.67314 | −0.28787 | 91.31183 | −0.24313 | 90.71399 | 0.39360 |

St. dev. | 1.99739 | 0.80951 | 2.14277 | 0.91155 | 2.04433 | 0.82016 |

Min | 87.40141 | −1.82238 | 84.62633 | −2.67715 | 85.32468 | −1.64857 |

Max | 96.35258 | 1.44858 | 95.02984 | 1.41679 | 95.50489 | 2.89549 |

1st Session | 2nd Session | |||
---|---|---|---|---|

Pitch (°) | Roll (°) | Pitch (°) | Roll (°) | |

Average | −0.38750 | −1.32690 | −0.60653 | −1.61740 |

St. dev. | 1.72962 | 1.66566 | 0.92112 | 1.69534 |

Min | −3.47135 | −6.02212 | −2.28265 | −5.20398 |

Max | 4.75898 | 0.93433 | 1.81105 | 2.41166 |

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**MDPI and ACS Style**

Gašparović, M.; Jurjević, L.
Gimbal Influence on the Stability of Exterior Orientation Parameters of UAV Acquired Images. *Sensors* **2017**, *17*, 401.
https://doi.org/10.3390/s17020401

**AMA Style**

Gašparović M, Jurjević L.
Gimbal Influence on the Stability of Exterior Orientation Parameters of UAV Acquired Images. *Sensors*. 2017; 17(2):401.
https://doi.org/10.3390/s17020401

**Chicago/Turabian Style**

Gašparović, Mateo, and Luka Jurjević.
2017. "Gimbal Influence on the Stability of Exterior Orientation Parameters of UAV Acquired Images" *Sensors* 17, no. 2: 401.
https://doi.org/10.3390/s17020401