# A Pragmatic Approach to the Design of Advanced Precision Terrain-Aided Navigation for UAVs and Its Verification

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design of the Proposed AP-TAN System

#### 2.1. Overall Design of the AP-TAN System

- A inertial measurement unit (IMU) consists of three ring laser gyros (RLGs) and three silicon pendulum accelerometers to measure the motion of the vehicle without external helps.
- A parallel process unit (PPU) processes the outputs of a IMU and auxiliary sensors. It also performs navigation algorithms including pure navigation, INS/GNSS-aided navigation, TRN, INS/TRN-aided navigation, and INS/GNSS/TRN integrated navigation.
- A GNSS receiver provides the navigation information of the vehicle using GNSS outputs
- A barometer provide the altitude information of the vehicle by measuring the air pressure from the average sea level.
- A IRA provides 3D terrain elevation information for the nearest point.
- A control and display unit (CDU) gives control commands to the PPU and monitors the navigation results in real time.
- A signal and power distributor (SPD) delivers the commands from the CDU and the outputs of the auxiliary sensors to the PPU. It also delivers the navigation results from the PPU to the CDU. In addition, it provides adequate power for the entire system components.

#### 2.2. Design of an INS/GNSS/TRN Integrated Navigation System

#### 2.2.1. Design of the Master Filter Based on the Federated Filter

- Case 1.
- The state variables and covariances when GNSS is not available.$${P}_{IGT}\left(k\right)={P}_{TRN}\left(k\right),\phantom{\rule{2.em}{0ex}}{X}_{IGT}\left(k\right)={X}_{TRN}\left(k\right)$$
- Case 2.
- The state variables and covariances when TRN is not available.$${P}_{IGT}\left(k\right)={P}_{GNSS}\left(k\right),\phantom{\rule{2.em}{0ex}}{X}_{IGT}\left(k\right)={X}_{GNSS}\left(k\right)$$
- Case 3.
- The state variables and covariances when both GNSS and TRN are available.$${P}_{IGT}\left(k\right)={\left[{\left({P}_{GNSS}\left(k\right)\right)}^{-1}+{\left({P}_{TRN}\left(k\right)\right)}^{-1}\right]}^{-1}$$$${X}_{IGT}\left(k\right)={P}_{IGT}\left(k\right)\left[{P}_{GNSS}{\left(k\right)}^{-1}{X}_{GNSS}\left(k\right)+{P}_{TRN}{\left(k\right)}^{-1}{X}_{TRN}\left(k\right)\right]$$
- Case 4.
- The state variables and covariance when both GNSS and TRN are not available.$${X}_{IGT}\left(k\right)=\left(I+{A}_{IGT}\Delta t\right){X}_{IGT}(k-1)={\mathsf{\Phi}}_{IGT}{X}_{IGT}(k-1)$$$${P}_{IGT}\left(k\right)={\mathsf{\Phi}}_{IGT}{P}_{IGT}(k-1){\mathsf{\Phi}}_{IGT}^{T}+{Q}_{IGT}$$

#### 2.2.2. Design of the Local Filters Based on the EKF

## 3. Hybrid TRN Algorithm Based on an Interferometric Radar Altimeter

#### 3.1. Error Compensation Method of IRA Measurements

#### 3.2. Acquisition Mode Based on Batch Processing

#### 3.3. Tracking Mode Based on a Particle Filter

#### 3.4. Real-Time Processing of a High-Resolution Terrain Database

## 4. Verification of a Three-Dimensional Terrain Based System

#### 4.1. Experiment Results in a SIL Environment

#### 4.2. Verification Using Captive Flight Tests

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Block diagram of federated filter-based inertial navigation system (INS)/global navigation satellite system (GNSS)/terrain referenced navigation (TRN) integrated navigation.

**Figure 8.**Results of SIL Test 1 when GNSS is unavailable in the mission area. (

**a**) Horizontal position error. (

**b**) Altitude error.

**Figure 9.**Results of SIL Test 2 when GNSS is unavailable in the mission area. (

**a**) Horizontal position error. (

**b**) Altitude error.

**Figure 10.**Results of SIL Test 3 when GNSS is unavailable in the whole area. (

**a**) Horizontal position error. (

**b**) Horizontal position error without INS/GNSS-aided navigation error. (

**c**) Altitude error without TRN and INS/TRN-aided navigation error. (

**d**) Altitude error.

**Figure 13.**Results of CFT 1 when GNSS is unavailable in the mission area. (

**a**) Attitude profile. (

**b**) Horizontal position error. (

**c**) Horizontal position error without INS/GNSS-aided navigation error. (

**d**) Altitude error.

**Figure 14.**Results of CFT 2 when GNSS is unavailable in the mission area. (

**a**) Attitude profile. (

**b**) Horizontal position error. (

**c**) Horizontal position error without INS/GNSS-aided navigation error. (

**d**) Altitude error.

**Figure 15.**Results of CFT 3 when GNSS is unavailable in the whole area. (

**a**) Attitude profile. (

**b**) Horizontal position error. (

**c**) Horizontal position error without INS/GNSS-aided navigation error. (

**d**) Altitude error.

No. of Test | Total Flight Time | Mission Time | Flight Altitude | GNSS Unavailable Area |
---|---|---|---|---|

SIL Test 1 | 1 h. 20 min. | 13 min. | 1.3 km | Mission Area |

SIL Test 2 | 42 min. | 23 min. | 5.3 km | Mission Area |

SIL Test 3 | 1 h. 50 min. | 1 hr. 40 min. | 2.3 km | Whole Area |

Hor. Pos. Error [m CEP] | SIL Test 1 | SIL Test 2 | SIL Test 3 |
---|---|---|---|

TRN | 4.89 m | 6.74 m | 9.13 m |

INS/TRN | 3.54 m | 5.62 m | 7.23 m |

INS/GNSS | 20.06 m | 39.52 m | 2242.68 m |

INS/GNSS/TRN | 3.50 m | 5.43 m | 6.73 m |

Altitude Error [m PE] | SIL Test 1 | SIL Test 2 | SIL Test 3 |

TRN | 2.29 m | 1.35 m | 1.49 m |

INS/TRN | 1.91 m | 1.13 m | 1.35 m |

INS/GNSS | 0.14 m | 1.86 m | 0.26 m |

INS/GNSS/TRN | 1.53 m | 0.90 m | 1.18 m |

No. of Test | Total Flight Time | Mission Time | Flight Altitude | GNSS Unavailable Area |
---|---|---|---|---|

CFT 1 | 3 hr. 33 min. | 1 hr. 58 min. | 1.5 km | Mission Area |

CFT 2 | 2 hr. 33 min. | 23 min. | 5.1 km | Mission Area |

CFT 3 | 3 hr. 40 min. | 1 hr. 42 min. | 1.3 km∼3.3 km | Whole Area |

No. of Test | Acquisition Time | Latitude Error | Longitude Error |
---|---|---|---|

CFT 1 | 47 sec | 5 m | 3.5 m |

CFT 2 | 30 sec | −10 m | −10 m |

CFT 3 | 24 sec | −16 m | −1 m |

Hor. Pos. Error [m CEP] | CFT 1 | CFT 2 | CFT 3 |
---|---|---|---|

TRN | 3.97 m | 6.45 m | 9.85 m |

INS/TRN | 3.07 m | 5.90 m | 8.87 m |

INS/GNSS | 78.92 m | 164.85 m | 1212.85 m |

INS/GNSS/TRN | 3.75 m | 6.28 m | 8.39 m |

Altitude Error [m PE] | CFT 1 | CFT 2 | CFT 3 |

TRN | 4.62 m | 3.33 m | 6.79 m |

INS/TRN | 4.60 m | 3.29 m | 6.74 m |

INS/GNSS | 4.76 m | 3.62 m | 6.47 m |

INS/GNSS/TRN | 4.46 m | 3.16 m | 6.48 m |

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**MDPI and ACS Style**

Lee, J.; Sung, C.-K.; Oh, J.; Han, K.; Lee, S.; Yu, M.-J.
A Pragmatic Approach to the Design of Advanced Precision Terrain-Aided Navigation for UAVs and Its Verification. *Remote Sens.* **2020**, *12*, 1396.
https://doi.org/10.3390/rs12091396

**AMA Style**

Lee J, Sung C-K, Oh J, Han K, Lee S, Yu M-J.
A Pragmatic Approach to the Design of Advanced Precision Terrain-Aided Navigation for UAVs and Its Verification. *Remote Sensing*. 2020; 12(9):1396.
https://doi.org/10.3390/rs12091396

**Chicago/Turabian Style**

Lee, Jungshin, Chang-Ky Sung, Juhyun Oh, Kyungjun Han, Sangwoo Lee, and Myeong-Jong Yu.
2020. "A Pragmatic Approach to the Design of Advanced Precision Terrain-Aided Navigation for UAVs and Its Verification" *Remote Sensing* 12, no. 9: 1396.
https://doi.org/10.3390/rs12091396