# Research on Algorithm of Airborne Dual-Antenna GNSS/MINS Integrated Navigation System

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## Abstract

**:**

## 1. Introduction

## 2. Introduction to the Main Index Requirements and Reference Coordinate System for Integrated Navigation Systems

## 3. Establishing the Mathematical Model of Dual-Antenna GNSS/INS Integrated Navigation System

#### 3.1. Discrete Kalman Filter

#### 3.2. State Equation, Measurement Equation and Parameter Selection of Design Navigation System

## 4. Calculation Error of Dual-Antenna GNSS System and Design of Updating Algorithm for Strapdown Inertial Navigation System

#### 4.1. Dual-Antenna GNSS System and Precision Factor

#### 4.2. Updating Algorithm of Strapdown Inertial Navigation System

- (1)
- Attitude updating algorithm

- (1)
- Velocity update algorithm

- (2)
- Location update algorithm

#### 4.3. Error Analysis of Strapdown Inertial Navigation System and Establishment of Error Equation and Model

- (1)
- Attitude error Equation

- (2)
- Velocity error Equation

- (3)
- Position error Equation

- (4)
- Mathematical model of gyroscope error

- (5)
- Mathematical model of accelerometer error

#### 4.4. An Initial Alignment Algorithm of Dual-Antenna GNSS and Magnetometer-Assisted MINS

- (1)
- The initial attitude alignment is based on angular velocity meter and magnetometer

- (2)
- Alignment algorithm of initial heading angle and pitch angle based on dual-antenna GNSS

#### 4.5. Aircraft Flight State Recognition and Attitude Compensation

- (1)
- When $\left|\delta {\widehat{f}}_{sb}^{h}\right|<{a}_{2}^{m}$ (${a}_{2}^{m}$ is another threshold parameter based on the specific value of the horizontal accelerometer noise), integrated with the gyroscope data to determine, the aircraft may be in a turning state or circling state.
- (2)
- When $\left|\delta {\widehat{f}}_{sb}^{h}\right|\ge {a}_{2}^{m}$, the aircraft has a large maneuvering state and is in the takeoff or landing phase, and the accelerometer can be used to compensate for the error and reduce the error of attitude angle in this phase.

## 5. Experimental Verification and Analysis

#### 5.1. Carry Out Indoor Static Experiment

#### 5.2. Conduct UAV Flight Test

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Schematic diagram of flight status identification and navigation correction data selection process.

Entry Name | Indicator Parameters | |
---|---|---|

Heading Accuracy | Double GNSS (2 m Baseline) | 1° (RMS) |

Heading holding (GNSS failure) | 1.5 °/min (RMS) | |

Attitude accuracy | GNSS valid (single point L1/L2) | 0.75° (RMS) |

Horizontal positioning accuracy | GNSS valid, single point L1/L2 | 1.5 m (RMS) |

Horizontal velocity accuracy | GNSS valid, single point L1/L2 | 0.2 m/s (RMS) |

Gyroscope | Measuring range | ±450 °/s |

Bias stability | 6 °/h | |

Accelerometer | Measuring range | ±16 g |

Bias stability | 0.3 mg | |

Environmental indicators | Working temperature | −40 °C~+60 °C |

Vibration | 5~2000 Hz, 2 g | |

To attack | 30 g, 11 ms |

Parameter | Pitch Angle Error (°) | Cross Roll Angle Error (°) | Heading Angle Error (°) |
---|---|---|---|

Means | 0.01493 | −0.01472 | −0.2335 |

Maximum value | 0.0329 | 0.001092 | 0.1458 |

Minimum value | −0.00667 | −0.03147 | −0.7275 |

RMS | 0.004792 | 0.003721 | 0.1307 |

Parameter | Pitch Angle Error (°) | Cross Roll Angle Error (°) | Heading Angle Error (°) |
---|---|---|---|

Means | 0.0522 | −0.1148 | 0.02089 |

Maximum value | 3.01 | 5.771 | 4.312 |

Minimum value | −2.784 | −5.935 | −2.123 |

RMS | 0.4574 | 0.7051 | 0.2251 |

Parameter | Eastward Position Error (m) | Northward Position Error (m) | Skyward Position Error (m) |
---|---|---|---|

Means | 0.03407 | 0.0341 | −1.035 |

Maximum value | 3.601 | 2.821 | 0.5304 |

Minimum value | −3.467 | −3.299 | −5.723 |

RMS | 0.4995 | 0.4323 | 1.445 |

Parameter | Pitch Angle Error (°) | Cross Roll Angle Error (°) | Heading Angle Error (°) |
---|---|---|---|

Means | −0.139 | −0.00824 | 0.03385 |

Maximum value | 5.352 | 6.955 | 4.987 |

Minimum value | −5.717 | −4.633 | −2.936 |

RMS | 0.8448 | 0.9444 | 0.4876 |

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**MDPI and ACS Style**

Xia, M.; Sun, P.; Guan, L.; Zhang, Z.
Research on Algorithm of Airborne Dual-Antenna GNSS/MINS Integrated Navigation System. *Sensors* **2023**, *23*, 1691.
https://doi.org/10.3390/s23031691

**AMA Style**

Xia M, Sun P, Guan L, Zhang Z.
Research on Algorithm of Airborne Dual-Antenna GNSS/MINS Integrated Navigation System. *Sensors*. 2023; 23(3):1691.
https://doi.org/10.3390/s23031691

**Chicago/Turabian Style**

Xia, Ming, Pengfei Sun, Lianwu Guan, and Zhonghua Zhang.
2023. "Research on Algorithm of Airborne Dual-Antenna GNSS/MINS Integrated Navigation System" *Sensors* 23, no. 3: 1691.
https://doi.org/10.3390/s23031691