# Research on Low-Cost Attitude Estimation for MINS/Dual-Antenna GNSS Integrated Navigation Method

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## Abstract

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## 1. Introduction

## 2. Reference Frame

## 3. System Model Analysis

#### 3.1. IMU Model

#### 3.1.1. Attitude Update

#### 3.1.2. Velocity Update

#### 3.1.3. Position Update

#### 3.2. Schematic of Inertial Navigation Process

#### 3.3. System Dynamic Model

## 4. Integrated Navigation Method

#### 4.1. Observation

#### 4.2. EKF Process and Work Sequence

#### 4.3. Integrated Navigation Structure

#### 4.4. Simulation Experiment

## 5. Experiment

#### 5.1. Design of the Prototype

#### 5.2. Dynamic Calibration of MEMS Devices

#### 5.3. Static test

#### 5.4. Dynamic Experiment

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Axes of the Earth-Centered Inertial Frame. This is nominally centered at the Earth’s center of mass and oriented with respect to the Earth’s spin axis and the stars. The rotation shown is that of the Earth with respect to space. The z-axis always points along the Earth’s axis of rotation from the center to the north pole (true, not magnetic); (

**b**) Axes of the Earth-Centered Earth-fixed Frame. The z-axis always points along the Earth’s axis of rotation from the center to the North Pole (true, not magnetic). The x-axis points from the center to the intersection of the equator with the reference meridian (IRM) or conventional zero meridian (CZM), which defines 0° longitude.

**Figure 2.**(

**a**) Axes of the Local Navigation Frame. The z axis, also known as the down (D) axis, is defined as the normal to the surface of the reference ellipsoid, pointing toward the center of the Earth roughly. True gravity deviates from this slightly due to local anomalies. The x-axis, or north (N) axis, is the projection in the plane orthogonal to the z-axis of the line from the user to the north pole. By completing the orthogonal set, the y-axis always points east and is hence known as the east (E) axis; (

**b**) Height and geodetic latitude of a body.

**Figure 3.**Block diagram of local-navigation-frame equation. (+) represents the t and (−) represents the (t − τ

_{0}).

**Figure 5.**(

**a**) The convergence characteristics of the velocity covariance; (

**b**) The convergence characteristics of the attitude angle for the Extended Kalman Filtering (EKF).

**Figure 6.**(

**a**) Covariance of the east, north, and down positions; (

**b**) The characteristic of the up position.

**Figure 7.**(

**a**) The convergence characteristic of the yaw error; (

**b**) The convergence characteristics of the roll angle error.

**Figure 8.**(

**a**) The device appearance of Micro-electromechanical Systems-Inertial Navigation System (MINS); (

**b**) The integrated circuit system.

**Figure 9.**(

**a**) The two-dimensional temperature control turntable; (

**b**) The output of the gyroscope after calibration.

**Figure 10.**(

**a**) The installation instruction of the dual-antenna/MINS; (

**b**) The convergence of the yaw for the static test.

**Figure 11.**(

**a**) The Synchronous Position, Attitude and Navigation (SPAN-CPT) reference system; (

**b**) The driving vehicle.

**Figure 14.**(

**a**) The standard deviation of GNSS heading angle; (

**b**) The yaw angle test of the dual-antenna GNSS is unavailable.

**Figure 16.**(

**a**) The position of the dual-antenna GNSS is blocked; (

**b**)The position of the dual-antenna GNSS/MINS integration.

**Figure 17.**(

**a**) The top view of the driving test trajectory from Google Earth; (

**b**) The magnified map of the test location.

Filter State | The Noise Value | Filter State | The Noise Value | Filter State | The Noise Value |
---|---|---|---|---|---|

${\delta}_{\alpha}$ | $(3\times {10}^{-3}{)}^{2}s$ | ${\delta}_{\beta}$ | $(3\times {10}^{-3}{)}^{2}s$ | ${\delta}_{\lambda}$ | $(3\times {10}^{-3}{)}^{2}s$ |

${\delta}_{VE}$ | $(1\times {10}^{-3}m/s{)}^{2}s$ | ${\delta}_{VN}$ | $(1\times {10}^{-3}m/s{)}^{2}s$ | ${\delta}_{VU}$ | $(1\times {10}^{-3}m/s{)}^{2}s$ |

$\delta L$ | $(6\times {10}^{-9}m{)}^{2}s$ | $\delta \lambda $ | $(6\times {10}^{-9}m{)}^{2}s$ | $\delta h$ | $(6\times {10}^{-9}m{)}^{2}s$ |

$\delta f$ | $(9\times {10}^{-4}{m/s}^{2}{)}^{2}s$ | $\delta {f}_{y}$ | $(9\times {10}^{-4}{m/s}^{2}{)}^{2}s$ | $\delta {f}_{z}$ | $(9\times 1{0}^{-4}m/{s}^{2}{)}^{2}s$ |

${\delta}_{\omega x}$ | $(0.01\xb0/s{)}^{2}s$ | ${\delta}_{\omega y}$ | $(0.01\xb0/s{)}^{2}s$ | ${\delta}_{\omega z}$ | $(0.01\xb0/s{)}^{2}s$ |

Performance Parameter | Axial | Parameter Value (°) |
---|---|---|

Position Error RMSE (m) | North | 0.1542 |

East | 0.1442 | |

Down | 0.2212 | |

Velocity Error RMSE (m) | North | 0.2321 |

East | 0.2451 | |

Down | 0.3264 | |

Attitude Error RMSE (°) | Pitch | 0.3342 |

Yaw | 0.2514 |

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**MDPI and ACS Style**

Wang, H.; Liu, N.; Su, Z.; Li, Q.
Research on Low-Cost Attitude Estimation for MINS/Dual-Antenna GNSS Integrated Navigation Method. *Micromachines* **2019**, *10*, 362.
https://doi.org/10.3390/mi10060362

**AMA Style**

Wang H, Liu N, Su Z, Li Q.
Research on Low-Cost Attitude Estimation for MINS/Dual-Antenna GNSS Integrated Navigation Method. *Micromachines*. 2019; 10(6):362.
https://doi.org/10.3390/mi10060362

**Chicago/Turabian Style**

Wang, Hailu, Ning Liu, Zhong Su, and Qing Li.
2019. "Research on Low-Cost Attitude Estimation for MINS/Dual-Antenna GNSS Integrated Navigation Method" *Micromachines* 10, no. 6: 362.
https://doi.org/10.3390/mi10060362