# GNSS RTK Positioning Augmented with Large LEO Constellation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Data Simulation

#### 2.2. Combined GNSS/LEO RTK Observation Model

## 3. Situation and Strategy

#### 3.1. Constellation Configuration

#### 3.2. Simulation Situation

#### 3.3. Data Processing Strategy

^{−3}$m/\sqrt{s}$. So the empirical model can be expressed as follow:

^{−4}$m/\sqrt{s}$. In addition, the code and phase error ratio of each frequency can be set based on an empirical value, e.g., 100:1. The observation weight is also used according to the criterion of elevation-dependent weight. Noteworthily, the large LEO constellation brings the challenge of high-dimensional ambiguity resolution. Once all ambiguities are simultaneously failed to fix, partial ambiguity-fixed strategy can be adopted to resolve a subset of the candidate ambiguities during data processing [32].

## 4. Performance of Different LEO Constellations Augmented GPS RTK

## 5. Assessment of Combined GPS/LEO RTK for Different Length Baselines

#### 5.1. RTK for Short Baselines

#### 5.2. RTK for Medium-to-Long Baselines

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Distribution of stations at the mid latitudes. The small map shows the stations constituting short baselines and the larger one is for medium-to-long baselines.

**Figure 3.**Comparisons of different scales of LEO constellations augmented GPS RTK solutions in east, north, and up components, respectively, for ‘P339-P341′ baseline scheme. The visible satellite numbers and position dilution of precision (PDOP) values are also presented.

**Figure 4.**The local enlarged picture of the Figure 3 (dotted box) shows the first 10-min comparison of different scales of LEO constellations augmented GPS RTK solutions at three components, for ‘P339-P341′ baseline scheme.

**Figure 5.**Average convergence time, time to first fix (TTFF), and fixing ratio of GPS RTK solutions in combination with different LEO constellations, for ‘P339-P341′ baseline scheme.

**Figure 6.**The 1-h sky plots (azimuth versus elevation) of GPS with the augmentations of different LEO constellations: (

**a**) GPS+60 LEO; (

**b**) GPS+96 LEO; (

**c**) GPS+192 LEO; (

**d**) GPS+288 LEO. Circular markers indicate the satellite (GPS in blue, LEO in red) positions at the initial epoch.

**Figure 7.**Average convergence time (

**left panel**) and TTFF (

**right panel**) of different LEO constellations augmented GPS RTK positioning for five short baselines.

**Figure 8.**Average convergence time and TTFF of different LEO constellations augmented GPS RTK positioning for ten medium-to-long baselines.

**Figure 9.**The solid lines describe the average convergence time and TTFF of five medium-baseline solutions with the augmentations of different LEO constellations, and the similar indexes of five long-baseline solutions are shown in dashed line.

Orbit | LEO | LEO | LEO | LEO |
---|---|---|---|---|

Satellite Number | 60 | 96 | 192 | 288 |

Altitude[km] | 1000 | 1000 | 1000 | 1000 |

Constellation | 10 planes × 6 satellites | 12 planes × 8 satellites | 12 planes× 16 satellites | 12 planes× 24 satellites |

Inclination[deg] | 90 | 90 | 90 | 90 |

**Table 2.**Slot assignments of the nominal GPS constellation. RAAN: Right Ascension of the Ascending Node.

Slot | RAAN | Argument of Latitude | Slot | RAAN | Argument of Latitude |
---|---|---|---|---|---|

A1 | 272.847° | 268.126° | D1 | 92.847° | 135.226° |

A2 | 272.847° | 161.786° | D2 | 92.847° | 265.446° |

A3 | 272.847° | 11.676° | D3 | 92.847° | 35.156° |

A4 | 272.847° | 41.806° | D4 | 92.847° | 167.356° |

B1 | 332.847° | 80.956° | E1 | 152.847° | 197.046° |

B2 | 332.847° | 173.336° | E2 | 152.847° | 302.596° |

B3 | 332.847° | 309.976° | E3 | 152.847° | 66.066° |

B4 | 332.847° | 204.376° | E4 | 152.847° | 333.686° |

C1 | 32.847° | 111.876° | F1 | 212.847° | 238.886° |

C2 | 32.847° | 11.796° | F2 | 212.847° | 345.226° |

C3 | 32.847° | 339.666° | F3 | 212.847° | 105.206° |

C4 | 32.847° | 241.556° | F4 | 212.847° | 135.346° |

Short Baselines | Medium Baselines | Long Baselines | |||
---|---|---|---|---|---|

P696-P695 | 1.1 km | P169-TRND | 33.0 km | P170-P339 | 138.2 km |

P698-P696 | 2.8 km | SBCC-P474 | 44.2 km | P698-P372 | 390.5 km |

P700-P695 | 4.7 km | P446-P698 | 57.0 km | P698-P663 | 514.7 km |

P700-P696 | 5.5 km | P339-P341 | 68.7 km | P698-P349 | 604.7 km |

P700-P701 | 6.8 km | P164-P339 | 88.0 km | P023-P343 | 739.2 km |

Items | Models |
---|---|

Satellites | GPS (G); GPS+LEO (GL); |

Estimator | Extended Kalman filter (EKF) |

Observations | Pseudorange and carrier phase observations |

Signal selection | GPS: L1/L2; LEO: L1/L2 |

Sampling Interval | 1s |

Elevation mask | 7.5° |

Observation weight | Elevation dependent weight |

Satellite orbit | Precise ephemeris by STK |

Satellite clock | DD elimination or weakening |

Receiver clock | DD elimination or weakening |

Station coordinate | Estimated in kinematic mode |

Ionospheric delay | Short baselines: Not estimated; Medium-to-long baselines: Estimated |

Tropospheric delay | Short baselines: Not estimated; Medium-to-long baselines: Estimated |

Process noise of vertical iono.delay | 10^{−3} m/sqrt(s) |

Process noise of wet ZTD | 10^{−4} m/sqrt(s) |

Phase ambiguity | LAMBDA |

Ratio | 3.0 |

Code/carrier-phase error ratio | 100 |

RMS[cm] | GPS-Only | G+60L | G+96L | G+192 | G+288L |
---|---|---|---|---|---|

East | 0.77 | 0.76 | 0.71 | 0.62 | 0.58 |

North | 0.93 | 0.90 | 0.83 | 0.69 | 0.65 |

Up | 1.73 | 1.71 | 1.67 | 1.55 | 1.37 |

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**MDPI and ACS Style**

Li, X.; Lv, H.; Ma, F.; Li, X.; Liu, J.; Jiang, Z.
GNSS RTK Positioning Augmented with Large LEO Constellation. *Remote Sens.* **2019**, *11*, 228.
https://doi.org/10.3390/rs11030228

**AMA Style**

Li X, Lv H, Ma F, Li X, Liu J, Jiang Z.
GNSS RTK Positioning Augmented with Large LEO Constellation. *Remote Sensing*. 2019; 11(3):228.
https://doi.org/10.3390/rs11030228

**Chicago/Turabian Style**

Li, Xingxing, Hongbo Lv, Fujian Ma, Xin Li, Jinghui Liu, and Zihao Jiang.
2019. "GNSS RTK Positioning Augmented with Large LEO Constellation" *Remote Sensing* 11, no. 3: 228.
https://doi.org/10.3390/rs11030228