# Exploring Signals on L5/E5a/B2a for Dual-Frequency GNSS Precise Point Positioning

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Real-Time Clock Estimation with RETICLE

#### 2.1. Overview

_{0}) observations are processed in a local station filter. Each filter processes single, uncombined observations and can process any number of different frequencies and signals for each constellation. The local station filters operate at an update rate of 1 Hz.

#### 2.2. Station Filter Description

#### 2.3. Clock Fusion Filter Description

#### 2.4. Modeling of GNSS Observations

## 3. Multi-GNSS, Real-Time Precise Point Positioning

#### 3.1. Algorithm Description

- Thirty-three worldwide IGS stations are used for the multi-GNSS analysis, shown in red in Figure 2. This set of stations is chosen randomly, as long as the station provides day-long observations from GPS, Galileo, and BeiDou. The signals used with these stations are L1/L2 for GPS, E1/E5a for Galileo, and B1-2/B3 for BeiDou-2 and -3.
- Eleven IGS stations are used for the L1/L5 analysis, shown in black in Figure 2. These stations are chosen by ensuring that they provide observations from the novel B1 and B2a BeiDou-3 signals, as well as GPS L5 measurements. Additionally, due to the limited number of stations observing these signals, they are split into 6 h sessions, and only the sessions with more than four visible GPS IIF satellites are kept for processing. The processed signals are L1/L5 for GPS, E1/E5a for Galileo, and B1/B2a for BeiDou-3; therefore, both frequencies are the same for all three constellations: 1575.42 and 1176.45 MHz.

#### 3.2. Combined GPS, Galileo and BeiDou Processing on Common Frequencies

#### 3.2.1. Multi-GNSS Analysis

#### 3.2.2. BeiDou-2 and BeiDou-3 Compatibility

#### 3.3. Combined GPS, Galileo, and BeiDou Processing on L1/L5 Frequencies

#### 3.3.1. Effect of GPS L5 Biases

#### 3.3.2. GEC Processing with GPS L5 Corrections Applied

## 4. Discussion and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Processing steps of the local station filters and the global clock merging filter in RETICLE.

**Figure 2.**Distribution of stations used in the processing. Red dots are stations used for the multi-GNSS analysis. Black dots are stations used in the GPS L5 analysis.

**Figure 3.**Average horizontal and vertical errors for different constellation combinations at the 100th, 95th, and 67th percentiles.

**Figure 4.**Convergence time (

**a**); horizontal rms (

**b**); and vertical rms (

**c**) corresponding to Figure 3 results—100th percentile EC convergence time and vertical rms exceed the limits of the y-axes.

**Figure 5.**Epoch-by-epoch mean number of GPS, Galileo and BeiDou satellites across all 33 stations over seven days.

**Figure 6.**Horizontal error and number of satellites for station SUTH on DoY 187, 2020 for different constellation combinations.

**Figure 7.**Difference between the estimated BeiDou-2 and -3 receiver clocks for station TLSE on DoY 183 between UTC Hours 8 and 15.

**Figure 8.**BeiDou-2 pseudorange PR (

**a**) and carrier-phase CP (

**b**) residuals and BeiDou-3 pseudorange PR (

**c**) and carrier-phase CP (

**d**) residuals for station TLSE on DoY 183 with separate receiver clocks for each generation.

**Figure 9.**BeiDou-2 pseudorange PR (

**a**) and carrier-phase CP (

**b**) residuals and BeiDou-3 pseudorange PR (

**c**) and carrier-phase CP (

**d**) residuals for station TLSE on DoY 183 with a common receiver clock for both generations.

**Figure 10.**Average horizontal (

**a**) and vertical (

**b**) errors for station CRO1 on DOY 186, 2020 between UTC Hours 6 and 12. GEC constellations processed in kinematic mode on [L1,E1,B1]/[L5,E5a,B2a] frequencies, with and without the application of the GPS L5 corrections.

**Figure 11.**Difference in the estimated GPS-related states when using the GPS L1/L2 and L1/L5 clocks for station BRST on DoY 187 (

**a**,

**c**–

**f**), and applied L5 corrections (

**b**).

**Figure 12.**Average horizontal (

**a**) and vertical (

**b**) errors based on 80 datasets in kinematic mode using [L1,E1,B1]/[L5,E5a,B2a] signals with GE, EC, and GEC. The horizontal black line represents the convergence threshold, defined based on the horizontal error.

Parameters | Strategy |
---|---|

Receiver coordinates | Static mode: estimated as constants |

Kinematic mode: 120 km/h process noise | |

Troposphere | Dry component: GMF model and mapping function [31] |

Wet component: estimated as random walk with process noise of | |

2 cm/$\sqrt{h}$ and GMF mapping function | |

Receiver clock | Estimated as white noise process. One receiver clock per constellation |

Ionospheric delays | Slant delays estimated as white noise processes |

Ambiguities | Estimated as constants over each continuous arc |

Satellite antenna | Corrected for using IGS14 ANTEX corrections [32] |

Satellites DCBs | Corrected for using Chinese Academy of Sciences (CAS) products [33] |

**Table 2.**Weighting factor ${\sigma}_{C}$ values for pseudorange measurement weighting (in nanoseconds).

GPS | Galileo | BeiDou-2 | BeiDou-3 | |
---|---|---|---|---|

${\sigma}_{C}$ | 0.24 | 0.13 | 0.86 | 0.43 |

Single Constellation | GPS (G) |
---|---|

Dual constellation | GPS + Galileo (GE) |

GPS + BeiDou-2/3 (GC) | |

Galileo + BeiDou-2/3 (EC) | |

Triple constellation | GPS + Galileo + BeiDou-2/3 (GEC) |

**Table 4.**Convergence (Conv.) time and horizontal and vertical rms statistics corresponding to the results in Figure 10.

Conv. Time (mins) | Horizontal rms (cm) | Vertical rms (cm) | |
---|---|---|---|

L5 corr. not applied | 235.5 | 18.9 | 17.3 |

L5 corr. applied | 56.5 | 11.6 | 10.2 |

**Table 5.**Convergence (Conv.) time and horizontal and vertical rms statistics corresponding to the results in Figure 12.

Conv. Time (min) | Horizontal rms (cm) | Vertical rms (cm) | |
---|---|---|---|

GE | 89.0 | 6.9 | 7.0 |

EC | 240.5 | 10.2 | 11.5 |

GEC | 53.0 | 6.9 | 7.1 |

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**MDPI and ACS Style**

Naciri, N.; Hauschild, A.; Bisnath, S.
Exploring Signals on L5/E5a/B2a for Dual-Frequency GNSS Precise Point Positioning. *Sensors* **2021**, *21*, 2046.
https://doi.org/10.3390/s21062046

**AMA Style**

Naciri N, Hauschild A, Bisnath S.
Exploring Signals on L5/E5a/B2a for Dual-Frequency GNSS Precise Point Positioning. *Sensors*. 2021; 21(6):2046.
https://doi.org/10.3390/s21062046

**Chicago/Turabian Style**

Naciri, Nacer, André Hauschild, and Sunil Bisnath.
2021. "Exploring Signals on L5/E5a/B2a for Dual-Frequency GNSS Precise Point Positioning" *Sensors* 21, no. 6: 2046.
https://doi.org/10.3390/s21062046