# Sampling Rate Impact on Precise Point Positioning with a Low-Cost GNSS Receiver

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. The Precise Point Positioning Method

_{1}and L

_{2}between a receiver j and satellite k is:

## 2. Methodology

#### 2.1. Experimental Setup and GNSS Data Collection

#### 2.2. PPP-GNSS Data Processing

## 3. Results

## 4. Conclusions

- The low-cost GNSS receiver presented high horizontal accuracy, nevertheless, the vertical component was the most affected. In both components, the obtained results were calculated without considering the low multipath suppression of the antenna of the low-cost GNSS receiver. Likewise, the antenna of the low-cost GNSS receiver did not have an IGS calibration or circular polarized antenna (irregular gain pattern and low multipath suppression), this affected the convergence in some circumstances making it slow (if the antenna is compared with geodetic-grade hardware).
- The results obtained at different sampling rates show that the low-cost GNSS receiver had a better performance (obtained positioning) by using PPP-static mode when the sampling rate was at 1 and 15 s.
- As was presented in Figure 14 and Figure 15, the low-cost GNSS presented data loss at 5, 15 and 30 s, and lower precision at 5 and 30 s. On the other hand, when the data were processed at high frequencies (0.1 and 0.2 s), the precision that was achieved was low in comparison with a 1 s sampling rate.
- An improvement of convergence time is clearly seen (Figure 16 and Figure 17) for the sampling rates of 0.1, 0.2 and 1 s. In the same way, the convergence time was reached at ~50 min in static mode. In the kinematic mode, the convergence time at each interval time was variable and constant with the behavior presented. The convergence was affected by the cycle slips presented or by a high multipath, nevertheless, it was faster than the static mode.
- For the high frequencies a low-cost GNSS receiver is a viable option for obtaining cm solutions if the project allows it.
- According to the results obtained, the low-cost GNSS receiver could be implemented in structural health monitoring systems, mainly due to the centimeter precision achieved in positioning. In addition, it could represent a potential economic alternative by replacing high-cost instruments used in SHM processes.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Multipath effect for the low-cost and geodetic GNSS receivers. Yellow line: IGS recommended value (MP < 0.3 m).

**Figure 5.**Signal-to-Noise ratio for the low-cost and geodetic GNSS receivers. Yellow line: IGS recommended value (SNR ≥ 36 dBHz).

**Figure 6.**Difference between estimated and precise coordinates of the low-cost and geodetic receiver by processing with PPP-static mode.

**Figure 7.**Standard deviation (95%) of estimated positions of low-cost and geodetic receivers by processing with PPP-static mode.

**Figure 8.**Difference between estimated and precise position of low-cost and geodetic receivers at 0.1 and 0.2 s respectively, by processing with PPP-static mode.

**Figure 9.**Standard deviation (95%) of estimated positions by processing with PPP-static mode: (

**a**) low-cost receiver at 0.1 s; (

**b**) geodetic receiver at 0.2 s.

**Figure 10.**Standard deviation (95%) of estimated positions of low-cost and geodetic receivers by processing with PPP-kinematic mode.

**Figure 11.**Difference between estimated and precise positions of low-cost and geodetic receivers by processing with PPP-kinematic mode.

**Figure 12.**Difference between estimated and precise positions of low-cost and geodetic receivers at 0.1 and 0.2 s respectively, by processing with PPP-kinematic mode.

**Figure 13.**Standard deviation (95%) of estimated positions of low-cost and geodetic receivers at 0.1 and 0.2 s respectively, by processing with PPP-kinematic mode.

**Figure 14.**Low-cost GNSS static mode obtained by processing with CSRS-PPP: (

**a**) sampling rate: 0.1, 0.2 and 1 s; (

**b**) sampling rate: 5, 15 and 30 s.

**Figure 15.**Low-cost GNSS kinematic mode obtained by processing with CSRS-PPP: (

**a**) sampling rate: 0.1, 0.2 and 1 s; (

**b**) sampling rate: 5, 15 and 30 s.

Processing Mode | Static and Kinematic | ||||
---|---|---|---|---|---|

GNSS System | GPS + GLONASS | ||||

Observations | Code and phase | ||||

Frequency | ${\mathrm{L}}_{1}$, ${\mathrm{L}}_{2}$ | ||||

Precise satellite orbits | Precise (IGS final) | ||||

Satellite product input | CLK-RINEX | ||||

Product interpolation | YES | ||||

Phase center corrections | IGS (ATX) | ||||

Tropospheric model | Davis (GPT) for hydrostatic delay; Hopf (GPT) for wet delay; GMF for mapping functions | ||||

Ionospheric model | Iono-free (${\mathrm{L}}_{1}\text{}\mathrm{and}$ ${\mathrm{L}}_{2}$) | ||||

Elevation cut off (degrees) | 15 | ||||

Observation intervals (s) | Low-cost | 0.1, 0.2, 1, 5, 15, 30. | |||

Geodetic | 0.2, 1, 5, 15, 30. | ||||

Duration of observations (h) | Low-cost | 2 | |||

Geodetic | 2 | ||||

Number of satellites tracked | Low-cost | GPS | 10 | GLONASS | 09 |

Geodetic | 17 | 13 | |||

Reference frame | ITRF in consideration to the epoch of GNSS data |

**Table 2.**Differences and Standard deviation obtained at different sampling rates for the PPP-static mode.

Receiver | Sampling Rate (s) | DLAT (m) | DLON (m) | DHGT (m) | SDLAT (m) | SDLON (m) | SDHGT (m) |
---|---|---|---|---|---|---|---|

Low-cost GNSS | 0.1 | 0.045 | −0.116 | −0.179 | 0.155 | 0.390 | 0.410 |

0.2 | 0.057 | −0.122 | −0.127 | 0.069 | 0.108 | 0.340 | |

1 | 0.007 | −0.135 | −0.112 | 0.035 | 0.050 | 0.236 | |

5 | 0.042 | −0.014 | −0.236 | 0.142 | 0.364 | 0.270 | |

15 | 0.001 | −0.169 | −0.159 | 0.048 | 0.037 | 0.152 | |

30 | −0.039 | −0.169 | −0.15 | 0.197 | 0.470 | 0.368 | |

Geodetic | 0.2 | −0.007 | −0.007 | 0.037 | 0.004 | 0.005 | 0.018 |

1 | −0.007 | −0.006 | 0.038 | 0.004 | 0.005 | 0.018 | |

5 | −0.007 | −0.007 | 0.038 | 0.004 | 0.005 | 0.018 | |

15 | −0.007 | −0.007 | 0.04 | 0.004 | 0.005 | 0.017 | |

30 | −0.007 | −0.007 | 0.041 | 0.005 | 0.006 | 0.022 |

**Table 3.**Differences and Standard deviation obtained at different sampling rates for the PPP-kinematic mode.

Receiver | Sampling Rate (s) | DLAT (m) | DLON (m) | DHGT (m) | SDLAT (m) | SDLON (m) | SDHGT (m) |
---|---|---|---|---|---|---|---|

Geodetic | 0.2 | −0.006 | −0.006 | 0.041 | 0.017 | 0.018 | 0.042 |

1 | −0.006 | −0.006 | 0.039 | 0.019 | 0.019 | 0.046 | |

5 | −0.006 | −0.006 | 0.041 | 0.019 | 0.020 | 0.048 | |

15 | −0.006 | −0.006 | 0.042 | 0.019 | 0.020 | 0.048 | |

30 | −0.006 | −0.006 | 0.042 | 0.019 | 0.020 | 0.048 | |

Low-cost GNSS | 0.1 | 0.062 | −0.195 | −0.129 | 0.032 | 0.043 | 0.082 |

0.2 | −0.021 | −0.432 | −0.100 | 0.035 | 0.052 | 0.093 | |

1 | 0.017 | −0.145 | −0.278 | 0.046 | 0.086 | 0.116 | |

5 | 0.096 | −0.177 | −0.019 | 0.105 | 0.241 | 0.222 | |

15 | 0.079 | −0.254 | −0.140 | 0.155 | 0.342 | 0.317 | |

30 | −0.007 | −0.272 | −0.033 | 0.322 | 0.573 | 0.624 |

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**MDPI and ACS Style**

Romero-Andrade, R.; Trejo-Soto, M.E.; Vázquez-Ontiveros, J.R.; Hernández-Andrade, D.; Cabanillas-Zavala, J.L.
Sampling Rate Impact on Precise Point Positioning with a Low-Cost GNSS Receiver. *Appl. Sci.* **2021**, *11*, 7669.
https://doi.org/10.3390/app11167669

**AMA Style**

Romero-Andrade R, Trejo-Soto ME, Vázquez-Ontiveros JR, Hernández-Andrade D, Cabanillas-Zavala JL.
Sampling Rate Impact on Precise Point Positioning with a Low-Cost GNSS Receiver. *Applied Sciences*. 2021; 11(16):7669.
https://doi.org/10.3390/app11167669

**Chicago/Turabian Style**

Romero-Andrade, Rosendo, Manuel E. Trejo-Soto, Jesús R. Vázquez-Ontiveros, Daniel Hernández-Andrade, and Juan L. Cabanillas-Zavala.
2021. "Sampling Rate Impact on Precise Point Positioning with a Low-Cost GNSS Receiver" *Applied Sciences* 11, no. 16: 7669.
https://doi.org/10.3390/app11167669