The Real-Time Detection of Vertical Displacements by Low-Cost GNSS Receivers Using Precise Point Positioning
Abstract
:1. Introduction
2. Materials and Methods
2.1. Precise Point Positioning
- —ionosphere-free linear combination of code-phase observations [m];
- —ionosphere-free linear combination of carrier-phase observations [m];
- s—number of satellites;
- —code- and carrier-phase observations for both frequencies [m];
- —carrier frequency [Hz];
- —geometrical range from the receiver to the antenna [m];
- —the vacuum speed of light [m/s];
- —satellite and receiver clock errors [s];
- —the signal path delay due to the neutral atmosphere [m];
- —phase ambiguity parameter in ionosphere-free combination [cyc.];
- —carrier-phase wavelength in ionosphere-free combination [m];
- —noise measurement in code- and carrier-phase observations [m];
- —vector of angular coefficients [.];
- —vector of corrections for the receiver’s position [m];
- /—code- and carrier-phase corrections for the receiver, satellite, and tidal effects in ionosphere-free combination [m].
- —original length of signal for i frequency [m];
- —integer phase ambiguity parameter;
- —code- and carrier-phase corrections for the receiver, satellite, and tidal effects for i-th frequency [m];
- —slant ionospheric delay [m].
2.2. Low-Cost GNSS Hardware
2.3. Butterworth Filter
- —the frequency response;
- n—order of the filter;
- —operating frequency of the circuit;
- —cut-off frequency;
- ε—maximum passband gain.
2.4. GNSS Data Processing
2.5. Field Work
2.6. Time-Series Variants
3. Results
3.1. GNSS Levelling
3.2. Displacement Detection
3.2.1. Impact of Selected Processing Parameters on Coordinate Time Series
3.2.2. Time-Series Analysis
3.2.3. Classification of Events
- Detected (DET.)—when displacement was simulated and a corresponding peak was detected by the algorithm;
- False alarm (F.A.)—when a peak was detected by the algorithm but there was no simulated displacement at this time;
- Undetected (UNDET.)—when the displacement was simulated, but it was not detected by the algorithm; this can be easily calculated by subtracting DET. from the total number of simulated displacements (20).
4. Summary
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Point Name | H (m) |
---|---|
WRO1 | 117.1331 |
WROC (measured) | 140.7275 |
WROC (catalog) | 140.7288 |
Source | Point | h [m] | H [m] | 1σ [mm] | N [m] |
---|---|---|---|---|---|
LGO | WRO1 | 157.2369 | 117.1460 | ±13 | 40.0909 |
BM_ROOF | 180.1167 | 140.0281 | ±6 | 40.0886 | |
BM_CP | 162.7319 | 122.6432 | ±3 | 40.0887 | |
POZGEO | WRO1 | 157.2250 | 117.1338 | ±11 | 40.0912 |
BM_ROOF | 180.1240 | 140.0358 | ±12 | 40.0882 | |
BM_CP | 162.7150 | 122.6268 | ±12 | 40.0882 | |
CSRS-PPP | WRO1 | 157.2710 | 117.1804 | ±18 | 40.0906 |
BM_ROOF | 180.1630 | 140.0747 | ±9 | 40.0883 | |
BM_CP | 162.7730 | 122.6846 | ±14 | 40.0884 | |
GNSS-WARP | WRO1 | 157.2612 | 117.1706 | ±6 | 40.0906 |
BM_ROOF | 180.1486 | 140.0603 | ±5 | 40.0883 | |
BM_CP | 162.7443 | 122.6559 | ±7 | 40.0884 |
Point | Height Type | 1st Survey [m] | 2nd Survey [m] | Mean [m] | N [m] |
---|---|---|---|---|---|
WRO1 WRO1 | Normal | 117.1840 | 117.1930 | 117.1890 | 40.0909 |
Ellipsoidal | 157.2830 | 157.2750 | 157.2790 | ||
BM_ROOF BM_ROOF | Normal | 140.0310 | 140.0470 | 140.0390 | 40.0891 |
Ellipsoidal | 180.1200 | 180.1360 | 180.1280 | ||
BM_CP BM_CP | Normal | 122.6480 | 122.6610 | 122.6550 | 40.0886 |
Ellipsoidal | 162.7368 | 162.7494 | 162.7430 |
1σ | 2σ | 3σ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
DET. | UNDET. | F.A. | DET. | UNDET. | F.A. | DET. | UNDET. | F.A. | ||
A | Number | 6 | 14 | 121 | 9 | 11 | 29 | 3 | 17 | 5 |
Ratio | 0.05 | 0.70 | 0.95 | 0.24 | 0.55 | 0.76 | 0.38 | 0.85 | 0.63 | |
B | Number | 12 | 8 | 191 | 16 | 4 | 73 | 10 | 10 | 14 |
Ratio | 0.06 | 0.40 | 0.94 | 0.18 | 0.20 | 0.82 | 0.42 | 0.50 | 0.58 | |
C | Number | 11 | 9 | 194 | 16 | 4 | 70 | 10 | 10 | 15 |
Ratio | 0.05 | 0.45 | 0.95 | 0.19 | 0.20 | 0.81 | 0.40 | 0.50 | 0.60 | |
D | Number | 16 | 4 | 164 | 12 | 8 | 44 | 7 | 13 | 6 |
Ratio | 0.09 | 0.20 | 0.91 | 0.21 | 0.40 | 0.79 | 0.54 | 0.65 | 0.46 | |
E | Number | 14 | 6 | 166 | 11 | 9 | 34 | 7 | 13 | 6 |
Ratio | 0.08 | 0.30 | 0.92 | 0.24 | 0.45 | 0.76 | 0.54 | 0.65 | 0.46 | |
F | Number | 7 | 13 | 123 | 5 | 15 | 30 | 1 | 19 | 9 |
Ratio | 0.05 | 0.65 | 0.95 | 0.14 | 0.75 | 0.86 | 0.10 | 0.95 | 0.90 | |
G | Number | 13 | 7 | 186 | 15 | 5 | 79 | 6 | 14 | 12 |
Ratio | 0.07 | 0.35 | 0.93 | 0.16 | 0.25 | 0.84 | 0.33 | 0.70 | 0.67 | |
H | Number | 13 | 7 | 193 | 16 | 4 | 79 | 7 | 13 | 13 |
Ratio | 0.06 | 0.35 | 0.94 | 0.17 | 0.20 | 0.83 | 0.35 | 0.65 | 0.65 | |
I | Number | 11 | 9 | 163 | 11 | 9 | 38 | 6 | 14 | 6 |
Ratio | 0.06 | 0.45 | 0.94 | 0.22 | 0.45 | 0.78 | 0.50 | 0.70 | 0.50 | |
J | Number | 9 | 11 | 163 | 12 | 8 | 42 | 6 | 14 | 10 |
Ratio | 0.05 | 0.55 | 0.95 | 0.22 | 0.40 | 0.78 | 0.38 | 0.70 | 0.63 |
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Maciejewska, A.; Lackowski, M.; Hadas, T.; Maciuk, K. The Real-Time Detection of Vertical Displacements by Low-Cost GNSS Receivers Using Precise Point Positioning. Sensors 2024, 24, 5599. https://doi.org/10.3390/s24175599
Maciejewska A, Lackowski M, Hadas T, Maciuk K. The Real-Time Detection of Vertical Displacements by Low-Cost GNSS Receivers Using Precise Point Positioning. Sensors. 2024; 24(17):5599. https://doi.org/10.3390/s24175599
Chicago/Turabian StyleMaciejewska, Aleksandra, Maciej Lackowski, Tomasz Hadas, and Kamil Maciuk. 2024. "The Real-Time Detection of Vertical Displacements by Low-Cost GNSS Receivers Using Precise Point Positioning" Sensors 24, no. 17: 5599. https://doi.org/10.3390/s24175599
APA StyleMaciejewska, A., Lackowski, M., Hadas, T., & Maciuk, K. (2024). The Real-Time Detection of Vertical Displacements by Low-Cost GNSS Receivers Using Precise Point Positioning. Sensors, 24(17), 5599. https://doi.org/10.3390/s24175599