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Development of a precise local quasigeoid model for the city of Krakow – QuasigeoidKR2019

Piotr Banasik
Piotr Banasik
, 
Kazimierz Bujakowski
Kazimierz Bujakowski
, 
Jacek Kudrys
Jacek Kudrys
 und 
Marcin Ligas
Marcin Ligas
   | 22. Mai 2020
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Article Category: Original Article
Online veröffentlicht: 22. Mai 2020
Seitenbereich: 25 - 31
Eingereicht: 27. März 2020
Akzeptiert: 03. Mai 2020
DOI: https://doi.org/10.2478/rgg-2020-0004
Schlüsselwörter
© 2020 Piotr Banasik et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Figure 1

Characteristics of quasigeoid models in Poland
Characteristics of quasigeoid models in Poland

Figure 2

Location of the measurement points over the Krakow area. Points measured in the first campaign – grey, points measured in second campaign – blue, additionally measured points – green
Location of the measurement points over the Krakow area. Points measured in the first campaign – grey, points measured in second campaign – blue, additionally measured points – green

Figure 3

Location of benchmarks over the Krakow area (1 – the primary base; 2 – detailed)
Location of benchmarks over the Krakow area (1 – the primary base; 2 – detailed)

Figure 4

Spatial distribution of GNSS/levelling points for the construction of a quasigeoid model for the Krakow area
Spatial distribution of GNSS/levelling points for the construction of a quasigeoid model for the Krakow area

Figure 5

Difference of height anomalies derived from the national model PL-geoid2011 and GPS/levelling-derived ones
Difference of height anomalies derived from the national model PL-geoid2011 and GPS/levelling-derived ones

Figure 6

Difference of height anomalies derived from the local model QuasigeoidKR2019 and GPS/levelling-derived ones
Difference of height anomalies derived from the local model QuasigeoidKR2019 and GPS/levelling-derived ones

Accuracy characteristics of the local quasigeoid model for the city of Krakow

Number of all points used to construct the model 66
Number of unknowns 4
Number of points removed 4
Final number of points 62
Residual standard deviation 0.0062 m
Mean absolute residual 0.0049 m
Median absolute residual 0.0046 m
Maximum absolute residual 0.0140 m
Coefficient of determination 0.8117
10 largest absolute residuals [m] 0.0086, 0.0092, 0.0097, 0.0097, 0.0098, 0.0103, 0.0105, 0.0121, 0.0131, 0.0140
Results of cross-validation (Leave-one-out)
Root mean square error 0.0064 m
Mean absolute error 0.0052 m
Median absolute error 0.0048 m
Maximum absolute difference 0.0144 m
Results of Monte Carlo cross-validation (1000-fold removal of 20% of points)
Root mean square error 0.0064 m
Mean absolute error 0.0053 m
Median absolute error 0.0050 m
Maximum absolute difference 0.0159 m

Summary statistics of absolute differences between models and GNSS/Levelling derived height anomalies

Characteristics National model PL-geoid2011 [m] Local model QuasigeoidKR2019 [m]
Minimum 0.000 0.000
First Quartile 0.007 0.002
Median 0.015 0.004
Third Quartile 0.024 0.007
Maximum 0.044 0.014
Mean absolute difference 0.016 0.005

First survey campaign – sessions 1–17. Point selected for second measurement are in bold. Second measurement – sessions 18–24 (shaded grey)

Session Points
1 4102 5201 5301
2 6301 6401 7501 7601 6201
3 3803 4902 5001 5103
4 1402 2501 2603 2701
5 5402 6503 6601 7701 7801
6 2806 3901 4001 BA00
7 0501 1501 1603 1702
8 1801 1902 2902 3002
9 3104 4204 4303 4401
10 4503 4603 5701
11 4700 5802 5901 7002
12 6904 8201 8300
13 6801 8001 8103
14 5501 5601 6704
15 9102 9301 9402
16 9604 5651 9501
17 9201 9701 9901 9902
18 6252 6352 6451 7552
19 3853 4952 5051 BA50 BA51
20 5351 6553 6754 7852
21 2653 2751 2856 4051
22 905A 905B 0551 1851
23 3154 4553 5951
24 5753 6851 8051 8251

Post-processing variants

Software Solution
Leica Geo Office Network solution, ASG-EUPOS reference stations (KRA1, PROS)
GNSS Solutions Network solution, one ASG-EUPOS reference station (KRA1 or PROS)
AUSPOS (internet service) https://www.ga.gov.au Network solution, EPN/IGS reference stations
MagicGNSS (internet service) https://magicgnss.gmv.com Precise Point Positioning
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