# Latvian quasi-geoid model

As of December 1, 2014, a new quasi-geoid model LV′14 is available, which has been developed by the Latvian Geospatial Information Agency (LGIA). The quasi-geoid model LV′14 has been issued to all distributors of instruments and computer software.

Validation report of the quasi-geoid model LV′14

When determining the normal height in the implementation of the European Vertical Reference System (hereinafter - EVRS) for the territory of Latvia with global positioning for the performance of state and local government functions, a validated quasi-geoid model is used.

The purpose of the quasi-geoid model validation is to determine the deviation of the altitude anomalies model final results to matched points of the leveling and global positioning network, which implements the altitude and coordinate reference system in the field, thus judging the model final certainty in a particular altitude reference system. Combined global positioning and leveling points with a known geodetic (ellipsoidal) and normal height are used for validation, from which the height anomaly is calculated.

The validation process can be divided into four main stages:

- cameral selection of possible connected and validation points;
- performing measurements at connected and validation points;
- measurement processing;
- comparison of the final result with the value to be validated.

Selection of connected and validated points

The connected points with the normal height in the implementation of EVRS for the territory of Latvia are the 1st class points of the leveling network.

The validated points with the normal height in the implementation of the EVRS for the territory of Latvia are the 1st and 2nd class points of the leveling network.

In the period from 2010 to August 2014, LGIA accumulated global positioning data at the 1st and 2nd class points of the leveling network, creating connected points for modeling and validation of the quasi-geoid model LV′14.. 84 points were selected from the measured points and used as connected points for quasi-geoid modeling.

In addition, in 2014, the LGIA selected 1st and 2nd class points of the leveling network or outcrops to be created in their immediate vicinity, in which real-time measurements could be performed in the system of permanent global positioning base stations “Latvian Positioning System”.

Measurements at connected and validation points

At the connected 1st class points of the leveling network, global positioning measurements were implemented in post-processing mode, accumulating data for 4 hours. The 84 points used for connecting are in the file GNSS_N1mod.dat.

At the leveling network 1st and 2nd class points used for validation, positioning measurements were performed in post-processing mode, accumulating data for 4 hours. 1st class 28 points that were not used in the modeling but were used only for validation are in the file GNSS_N1.dat.

The 2nd leveling class 30 points used in the validation and three LatPos base stations determined by geometric-trigonometric leveling, which were not used in modeling and measured from 2013 to 2014, are in the file GNSS_N2_LatPos.dat.

Global positioning measurements in real time in the LatPos system were performed in accordance with the “Terms of Use of the Permanent Global Positioning Base Station System “Latvian Positioning System””, ie 10 sessions, 10 measurements in each session with an interval of 1 second. The nearest station solution is selected.

At 7 points, real-time observations were made on outriggers approximately 80 m away. For the outriggers, the normal elevation is determined by geometric leveling in the middle according to the accuracy of 1st leveling class, and the height is determined against the nearest leveling mark.. Real-time validation measurements in the Latvian permanent base station system were performed in August 2014. The 69 points used for validation are in the file RTK_N1_N2.dat.

Measurement processing

For the connected and validation points, for which the geodetic height was determined by collecting data for 4 hours in the post-processing mode, the Bernese Software 5.2 program with precise satellite ephemeris and following the principle of independent vectors was used for global positioning calculations.

For validation points for which the geodetic height was determined in real time in the LatPos system in accordance with the “Terms of Use of the Permanent Global Positioning Base Station System “Latvian Positioning System” - 10 times in 10 seconds with the nearest station solution - geodetic height was determined as the average of all measurements gross or systematic deviations.

Comparison of the final result with the validated value

Validation of the quasi-geoid model is performed by comparing the empirical height anomalies of the model with those obtained by field measurements. Elevation anomalies are values used by geodetic programs to transition from geodetic (ellipsoidal) to normal elevation in both global positioning tools and data calculation programs.

When assessing the compatibility of a quasi-geoid with an altitude reference system, it should be taken into account that the altitude system, the connected and validation points, and the global positioning measurements are also realized with certainty. The obtained normal heights for the combined and validation points shall be evaluated at least five times better than the obtained geodetic height, therefore their influence on the final assessment shall be excluded.

The difference obtained in the comparison can be assessed as the total deviation from the true value or the total error. To obtain the standard deviation of one sigma, it is necessary to divide it by three.

At the 1st and 2nd leveling network class points used for validation, where the global positioning was performed by post-processing, the standard deviation of the height anomalies of the quasi-geoid model against the measured points within one sigma is up to 14 mm.

The maximum values of the height anomaly difference at the finishing points are up to 53 mm.

At the leveling points of the leveling network used for validation, where the global positioning is performed by real-time measurements, the maximum value of the standard deviation within one sigma is up to 22 mm. Elevation anomalies differences are up to 65 mm.

When performing real-time global positioning measurements, special attention should be paid to scattering of observations, exclusion of gross errors, jumps in the series of observations, as well as control observations.

The standard deviations obtained in the validation of the quasi-geoid model LV′14 in post-processing and real mode show that the accuracy of the quasi-geoid model LV′14 ensures the acquisition of basic geospatial data for the performance of state or municipal functions and tasks.