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Altitude and Vertical Coordinate System:
here.
The Z coordinate (altitude) can be given with respect to an ellipsoid (ellipsoidal height) or with respect to a geoid (orthometric or geoid height). Both geoid and ellipsoid are mathematically defined surfaces; the ellipsoid (left) is relatively simple, whereas the geoid (right) is much more complex:
More information about the difference between both altitudes can be found in this article: Orthometric vs ellipsoidal height
Note: Nowadays, Global Navigation Satellite System (GNSS), a satellite-based technology, is widely used for surveying throughout the world, and it provides the altitude with respect to the WGS84 ellipsoid, that is to say, ellipsoidal height (not orthometric).
In order to convert from an ellipsoidal height into geoid or orthometric height, there are three different approaches that could be used depending on the required accuracy:
- Constant height shift
Recommended for small areas where geoid and ellipsoid can be considered parallel in a small portion of terrain. In case of a large area or significant variations between the ellipsoid and geoid, this approach will introduce inaccuracies.
In order to define the height shift in Pix4D, the Geoid Height Above the Ellipsoid function can be used:
More information can be found here: When to use the Geoid Height Above the Ellipsoid function?
- Global geoid model
Over the years, international organizations have developed geoid models which cover the whole earth's surface. The expected accuracy is around 2-3 meters depending on the area and the geoid model. Pix4D supports the EGM84, EGM96, and EGM2008 global models:
- Local geoid model
In order to improve the accuracy of the global models, some countries established local geoid models with a better resolution to cover their territory. Typically, the local geoid models in different formats (ASCII, .grd, .tiff, etc.) and the transformation tools are provided by the national mapping institutions. Using a local geoid model will provide the best accuracy reaching up to a few cms.
Important: For now, Pix4D does not support the use of local geoid models. Only a global geoid model or a constant shift can be applied.
Therefore, whenever ellipsoidal coordinates are given, the recommendation is to convert them into orthometric by using a precise local geoid model in a third-party application.
How does it work within Pix4D?
There are four different cases.
Note: The coordinates imported in Pix4D can be:
- Image Geolocation:
- Standard image geolocation. Most of the drones in the market provide image geolocation which has an accuracy of a few meters.
- Precise image geolocation (RTK/PPK drones). They can reach up to a few cms accuracy.
- GCPs (Ground Control Points). They are usually measured with high accuracy (2-5 cm)
- Case 1. Standard image geolocation and no GCPs
The accuracy of the project will be the same as the image geolocation (a few meters). Pix4D allows applying a constant shift or selecting a global geoid for the output vertical coordinate system. If that is applied, the result will be given with respect to the geoid, but as the image geolocation absolute accuracy is not very high, the absolute accuracy will not be high either.
- Case 2. Standard image geolocation and GCPs
When using GCPs, Pix4D software will use them for georeferencing the project. Therefore if they are already given in orthometric (geoid) height, the result will also be given in orthometric height even if the image geolocation is given with respect to the ellipsoid.
As the GCPs are usually measured with a GPS device, the measured height will be ellipsoidal. The recommendation is to convert the heights before they are imported in Pix4D by using a precise local geoid model. Some GPS devices already have the geoid models preloaded, and the transformation to the orthometric (geoid) heights is done automatically.
If the local geoid model is not available, the GCPs can be imported into Pix4D, and a constant shift or global geoid should be applied. If this is the case, the result in Z will not be precise as any of these conversions are not precise either, so the expected accuracy will be similar to the previous case.
- Case 3. Precise image geolocation and GCPs
The recommendation is to convert the heights of the image geolocation and GCPs before importing them into Pix4D by using a precise local geoid model. A constant height and a global geoid could also be used, although the accuracy would be lower.
- Case 4. Precise image geolocation and no GCPs
As there are no GCPs, the only way to get the result with respect to the geoid is by converting the image geolocation altitude beforehand using a precise local geoid model. A constant height and a global geoid could also be used, although the accuracy would be lower.
What to do to get the result wrt the geoid
Orthometric height absolute accuracy
1. Standard image geolocation and no GCPs
Convert image geolocation by:
a) applying a constant shift or
b) using a global geoid model
Same as image geolocation (a few meters)
2. Standard image geolocation and GCPs
Convert GCPs by:
a) applying a local geoid model beforehand or
b) applying a constant shift or
c) using a global model
a) same as GCP accuracy (2-3 cms usually)
b) (*)
c) 2-3 m
3. Precise image geolocation and GCPs
Convert GCPs and image geolocation (optionally) by:
a) applying a local geoid model beforehand or
b) applying a constant shift or
c) using a global model
a) same as GCP accuracy (2-3 cms usually)
b) (*)
c) 2-3 m
4. Precise image geolocation and no GCPs
Convert image geolocation by:
a) applying a local geoid model beforehand or
b) applying a constant shift or
c) using a global model
a) same as image geolocation accuracy (2-10 cms usually)
b) (*)
c) 2-3 m
(*) Depends on how large the project is and where is located
This article refers to vertical coordinate systems. It is also recommended to read the following Community post about 2D coordinate systems transformations: Horizontal grid corrections and transformations.