Hi Martin,
If my understanding is correct, your GCPs have been measured in WGS84 UTM Zone 32N (EPSG 32632) and Deutsches Haupthöhennetz 2016 (EPSG 7837).
You need to define the correct coordinate system of the GCPs in Pix4D, otherwise they will be wrongly located horizontally and/or vertically. These are the ways to define DHHN2016 heights:
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you could provide the offset between the desired datum and the ellipsoid of the selected horizontal coordinate system (WGS84). For this, you should know the shift/offset between the current vertical coordinate system and the target vertical coordinate system (DHHN2016). This shift can be added in the Geoid Height Above XXX Ellipsoid option. It might be difficult to know this shift. Even if you know it, it will only be an approximation as to convert from one system to the other, just one shift is not enough. Therefore, the vertical coordinates will not have everywhere the same accuracy.
You can find more information about when to use the Geoid Above the Ellipsoid Function here: When to use the Geoid Height Above the Ellipsoid Function?According to this website (see source here), the DHHN2016 elevations don’t seem to be parallel with the ellipsoid elevations (see figure below). However, a local land surveyor might know much more about the mathematical approximation of this vertical reference system, because I am not an expert.
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you could select the option Arbitrary for the vertical coordinate system of the outputs and the GCPs, then import GCPs with coordinates in the coordinate system you specified. In this case, the software will respect the GCPs values and will try to fit the model as well as possible to the GCPs. Then, all your outputs will still be in an arbitrary reference system but this system will be based on the system defined by the GCPs (even if the name DHHN2016 is replaced by Arbitrary). Since you have GCPs in DHHN2016, this second option is the most suitable for you. To check the accuracy of this method and see if it is suitable for your purposes, you could possibly try to run a project setting the vertical coordinate system of both the GCPs and the outputs to Arbitrary and using checkpoints. The checkpoints assess the accuracy of the model.
Cheers,
Teodora