How to define Pix4D outputs with respect to a Geoid model

 
Video: Watch the instructional video related to 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 easy whereas the geoid (right) is much more complex:

geoide.JPG

More information about the difference between both altitudes can be found in this article: Orthometric vs ellipsoidal height

 
Note: Nowadays, Global Positioning System (GPS) satellite-based technology is being 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 which 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:

geoidheight.JPG

More information can be found here: When to use the Geoid Height Above the Ellipsoid function?

  • Global geoid model

 

Along the years, international organizations have developed geoid models which cover the whole earth 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 better resolution to cover its 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 with 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 which are imported in Pix4D can be:
  • Image Geolocation: coordinates of the image position with respect to the WGS84 ellipsoid.
    • 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). As they are given with respect to the WGS84 ellipsoid, Pix4D allows applying a constant shift or a global geoid when importing the images. 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.

It doesn't really matter which approach to use to convert the ellipsoidal altitudes, either applying a constant shift or a global geoid will result in low absolute accuracy (a few meters).

 

  • 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 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. 

If there is not a local geoid model 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

 

As described in case 2. converting the GCPs altitude before importing them into Pix4D is enough to get the height with respect to the geoid. Therefore, the recommendation is to convert the heights before they are imported in Pix4D by using a precise local geoid model but a constant height and a global geoid could also be used although the accuracy would be lower. It is optional to convert the Image geolocation in this case.

 

  • Case 4. Precise Image geolocation and no GCPs

 

As there are not GCPs, the only way to get the result with respect to the geoid is by converting the Image geolocation altitude in beforehand. The recommendation is to convert the heights before they are imported in Pix4D by using a precise local geoid model but 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) 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) 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) 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) 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

 

 

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3 comments

  • Miguel Benguría arana

    Yo estoy en el caso de tener RTK, concretamente el Panthom 4 rtk, y tengo el problema de que no está cargado el geoide de  donde llevo a cabo mis trabajos. Creo que es algo obvio y necesario que Pix4D deje la opción de poder cargar el geoide local. No poner el geoide de cada parte del mundo pero sí que uno mismo pueda cargarlo. Si no no veo muy práctico lo del rtk, concretamente el del panthom que no te deja o no he adivinado cómo hacerlo con las coordenadas de las imágenes que me proporciona. 

    He hablado con mucha gente y está  de acuerdo conmigo en que Pix4d debería tener en cuenta ésta opción.

    Un saludo 

  • Marco (Pix4D)

    Hola Miguel,

    Aquí puede seleccionar el sistema de coordenadas de salida deseado:





    Si su sistema de coordenadas no aparece en la lista, puede agregar el archivo *.prj. 

    How-to-select-change-the-Image-GCP-Output-Coordinate-System!
    Select Image / GCP / Output Coordinate System

    Espero que esto ayude,

    Saludos

  • Miguel Benguría arana

    Hola Marco, no me refería al sistema de coordenadas, proyección UTM, mi pregunta era relativa al sistema de coordenadas vertical, es decir, a meter un geoide local. Lo mismo que se puede insertar un sistema de proyección, en mi caso wgs84 28N, que se pueda insertar el geoide, en este caso de las Islas Canarias. La opción que da pix4d son geoides globales y si se busca precisión no sirve en mi caso. Un saludo

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