Ellipsoidal height describes a point relative to a mathematical reference ellipsoid. Orthometric height describes it relative to a gravity-related vertical reference, represented through a geoid and its datum realization. For compatible references at the same point, the usual conversion is H = h − N: orthometric height H equals ellipsoidal height h minus the signed geoid height N. An RTK Fixed result does not select the required vertical datum or prove that this conversion has been applied correctly.
Before comparing a GNSS height with a site elevation, identify both the physical point and the height system. A difference can come from a different reference surface, an antenna-to-mark offset, a model mismatch or an actual positioning error. Those are different questions, even when the display labels every value “height.”
Three quantities, not three competing accuracy grades
GNSS positioning determines geometric coordinates. Converting Earth-centred coordinates to geodetic latitude, longitude and height produces an ellipsoidal height for the selected ellipsoid and reference frame. That height is not automatically the elevation used by a local survey. The NGS explanation of height relationships distinguishes the geometric height from the gravity-related height obtained through leveling and height-system definitions.
| Quantity | What it refers to | What the number alone does not establish |
|---|---|---|
| Ellipsoidal height, h | A point's geometric height relative to the reference ellipsoid | The required local vertical datum or terrain clearance |
| Geoid height or undulation, N | The signed separation used to relate the compatible ellipsoidal and orthometric systems at that location | A constant correction valid everywhere, or the antenna mounting height |
| Orthometric height, H | The point's height in the specified gravity-related vertical system | That the source coordinates, model and physical point were correctly identified |
The geoid is associated with a gravity equipotential surface close to global mean sea level; it is not the instantaneous water surface, terrain or the top of the antenna. EarthScope's geoid tutorial explains why the ellipsoid and geoid can be separated at the same location. “Above mean sea level” still needs an actual system or model definition for precise integration work.
Keep the sign when converting the height
Use the relationship h = H + N, or equivalently H = h − N, with all three quantities in the same length unit and with compatible references. N is signed: it is not an unsigned distance that should always be subtracted as a positive magnitude.
Hypothetical calculation, not a receiver test: a survey mark has h = 45.350 m in the specified ellipsoidal frame. Assume the appropriate model gives N = −30.200 m at that mark. Then:
H = 45.350 − (−30.200) = 75.550 m.
The orthometric value is larger here because N is negative. Using h + N instead would give 15.150 m, which is the wrong operation under the stated convention. Conversely, if a field already contains H = 75.550 m, subtracting the same N again gives 105.750 m: a double conversion, not a new GNSS observation.
These assumed numbers have no geographic location or named model attached. They demonstrate sign and processing order only. A model-derived value must come from the correct location and reference definitions; it cannot be taken from this example or borrowed from another site.
A geoid model has a reference contract
The conversion equation does not make arbitrary height systems compatible. A geoid or height-conversion model is tied to particular reference choices. NGS's technical notes on undulations identify the ellipsoidal reference system, selected equipotential surface and permanent-tide system as necessary definitions. The historical models in that note are not recommendations for a new project.
A concrete example is GEOID18. Its technical description specifies a connection between NAD 83(2011) epoch 2010.0 ellipsoidal heights and the NAVD 88 orthometric heights used for that realization. Its hybrid conversion surface incorporates benchmark information. That makes it more specific than a generic picture of a global gravity surface. This is a documented model example, not a claim that GEOID18 is the default for every region or current project.
Record the model name and version, geographic applicability, input reference frame and relevant epoch, output vertical datum, units and interpolation procedure. A successful lookup outside the intended region, or a model with a familiar name but a different reference contract, is not proof of a valid conversion. The NGS geoid service documentation, for example, makes location and model identity explicit inputs.
Changing horizontal coordinates between frames and converting height type are also different operations. The NGS NCAT documentation explicitly distinguishes its ellipsoidal-to-ellipsoidal and orthometric-to-orthometric transformations from a conversion between those height types. A tool accepting a height field does not necessarily perform the particular vertical operation your workflow requires.
Check the actual output field before applying a model
A GNSS receiver can output a height that has already undergone vertical processing. Do not assume every receiver message carries raw ellipsoidal height, or that a field called “altitude” uses the same convention across devices and software.
As a NovAtel OEM7 example, BESTPOS defines its hgt field as height above mean sea level and reports undulation separately. The undulation description also notes a datum-dependent vertical-shift contribution when a non-WGS84 datum is used. Its datum field has a further caveat for differential solutions: the actual solution can follow the base datum even when the reported label is WGS84. These are message-specific definitions, not ResiNav output fields or a universal GNSS format rule.
The integration consequence is practical: determine what was done before a value reached the host. A receiver, data collector, GIS import or processing package may apply a vertical operation. Preserve the original field values and metadata so that the host does not repeat it. Only reconstruct h from H and N when the message documentation and active configuration establish that relationship for those fields.
A reference-surface conversion does not move the antenna to the mark
Height type and physical reference point are separate. A position at an antenna reference point is not yet a position at the ground mark, even after conversion to the required vertical datum. Likewise, antenna phase-centre corrections do not identify the measured mounting distance.
The surveying and mobile-mapping guide explains ARP, antenna calibration and software height conventions. Its electrical and mechanical corrections should not be applied again merely because a geoid model is being used. For a vehicle or camera point that changes orientation, use the separate lever-arm geometry rather than treating a three-dimensional offset as a constant vertical subtraction.
For a static upright installation, a documented antenna-to-mark height reduction may be sufficient for that geometric step. A slant measurement, tilted pole or transformed platform point needs its actual geometry. The key is to know which point the value represents before comparing heights—not to apply every available correction to the same number.
Why Fixed and repeatability cannot resolve a datum mismatch
Integer ambiguity acceptance belongs to the carrier-phase positioning solution. Choosing a vertical datum belongs to coordinate delivery. A receiver can retain its accepted ambiguity solution while the host changes the model used to present the same position as an elevation.
Continue the hypothetical example, holding h = 45.350 m fixed. Replacing the assumed N = −30.200 m with N = −30.000 m changes the computed H from 75.550 m to 75.350 m: a −0.200 m change without any change to the held GNSS height. This isolates model-value sensitivity; it is not a prediction that two real models differ by 0.200 m.
Repeated occupations can preserve the same conversion mistake. The RTK Fixed verification guide covers why agreement and status are not independent coordinate truth. Here the additional diagnostic is to compare the unconverted height, the model separation and the delivered height as separate quantities. A stable offset suggests checks; its magnitude alone does not identify a wrong geoid, bad antenna height or incorrect integers.
Validate the delivered elevation, not just the subtraction
Check a suitable control point in the required vertical system, with known provenance and uncertainty, using the same physical point and units as the delivery. A height on a drawing, a fitted site calibration and a receiver's sea-level field are not automatically in that same system. Over a larger area, do not assume an offset fitted at one point captures spatial variation in the required transformation.
A model conversion also does not make uncertainty disappear. NGS's GEOID18 documentation distinguishes uncertainty of the fitted model surface from errors in the underlying datum and gravity model. A small receiver-reported height standard deviation is therefore not, by itself, the uncertainty of the final project elevation. Retain the relevant positioning, reference, model and point-reduction contributions rather than adding or combining them without an appropriate error model.
For a useful handover, state the physical point, input frame and epoch where relevant, output vertical datum, model/version, units, and where each correction was applied. Include an original output record and an independently checked conversion example. If the consumer actually needs height above ground, it additionally needs the applicable ground surface or range measurement; neither h nor H alone supplies that clearance.
The result is a clear separation of tasks: GNSS estimates coordinates, antenna geometry identifies the point, and a documented vertical operation supplies the required elevation reference. Better reception can support obtaining observations, but it does not choose or validate this height transformation.
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