geo URI scheme

1. Ocean
2. Reference ellipsoid
3. Local plumb line
4. Continent
5. Geoid

The syntax of the Geo UI defines coordinates as coordinates = coord-a "," coord-b [ "," coord-c ], where coord-c is optional. The semantic of coord-c for WGS-84 is altitude (specifically the "ground elevation", relative to the current geoid – Earth Gravitational Model – attached to WGS84),[5] and the concept is extended for other coordinates (of non-default CRS).

The RFC explains that "... undefined <altitude> MAY assume that the URI refers to the respective location on Earth's physical surface." However, "... an <altitude> value of 0 MUST NOT be mistaken to refer to 'ground elevation'".[6]

In other words, when an altitude is defined, the measurement is done relative to the geoid (#5; black line in the image), a surface defined by Earth's gravity approximating the mean sea level. When it is undefined, the elevation is assumed to be the altitude of the latitude-longitude point, that is its height (or negative depth) relative to the geoid (i.e. "ground elevation"). A point with a measure "altitude=0" is, however, not to be confused with an undefined value: it refers to an altitude of 0 meters above the geoid.

The use of a geoid stands in contrast to GeoJSON, which uses direct ellipsoid height.[7]

Facets of the uncertainty. According to ISO 5725-1: accuracy is the proximity of measurement results to the true value; precision is the degree to which repeated (or reproducible) measurements under unchanged conditions show the same results.

Remembering the example above,

geo:37.786971,-122.399677;u=35

The u=35 part informs the uncertainty. As will be showed, geometrically the uncertainty is a disc of radius u in turn of the point of the geo URI.

Geo URI is not about exact abstract positions, strictly it is a location estimate, and we can interpret it (from RFC 5870 and RFC 5491) as the approximate physical position of an object in the Earth's surface.

The RFC 5870 does not formalize the use of the "uncertainty" term. So, in a coarse-statistical or any non-statistical numerical analysis, the GeoURI uncertainty is a condition number. The statistical meaning is implicit, come from the references of the RFC: the only normative reference with something about uncertainty is the RFC 5491 (section 5). The main informative reference, ISO 6709:2008, not use the term "uncertainty", but use the terms "accuracy" and "precision", which are uncertainty facets and can be interpreted in accordance with ISO 5725-1 (illustrated).

Putting all together, adopting these clues, the usual statistical assumptions, and the explicit definitions of the RFC, we obtain the Geo URI's uncertainty mathematical properties:

1. uncertainty is symmetric: the RFC is explicit, and we can understand it as valid simplification hypothesis. "The single uncertainty value is applied to all dimensions given in the URI" (section 3.4.3). Results in a spherical volume around the point (or a disk by 2D projection).
   By RFC 5491 "locations are expressed as a point (...) and an area or volume of uncertainty around the point".
   • Using RFC 5491, we can suppose that "It is RECOMMENDED that uncertainty is expressed at a confidence of 95% or higher". Therefore, the uncertainty is two standard deviations, 2σ, and it is the radius of the disk that represents uncertainty geometrically.
2. fixed measure unit: the RFC obligate the use of meters as uncertainty measure units, even when coordinates (CRS) use other (like default that is decimal degrees). It is a semantic and a conversion problem: the
3. Gaussian error model: RFC say nothing, we interpreting the phrases "amount of uncertainty in the location" and "the uncertainty with which the identified location of the subject is known", all in the context of the normative reference, RFC 5491 (and the informative references like ISO 6709:2008).
   • adopting standard error model: the model of the most common descriptive statistics modeling.
   • It is imposed, is independent of selection process of uncertainty description, there are no other choices.
4. total uncertainty: it is only one parameter representing "all uncertainty", the uncertainty in the spatial measure and uncertainty about object definition or object's center. It is a sum of random variables. There is no simplification hypothesis defined to reduce it to a one-variable model.

Imagining the location of an ant colony to illustrate:

• the colony is a 3D object at the (exactly) the Terrain surface, so at precise altitude (approximated to a zero uncertainty measure).
• the 3D object has some consensual definition, but it is not precise, so, its uncertainty can not be neglected. This lack of precision can be about the fact that the anthill is hidden under the ground (it is an "estimated object"), or the formal definition of its delimitation, etc.[8] This kind of uncertainty has no correlation with the location (e.g. GPS) uncertainty measure.
  • the disk representing the anthill (as uncertainty of the object) is modeled as 2σ to be a 95% of confidence area.
• the point is a GPS location measure, that is, the "center" of the projection of the 3D object in the 2D surface.

The total uncertainty is the sum of GPS error and object-definition error. The latitude and longitude GPS errors need to be simplified (to a disk) and converted into meters. If the errors were inferred from a different model, they need to be converted to the Gaussian model.