reference frame. When representing positions relative to the Earth, it is often most convenient to represent vertical position
(height or depth) separately, and to use some other parameters to represent horizontal position.
There are also several applications where only the horizontal position is of interest, this might e.g. be the case for ships and ground vehicles/cars.
It is a type of geographic coordinate system.
There are several options for horizontal position representations, each with different properties which makes them appropriate for different applications. Latitude/longitude and UTM are common horizontal position representations.
The horizontal position has two
singularities
, and thus three parameters are required for the horizontal position to avoid this.
The most common horizontal position representation is latitude and longitude. The parameters are intuitive and well known, and are thus suited for communicating a position to humans, e.g. using a position plot.
However, latitude and longitude should be used with care in mathematical expressions (including calculations in computer programs). The main reason is the
, which makes longitude undefined at these points. Also near the poles the latitude/longitude grid is highly non-linear, and several errors may occur in calculations that are sufficiently accurate on other locations.
[1]
Another problematic area is the
F-22 Raptor fighter aircraft while crossing this meridian.[2]
Earth centered earth fixed coordinate system. It behaves the same at all Earth positions, and it holds the mathematical one-to-one property. The vector formulation makes it possible to use standard 3D vector algebra
, and thus n-vector is well-suited for mathematical calculations, e.g. adding, subtracting, interpolating and averaging positions.
Using three parameters, n-vector is inconvenient for communicating a position directly to humans and before showing a position plot, a conversion to latitude/longitude might be needed.
Local flat Earth assumption
Main article:
Local tangent plane
When carrying out several calculations within a limited area, a
For small areas a local coordinate system can be convenient for relative positioning, but with increasing (horizontal) distances, errors will increase and repositioning of the
tangent point may be required. The alignment along the north and east directions is not possible at the Poles
, and near the Poles these directions might have significant errors (here the linearization is valid only in a very small area).
Grid reference system
Main article:
Grid reference system
Instead of one local Cartesian grid, that needs to be repositioned as the position of interest moves, a fixed set of
UTM is widely used, and the coordinates approximately corresponds to meters north and east. However, as a set of map-projections it has inherent
distortions
, and thus most calculations based on UTM will not be exact. The crossing of zones gives additional complexity.
Comparison
When deciding which parameters to use for representing position in a specific application, there are several properties that should be considered. The following table gives a summary of what to consider.
