Linear Positioning / referencing

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Linear Positioning / referencing

Linear Referencing Systems (LRS) are widely used in the transportation world. They allow specifying positions along linear elements by using distances measured along the element (possibly with a lateral and horizontal offset), not by using classical 2D or 3D coordinating systems (CRS).

Locating an object with linear coordinates makes sense for various reasons. First of all, a large amount of information is stored in databases from legacy systems, anterior to geographical information systems which are specifically designed to deal with classical CRS. Knowing where an object is located along a route or a pipeline is sufficient to use the data from those databases, and can be seen as an integration mean for data coming from different sources.

It is even sometimes more interesting to have a linear position than a spatial position. Knowing that you have train stopped at about the kilometre 45 on the Line 36 Track A is better than having a potentially more accurate GPS position, which does neither tell without ambiguity on which line nor track it stands.

Norms

Linear Referencing is the object of the European Norm EN19148:2012.

The RailTopoModel® follows the same principles, but uses a simplified version of the model as a lot of cases foreseen in the norm are not encountered in the railways world.

Axis

A linear referencing system has an axis along which the measures are done. The axis can be any linear entity, a track segment or a whole line. It does not need to have geometry as knowing its length is enough to use an LRS.

Referencing Methods

A Linear Referencing System may use several methods to describe a position along an axis:

  • Absolute : the position is specified by giving the distance starting at the beginning of the axis (with an eventual offset)

ReferencingMethodAbsolute

Its main disadvantage is the fact that the whole length of the axis is taken into account when measuring. It means :

  1. that the field workers always have to begin measurement at the start of the axis. It makes it unpractical for long axes,
  2. that each change happening in the axis before the referenced object changes the coordinate of the measured point.

It is thus only suitable for short axes, or axes which are very stable in the scope of the measurement.

  • Relative : The position is specified by giving the distance starting from an element (referent) whose position is known.

ReferencingMethodRelative

This is the most commonly used in railways, with mileposts as referents. Amongst its advantages is the stability of the coordinate which is now independent from works or axis changes happening before the referent, unless the change also affects the referent.
It is also more practical for the field workers as the measurement only has to start at the referent.
On the other hand, it forces to maintain a whole set of referents, ensuring they never move, and recalculating their position at each infrastructure change.
It makes it most suitable for long axes, such as lines, but poorly adapted to short segments (work reservations or sidings).

While it is possible to measure in both directions, (km x + y meters or km x+1 – z meters), the former method is the most widely used.

It is also the most suited to store long term information, because of the stability of the coordinates. However, it is very poorly suited to calculations as true distances are difficult to deduce from the coordinates. Both methods can include lateral or vertical offsets.

Expression of the distance

The distance from the start of the measure (be it the start of the axis or the referent) can be expressed in several ways.

  • In metres (or miles, or any unit of choice)
  • Relative to the length of the element
    • As a percentage of the element (0…100 %)
    • Normalized (0…1). 75 % being expressed as 0.75
  • Hybrid : as a percentage of the length between two successive referents
Hybrid expression

The major problem with the relative method of linear referencing is the fact that it cannot be stored as a number when the system has mileage anomalies.
As the distance between two successive referents may be more than one kilometre (or 1000 units), the coordinate needs two fields to be stored. On top of that, not all reference points have a numeric name, a referent 12A might be inserted when lengthening the track between the mileposts 12 and 13.

The hybrid method aims to deal with this issue by assigning a fixed coordinate to each successive referent (usually a multiple of 1000) and adding the percentage of the distance between the two referents.
While it doesn’t allow true distance measurement, it keeps the sequence of the objects.

For example, assuming the distance between the kilometre post 12 and 13 is 1200m and that the object needing to be located is at km 12 + 1050m,

  • Kilometre post 12 : coordinate 12000
  • Kilometre post 13 : coordinate 13000
    Object coordinate : coordinate of the referent (12000)+ percentage of the distance of the object regarding the distance between the referents (1050/1200) multiplied by the difference of coordinates between the two successive referents (1000)
  • Object coordinate : 12000 + (1050/1200)*1000 = 12875, which is a number that can be stored in one field and on which operations may be made.









What you should have learned

  • Coordinate reference systems are (besides intrinsic and conventional linear referencing) the third option to define positions/locations in the RailTopoModel®.
  • All geodetic coordinate reference systems can be defined by a unique identifier: the EPSG code.
  • RailTopoModel® implementation shall follow concepts of the existing international standard GML.
  • Coordinate reference systems can also be used to define schematic coordinates as they are used in terms of screen coordinates.
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Section Structure Positioning Object positioning in the network
Subection Coordinate positioning Linear Positioning / referencing Return to Positioning