# Multiple linear referencing methods

## What is a linear referencing method?

A linear referencing method, or LRM, is a means of determining locations along linear features. A location is a distance along a route from a known point of reference. Locations are relative to the length of the route and may change positionally when the route changes. Positions, on the other hand, are discrete points on the ground and have no direct relationship to a route. Positions do not change when the route changes. LRMs must consider both location and position when referencing assets along a highway.

## Types of linear referencing methods

There are two basic types of LRMs: interpolative and referent. All other LRMs are derivatives of these two.

### Interpolative LRM

Interpolative LRMs determine location by interpolating between two known locations along a route. To determine an interpolated location, the distance between the two known locations is calculated and the target location is represented as a proportion between them. The proportion value is then converted to the actual measure value:

```m = m1 + (m2-m1) * p
where p is the proportional location of m between m1 and m2```

### Referent LRM

Referent LRMs determine location by measuring a discrete distance along a route from an existing known location, called a referent. Referents can be geographic coordinates, calibration points, intersections, other assets in the database, or specific m-value locations determined from interpolative LRMs.

The important thing to note about referent LRMs is that the distance from a referent, such as a milepost, in an increasing direction will not always provide the same location as the inverse proportional distance from the next referent in decreasing direction. This is because the referents may have different nominal distances than the actual measured distance between them. A common example is when mileposts are used as referents. Mileposts are rarely exactly one mile apart as they may be shifted at bridge locations or intersections or may be not be adjusted when highway alignments change the physical length of the roadway. Therefore, a distance of 0.6 miles beyond milepost 3 is not necessarily the same as a distance of 0.4 miles before milepost 4. Because of this potential discrepancy, referent LRMs are almost always described as referent plus or minus distance (for example, 3+0.6 or 4-0.4). In many cases, the measure of the referent is omitted and the unique identifier or the name of the referent is used instead (for example, Exit 4 - 0.4). The location of the referent must therefore be determined before the location of the target can be derived.

## How are linear referencing methods used?

Typically, an LRM is used to locate an asset or incident along a highway in a way that is meaningful to a particular group of users. This is similar to the way addresses are used to locate homes or businesses. While global positioning systems (GPS) are virtually ubiquitous, x,y coordinates or maps are not always the easiest way to communicate location. Highway engineers may use a map or GPS driving directions to travel to a construction site, but once there they use a linear location along the highway that is relative to the starting point of the project when they want to identify traffic control devices or pavement sections that will be impacted by construction. State police often use a distance from a milepost or a distance from the GPS location of their cruiser when they report a crash or other incident.

## Configuring linear referencing methods in Esri Roads and Highways

LRMs are managed in calibration point features and LRS Networks. There is a one-to-one relationship between LRMs and LRS Networks. An LRS Network is a collection of routes in the advanced linear referencing system (ALRS). Each individual business unit is likely to have its own LRS Network that depicts how its highways are subdivided and measured. Calibration points are used to assign measure values to routes within an LRS Network.

Calibration points must have a route identifier, a measure value, and a network identifier. The network identifier indicates which LRS Network each calibration point feature will be associated with. Calibration points, as with all elements that participate in the ALRS, must also have from and to dates.

The network identifier relates to a domain in the geodatabase, called dLRSNetworks. This domain is created for you when you create an LRS. It is not populated with coded values until you begin adding networks. The coded values are entered in the order in which the networks are added.

## Assigning linear referencing methods to networks

Each LRS Network may have one and only one LRM. Therefore, LRS Network is, in a way, synonymous with LRM. To assign an LRM to a network, you need only create the LRS Network and specify its units of measure. The LRSNetworkId is populated automatically in the dLRSNetworks coded value domain.

## Assigning linear referencing methods to calibration points

Assigning linear referencing methods to calibration points can be somewhat trickier. The process can seem unwieldy when attempting to populate a massive enterprise database with multiple LRMs. It may seem like a bit of a chicken and egg problem. To calibrate a route in an LRS Network, you must have calibration points. Each of these calibration points must contain an attribute value that indicates which network they are intended to calibrate. The attribute value must be populated before the route can be calibrated. But how do you know what value to populate in the calibration point if your networks have yet to be created?

The simple solution is to create your networks and calibration points in sequence. Rather than trying to load all calibration points at once and then populating the network IDs individually, first create a network, then load only the calibration points for that network, and populate the calibration point network IDs with the next sequential network ID. If you are unsure of the network ID for a given LRM, simply open the properties of the geodatabase, click the Domains tab, and review the coded values of the dLRSNetworks domain.

## Assigning linear referencing methods to events

Assigning linear referencing methods to events is very straightforward. Like networks, events can have one and only one LRM. To locate an event on a route, you must have a route reference and a measure value (two measure values if it is a line event). The route reference and measure values must have context to be meaningful to the user or display in the proper location along a highway. The LRS Network provides that context. There is a hierarchical relationship between events, networks, and linear referencing systems. An LRS contains LRS Networks. Each LRS Network may have multiple event layers associated with it. An event layer can be associated with one and only one LRS Network. Therefore, to create an event layer, you must add it to an LRS Network. The relationship between the event layer and the network it belongs to is explicit. Because the LRS knows about all the networks within it, it is possible to display multiple event layers from a variety of networks in the same location on the same map.

12/19/2012