Dylan,
this is a Linear Referencing Toolsapplication involving the "Locate Features Along Routes" tool.
First you need to set up your polyline FC with a field that identifies the individual trails consistently then run the Create Routes tool on them with the trail name field as the Route Identifier Field, Measure Source as Length and Coordinate Priority as the position of the trail head relative to the trails.
This creates a new feature class that is aware of its length, or "M" value, at any point.
Now you intersect that with the signpost GPS points using the Locate Features Along Routes tool.
Again you will need to have an identifier field in your GPS point FC that shows the trail name with exactly the same syntax as in the Route Identifier field in your route FC.
One caution when using the tool: you may have to play with the "search radius" unless your signpost points are "snapped" to the polyline that form the routes. Or you could also set the precision of your FCs to a value like 5 m. This is because your GPS precision will not show the points as intersecting the polylines if you use the default 0.0001 m precision even if they were taken with a top of the line RTK unit rather than a Garmin Map 60 CSx or whatever.
Also make sure nothing in the point or route file is left selected or you will get only a partial output.
Open the Output Event Table and look under the "MEAS" field for the distances of the GPS points along the trails. The output Event Table can be exported as a new FC that records the trail sign distances.
Good luck,
