How to calculate 'off track' error from GPS data?

Question

I'd like to analyse navigational accuracy, comparing planned transects with the actual track flown from GPS data.

For example, the planned transects below (green) don't match perfectly with the actual flown (blue) - for the areas adjacent to the transects, what is the average error (distance), IGNORING the bits beyond the ends of each transect?

The planned transects are lines, typically only with start and end nodes. The tracks are from GPX files and may be made of many, many nodes - but may only have a few nodes recorded when the aircraft is flying particularly straight.

I'd like to use QGIS. One thought was to use the v.to.points tool from GRASS in the Processing toolbox to split each transect into points of, say, 50m spacing, and determine the nearest distance to the track for each point (then average them).

Is there, perhaps, a better way of calculating average distance than splitting the lines into individual points?

Answer 1

From the above example, I suggest that you

1. Create points along the green lines at a regular interval
2. Get the perpendicular distance from those points to the blue line and, finally,
3. Compute the average error based on those distances.

Note that you could reject points that are too far (above a given tolerance for GPS worst precision) due to the absence of blue line in front of a green line (this does not happen on your drawing, but it could be an issue).

For the first and the second step, there are two excellent answers (both by gene) here for step 1 and here for step 2. The last step shouldn't be a problem for you (using postgis, or group stats plugin, or python...).

Alternatively, you can draw the perpendicular line for each end point of the green line. Then you build an area from you set of lines (e.g. with GRASS), then you divide your area by the length of the green lines => this gives you the average absolute error.

Answer 2

I think Hausdorff distance may be what your looking for. It's basically a measure of how similar two geometries are.

General steps to apply it to this problem:

1. Find the closest point on the track to beginning and end of each planned segment.
2. divide the track into segments between these sets of points.
3. Calculate the Hausdorff distance between the planned segment and the closest segment.

Your question said qgis, but the bounty says any FOSS solution, so im going for PostGIS:

SELECT ST_HausdorffDistance(
  (SELECT geometry FROM segments WHERE fid=1),
  ST_Line_Substring(geometry,
        ST_Line_Locate_Point(geometry, (select st_pointn(geometry, 1) from segments)), 
        ST_Line_Locate_Point(geometry, (select st_pointn(geometry, ST_NPoints(geometry)) from segments))
  )
)
FROM tracks WHERE ogc_fid=1

Answer 3

The following workflow is for QGIS and will give you the mean distance from the route for each transect in metres. I'm assuming the data will be using a projection in metres.

Buffer your transects and route, for example, by 1m with Vector > Geoprocessing Tools > Buffer(s). You now have two polygon layers - the transects and the route. Give the route polygon a value of 1 in its attribute table. Now covert the route polygon to a raster with Raster > Conversion > Rasterize. Choose the route polygon as the input file, and the attribute field to the whatever you gave the value of 1. Set the raster resolution in map units per pixel to 1 metre and create your raster.

Now run Raster > Analysis > Proximity (Raster Distance) on this new 'route' raster layer. Choose it as the input file, set Values to 1 and Dist Units to GEO. This second raster layer gives the distance value from your route polygon and allows us to use the Raster > Zonal Statistics plugin, available from the plugin manager. Run the plugin with the Raster layer set to our 'distance' raster and the Polygon layer to the transects polygon. You will now have mean distances for each transect to the route listed in the attribute table.