Smarter search radius formula for map matching

docs/http.md

@@ -283,6 +283,12 @@ In addition to the [general options](#general-options) the following options are
 |timestamp   |`integer` UNIX-like timestamp |
 |radius      |`double >= 0` (default 5m)    |
 
+The radius for each point should be the standard error of the location, measured in meters from the true location. Use
+`Location.getAccuracy()` on Android or `CLLocation.horizontalAccuracy` on iOS. This value is used to determine which
+points should be considered as candidates (larger radius means more candidates) and how likely each candidate is (larger
+radius means far-away candidates are penalized less). The area to search is chosen such that the correct candidate
+should be considered 99.9% of the time (for more details, see https://github.com/Project-OSRM/osrm-backend/pull/3184).
+
 ### Response
 - `code` if the request was successful `Ok` otherwise see the service dependent and general status codes.
 - `tracepoints`: Array of `Waypoint` objects representing all points of the trace in order.

src/engine/plugins/match.cpp

@@ -19,6 +19,13 @@
 #include <string>
 #include <vector>
 
+static double search_radius_for_gps_radius(double gps_radius) {
+    // For a given GPS radius, determine the radius we need to search for candidate street segments
+    // to have a 99.9% chance of finding the correct segment.
+    // For more detail, see the analysis at https://github.com/Project-OSRM/osrm-backend/pull/3184
+    return std::min(gps_radius * 3.5 + 45, 200.0);
+}
+
 namespace osrm
 {
 namespace engine
@@ -152,16 +159,9 @@ Status MatchPlugin::HandleRequest(const std::shared_ptr<datafacade::BaseDataFaca
         std::transform(parameters.radiuses.begin(),
                        parameters.radiuses.end(),
                        search_radiuses.begin(),
-                       [](const boost::optional<double> &maybe_radius) {
-                           if (maybe_radius)
-                           {
-                               return *maybe_radius * RADIUS_MULTIPLIER;
-                           }
-                           else
-                           {
-                               return DEFAULT_GPS_PRECISION * RADIUS_MULTIPLIER;
-                           }
-
+                       [&](const boost::optional<double> &maybe_radius) {
+                           double gps_radius = maybe_radius ? *maybe_radius : DEFAULT_GPS_PRECISION;
+                           return search_radius_for_gps_radius(gps_radius);
                        });
     }