Use non-normalized transition metric and remove timeDiff check (#70)

For GPX traces with equal timestamps, all transitions had a
probability of 1 and hence transitions were not considered during map
matching. With directed candidates the siutation got even worse
because it could happen that the Viterbi algorithm chose a candidate
with wrong direction because penalties from unfavored edges would still
result in a transition probability of 1. In this case the resulting
map matching path would take unnecessary detours.

matching-core/src/main/java/com/graphhopper/matching/MapMatching.java

@@ -71,7 +71,7 @@ public class MapMatching {
     private final Graph routingGraph;
     private final LocationIndexMatch locationIndex;
     private double measurementErrorSigma = 50.0;
-    private double transitionProbabilityBeta = 0.00959442;
+    private double transitionProbabilityBeta = 2.0;
     private final int nodeCount;
     private DistanceCalc distanceCalc = new DistancePlaneProjection();
     private final RoutingAlgorithmFactory algoFactory;
@@ -474,8 +474,7 @@ private void computeTransitionProbabilities(TimeStep<GPXExtension, GPXEntry, Pat
                             from, to, penalizedPathDistance);
 
                     final double transitionLogProbability = probabilities
-                            .transitionLogProbability(penalizedPathDistance, linearDistance,
-                                    timeDiff);
+                            .transitionLogProbability(penalizedPathDistance, linearDistance);
                     timeStep.addTransitionLogProbability(from, to, transitionLogProbability);
                 } else {
                     logger.debug("No path found for from: {}, to: {}", from, to);

matching-core/src/main/java/com/graphhopper/matching/MapMatchingMain.java

@@ -89,7 +89,8 @@ private void start(CmdArgs args) {
                     hints(new HintsMap().put("weighting", "fastest").put("vehicle", firstEncoder.toString())).
                     build();
             MapMatching mapMatching = new MapMatching(hopper, opts);
-            mapMatching.setTransitionProbabilityBeta(args.getDouble("transition_probability_beta", 0.00959442));
+            mapMatching.setTransitionProbabilityBeta(args.getDouble
+                    ("transition_probability_beta", 2.0));
             mapMatching.setMeasurementErrorSigma(gpsAccuracy);
 
             // do the actual matching, get the GPX entries from a file or via stream

matching-core/src/main/java/com/graphhopper/matching/util/HmmProbabilities.java

@@ -26,23 +26,11 @@ public class HmmProbabilities {
     private final double sigma;
     private final double beta;
 
-    /**
-     * Sets default values for sigma and beta.
-     */
-    public HmmProbabilities() {
-        /*
-         * Sigma taken from Newson&Krumm.
-         * Beta empirically computed from the Microsoft ground truth data for shortest route
-         * lengths and 60 s sampling interval but also works for other sampling intervals.
-         */
-        this(4.07, 0.00959442);
-    }
-
     /**
      * @param sigma standard deviation of the normal distribution [m] used for
      *              modeling the GPS error
-     * @param beta  beta parameter of the exponential distribution for 1 s
-     *              sampling interval, used for modeling transition probabilities
+     * @param beta  beta parameter of the exponential distribution used for modeling
+     *              transition probabilities
      */
     public HmmProbabilities(double sigma, double beta) {
         this.sigma = sigma;
@@ -67,33 +55,12 @@ public double emissionLogProbability(double distance) {
      *                       consecutive map matching candidates.
      * @param linearDistance Linear distance [m] between two consecutive GPS
      *                       measurements.
-     * @param timeDiff       time difference [s] between two consecutive GPS
-     *                       measurements.
      */
-    public double transitionLogProbability(double routeLength, double linearDistance,
-                                           double timeDiff) {
-        if (timeDiff == 0) {
-            return 0;
-        }
-        Double transitionMetric = normalizedTransitionMetric(routeLength, linearDistance, timeDiff);
-        return Distributions.logExponentialDistribution(beta, transitionMetric);
-    }
+    public double transitionLogProbability(double routeLength, double linearDistance) {
+        // Transition metric taken from Newson & Krumm.
+        Double transitionMetric = Math.abs(linearDistance - routeLength);
 
-    /**
-     * Returns a transition metric for the transition between two consecutive
-     * map matching candidates.
-     *
-     * In contrast to Newson & Krumm the absolute distance difference is divided
-     * by the quadratic time difference to make the beta parameter of the
-     * exponential distribution independent of the sampling interval.
-     */
-    private double normalizedTransitionMetric(double routeLength, double linearDistance,
-                                              double timeDiff) {
-        if (timeDiff < 0.0) {
-            throw new IllegalStateException(
-                    "Time difference between subsequent location measurements must be >= 0.");
-        }
-        return Math.abs(linearDistance - routeLength) / (timeDiff * timeDiff);
+        return Distributions.logExponentialDistribution(beta, transitionMetric);
     }
 
 }