Implementing HMM Map Matching with Spatial Indexes

HMM Formulation
Model the matching problem as Hidden Markov Model. Hidden states are road segments. Observations are GPS points. Emission probability: how likely this GPS point given vehicle is on this road segment (based on distance). Transition probability: how likely moving from segment A to segment B (based on routing distance).
The Viterbi algorithm finds the most likely sequence of road segments given the GPS observations. It considers the entire trace globally, balancing point-to-road distance against path continuity.
Candidate Generation
For each GPS point, find nearby road segments. Use spatial index: geohash, R-tree, or grid. Query for segments within some radius (50-100 meters typically). These are candidate states for that observation.
Too few candidates miss the correct road. Too many candidates slow computation and may include irrelevant roads. Tune radius based on GPS accuracy in your use case. Urban canyons need wider radius.
Transition Probabilities
Transition probability between segments should favor valid routes. If segment A connects to segment B via legal turn, high probability. If reaching B from A requires impossible U-turn or driving wrong way, low probability.
Compute route distance between segment endpoints. Compare to straight-line distance. Large detour factor suggests unlikely transition. Pre-compute common transitions; use shortest-path for rare ones. Cache results for performance.
✅ Best Practice: Use spatial index for candidate generation (50-100m radius). Pre-compute transitions for common segment pairs. Tune emission probabilities based on your GPS accuracy distribution. Log low-confidence matches for algorithm improvement.

💡 Key Takeaways

✓HMM: hidden states are road segments, observations are GPS points

✓Emission probability: likelihood of GPS point given road segment (distance-based)

✓Transition probability: likelihood of moving between segments (routing-based)

✓Viterbi algorithm finds most likely path considering entire trace

✓Spatial index generates candidates; 50-100m radius typical

📌 Interview Tips

1Explain HMM intuition: balance wanting to be close to GPS point (emission) vs wanting valid connected path (transition)

2For candidate generation, use R-tree or geohash to find segments within 50m of each GPS point

3Transition probabilities: pre-compute for common pairs, use shortest-path algorithm for rare transitions

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