Jianyu (Jack) Zhou Advisor: Reginald Golledge Department of Geography

1. Map Matching of GPS-traced Travel Data in GIS Environment: A Travel/Transportation Study Perspective Jianyu (Jack) Zhou Advisor: Reginald Golledge Department of Geography University of California Santa Barbara, CA

2. Outline • Introduction • Problem Statement • Case study: Review of three map matching methodologies. • A unified map matching methodology that combines heterogeneous techniques. • Conclusion and future work.

3. Introduction • Map matching: the process of correlatingtwo sets of geographical positional information. • Application area: travel behavior/transport study, car navigation, car tracking, spatial data conflation, etc. • On-line scenario: Only the current and the previous GPS points are available. Snap GPS positions to the base reference in real-time. • Off-line scenario:all the GPS points are available.

4. Problem Statement-matching factors • The simple solution is to snap the GPS recorded location to the nearest road link node or link arc. • Travel direction can be added onto the second dimension to further filter matching candidates. • Other potential selecting criteria may include • “GPS position relative to the road link” ; • “whether the link between two consecutive GPS points and road link under consideration physically intersect”; • “average distance traveled on current link” and; • “large distance traveled on current road link”

5. Problem Statement-matching factors • Different select criteria could also result in conflicting matching conclusions. • Combine the selection factors with a weighting scheme. • Or use Bayesian Belief Theory and Dempster-Shafter’s rule for deriving the unique non-ambiguous selection.

6. Problem Statement- topology • Selection criteria helps identify a series of the matched road segments from the pool of candidate links. They might show up as a group of disconnected “paths.” • Curve-to-curve matching: connecting the GPS points in sequence to form piece-wise linear curves, which are further matched against the base road network. • Improvement on point-to-point point-to-curve matching: topology relations (especially, connectivity) among road links can be used to guide the search for the next matching candidate and eliminate unreachable links. • Con: The effectiveness of the approach depends greatly on the extent to which we can trust the previous match. • Solution: maintain multiple matching hypotheses and dynamic pruning.

7. Problem Statement-Statistical estimates based approach • More tolerant of the uncertainty, partial truth, and approximation in GPS data and base street network. • Road reduction filtering:simulate the working mechanism of differential GPS. Filter false matching based on the fact that bearing and distance between successive “Raw” GPS points and the bearing and distance between successive “Ref” positions are highly correlated. • Linear regression analysis to fit GPS points to the road centerlines • Information transmission through a communication channel. The aim becomes minimizing the amount of information loss during the transmission or maximizing the mutual information shared between data sets. (Walter and Fritsch, 1999)

8. Problem statement- Data enhancement • GPS data enhancement • While GPS recorded points comprise the single data source, Kalman filter is executed to estimate the bias associated with a previous map-matching epoch. Then the estimation can be used to compensate the next GPS positioning input. • GPS receiver is complemented and integrated with other data sources, digital compass, gyroscope, velocity sensors or Antilock Brake System (ABS) etc. • Centralized Kalman filter (Extended Kalman Filter- EKF) can be used to incorporate the measurements from all data sources and generate a single stream of complex position estimates.

9. Problem statement- Data enhancement • Base map enhancement • either contain errors or do not possess enough resolution power for some of the map matching applications. • Map details need to extend to the level of lanes and cover particular types of roads such as bike paths or walking surfaces such as sidewalks. • Reverse map generalization: Replaced road with oriented links derived by adding small shifts (3 meters) perpendicular to the road centerline. This requires “number of lanes” information. • Repetitive differential GPS (DGPS) measurements.

10. Review of three map matching algorithms • Weight-based map matching by Yin and Wolfson (2004): • Always generates a topologically correct travel route from the matching process. • The application of Dijkastra’s shortest path algorithm to best matching-route searching implies the assumption that none of the road links would be traversed more than once • Fuzzy-logic based map matching by Syed and Cannon (2004): • A set of “if-then” rules defines the Sugeno-type fuzzy inference system to generate fuzzy output • Empirically derived thresholds are used to determine if the link under consideration should be matched or not. • General map matching by Quddus et al (2003) (Vehicle navigation purposes): • gaps and overshoots in the matched travel route. • does not always generate a topologically corrected route.

11. Overshoot

12. Gap

13. Unified map matching methodology • In travel behavior/transportation studies, map matching is used as a means to transfer the road network attributes to the mapping travel route in order to derive certain travel behavior. • Map matching in travel/transportation studies aims at: 1) identifying the correct road links traversed by the traveler; 2) ensuring that the identified links form a meaningful travel route; and 3) expect to help answer queries beyond the direct matching result.

14. Unified map matching methodology • Data Preprocessing --Cluster reduction: • Reduce the systematic noise in the data. Clusters phantom the slow moving speed and random travel directions of the GPS carrier. • DBSCAN (Ester et al., 1996) clustering algorithm for cluster searching since it doesn’t need assumption on the number and shape of the clusters in the input data. • constrain the maximum searching radius of the neighborhood • minimum number of entities that fall within searching neighborhood

15. Cluster of GPS points is recovered via DBSCAN algorithm and replaced with its centroid

16. Unified map matching methodology • Data preprocessing - Density leverage: • Dynamically adjust the data sampling frequency against the model resolution of the base street map. • GPS sampling interval can be greater than the length of a traversed street link (e.g., signal loss under an overpass, or high travel speed over a short link), • Every two GPS points are processed to generate a combined buffer area around them. If the sample distance between the two GPS Points is greater than half of the minimum-length street link that falls in the buffer, additional false data points are interpolated and inserted into the trace sequence.

17. Density Leverage

18. Unified map matching methodology • Matching procedure -Curve-to-curve Matching: • Develop a pool of the best candidates simultaneously and incrementally. • GPS recorded travel trace is treated as a translated and rotated version of the match route. • Dual selection criteria: accumulated 2-norm distance (A2ND) and rotational variation metric (RVM). • A2ND and RVM both serve to constrain the match search in the street network space. Two ranked solution pools are derived in terms of A2ND and RVM separately.

19. Unified map matching methodology • Topological completeness: determining potential turning action around a street intersection: • 1) The projection of current GPS point falls on or out of the end point of the current link, which typically occurs when the travel direction change is less than or equal to 90 degrees; • 2) The projection of the current GPS point comes near to the end point of the current link, but the point’s position is getting away from the current link, which typically occurs when the travel direction change exceeds 90 degrees. • 3) All the topologically connected links to the intersection node are considered as the potential next links. Prohibited maneuver and turn restrictions information is used to pre-eliminate certain search branches intelligently.

20. Unified map matching methodology • Use the rank aggregation method to combine the ranking solution list in A2ND and RVM to obtain a combined ordering: • Kemeny ordering minimizes the sum of the “bubble sort” distances and thus generates the best compromise ranking. It is a NP-hard problem. • Borda’s method: Each candidate in the list is assigned a score of the number of candidates ranked blow it. Its total score across the different ranking list is finally sorted in a descending order. • Footrule optimal aggregation:Given n lists of same set of elements, generate the median permutation of the candidates in the lists.

21. Best sample match result

22. Second best sample match result

23. Conclusion and future research • The method is uniquely characterized by: • 1) data preprocessing with point cluster reduction and density leverage, • 2) offering the candidate solution within a pool of “the best,” • 3) balancing of matching results from multiple matching factors with rank aggregation, and • 4) intelligently utilizing the basic network constraint attributes with “expert rules” to increase the matching accuracy • Further research includes: • Needs to quantify the performance of this algorithm and others with respect to a complete set of survey travel routes recorded. • A matching index needs to be developed to evaluate the matching accuracy among the algorithms quantitatively. • A post processing mechanism to identify situation when the GPS trip has left the roadway to enter a parking lot or private driveway or changed travel mode to walking or biking.