1. 1 Travel Times from Mobile Sensors Ram Rajagopal, Raffi Sevlian and Pravin Varaiya University of California, Berkeley Singapore Road Traffic Control TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A

2. 2  1982 to 2001: – 20% population increase – 236% travel time increase  Congestion costs per year: – $78 billion – 4.2 billion lost hours – 2.9 billion gallons of wasted gas  Highways operated at 100% efficiency can reduce this by 40%  Providing drivers with travel time estimates will help Complex System Challenges: Urban Traffic Source: 2007 Urban Mobility Report, Texas Transportation Institute

3. 3 Challenges for Travel Time (TT) Measurements  Street TT distributions poorly characterized by means and variances  Need to measure individual vehicle travel times  Need real-time estimates Travel times in a typical link

4. 4 Proposed Approach  Localization signatures from vehicle probes: –GPS from navigation devices –Received Signal Strength Indicators from GSM phones  Existing work maps each signature to a location causing: –Large individual localization errors (RSSI) (90 m median error) –Localization errors propagate  Proposed approach maps signature sequence to paths--inspired by bio-sequence matching and Viterbi algorithms

5. 5 Description of Method  This talk: Map Matching Sequence of time stamped signatures  Each link characterized by signature set  Road map : set of road links and junctions Map Matching Locate with motion and traffic constraints Time Splitting Split TT between links using Sparse Network Coding Historic Flows Multiple vehicles Estimates of link TT distributions for period S

6. 6 Map Matching (MM)  Split GIS map into L links of size U (e.g. U = 20m)  Data given by signature distance matrix:  Estimate matching  Performance metrics Prob. of Error Meter Error

7. 7 Signature Distance  Database of GIS-signature pairs for each link:  Distance:  e.g.: Euclidean norm (RSSI)  Statistical model: Distributions from experimental data RSSI measurement for base station r

8. 8 Statistical Model for MM  Conditional on true, independent links, data D distributed as:  Minimize negative log-likelihood, using a proper prior

9. 9 Constrained MM (Routes)  Consider a route 1, …, l, l+1,…,L  Statistical model does not incorporate motion constraints  Vehicles only move forward on the route, speed limits, giving constraint is the furthest link reachable using multiple of speed limit during time

10. 10 Matching Graph (Routes)  Edit graph representation One node per matching (n,l) Links l=1,|L| Samples n = 1, N (N,|L|) (n,l) Edge from (n,l) to (n+1,l’) if l’ in Reach(l) Diagonal edge weights Vertical edge weights = 0 (n’,l’)  Viterbi decoding = shortest path on matching graph

11. 11 Example of Signature Distance Matrix

12. 12 Real-Time Matching  Error correction: future positions constrain past positions  Real-time matching: future continuously updated  Estimate when sample r arrives:  Edit graph updated: –Columns added for new observations –Columns deleted for committed matches –Matching recomputed  Commit n’ if r > R or if n’ Real time matching

13. 13 Beyond Routes  Assign a weight for each road section: –distance, frequency of use, … –Vehicle takes shortest weight route between observations  Match graph (“edit graph”) still valid: –Reachable set defined by map graph constraints –Furthest reachable node computed with all-pairs shortest path in map graph  Heuristics used to avoid calculating every

14. 14 Performance Bound (“High SNR”)  Size of search space ( ):  Expected number of correct matches ( ):  Unconstrained case: Goes to zero for N large (“Large map, long path”) Under (n,l) being true match Unconstrained matching Constrained matching

15. 15 Experimental Data  Data collected for a route: RSSI and corresponding GPS, every 2 seconds  Route is 8 Km long  Road sections are 9m long

16. 16 Error Distribution  10-fold cross-validation, database = 8 route logs  Database is the prerecorded set of signatures for a map

17. 17 Error for Varying Sample Separations  Vary sampling rate: no benefit below 3 m/sample

18. 18 Position Dependency of Error Error peaks at entrance of highway section and parking For single track: dependency of meter-error and distance to previous observation

19. 19 GPS Interpolation Performance  Periodically use GPS, in between use RSSI

20. 20 Time Splitting  is section travel time R.V. for fixed period  If observations are infrequent:  Distributions of from such observations?  Issue: few observations, but history is available as  Idea: for most l, close to, e.g.  ML Deconvolution, LASSO, Sparse Sum Decoding TT between observations Path followed from n to n+1: 1 if link l was used

21. 21 Mobile Travel Time Problem (unified view)  Factor Model ( v is vehicle) and/or  Observation Model  Assumptions  Goals

22. 22 Conclusions and Future Work  Analogy with coding/decoding powerful  Constraints reduce search space  1/SNR error behavior suggests using multiple measurements  Compute mean-field approximation for probability of error  Compute achievable error rate for Mobile Travel Time problem  Large Scale Field Test algorithms with data from Dubai and New Delhi