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B. Fazzinga, S.Flesca, F. Furfaro, F. Parisi DIMES – University of Calabria

Cleaning trajectory data of RFID-monitored objects through conditioning under integrity constraints. B. Fazzinga, S.Flesca, F. Furfaro, F. Parisi DIMES – University of Calabria. 17th International Conference on Extending Database Technology (EDBT) Athens, Greece, March 24-28, 2014.

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B. Fazzinga, S.Flesca, F. Furfaro, F. Parisi DIMES – University of Calabria

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  1. Cleaning trajectory data of RFID-monitored objectsthrough conditioning under integrity constraints B. Fazzinga, S.Flesca, F. Furfaro, F. Parisi DIMES – University of Calabria 17th International Conference on Extending Database Technology (EDBT) Athens, Greece, March 24-28, 2014

  2. Scenario • The RFID technologyiswidelyused to trackmovingobjects (supplychain, people inside buildings, luggages in airports, etc.) • How RFID-basedtrackingworks: tagsand readers • Tags can emit radio signalsencodingidentifying information; • Readers detect the presence of tagsthanks to theirantennas • LIMITATION:evenif inside the detectionrange of an antenna, a tagmaynot be detected (malfunctions, reflections, interferences)

  3. Scenario • The RFID technologyiswidelyused to trackmovingobjects (supplychain, people inside buildings, luggages in airports, etc.) • How RFID-basedtrackingworks: tagsand readers • Tags can emit radio signalsencodingidentifying information; • Readers detect the presence of tagsthanks to theirantennas • LIMITATION:evenif inside the detectionrange of an antenna, a tagmaynot be detected (malfunctions, reflections, interferences) r2 The tagmay be detected by: r1

  4. Scenario • The RFID technologyiswidelyused to trackmovingobjects (supplychain, people inside buildings, luggages in airports, etc.) • How RFID-basedtrackingworks: tagsand readers • Tags can emit radio signalsencodingidentifyinginformation; • Readers detect the presence of tagsthanks to theirantennas • LIMITATION:evenif inside the detectionrange of an antenna, a tagmaynot be detected (malfunctions, reflections, interferences) r2 The tagmay be detected by: • {r1, r2} r1

  5. Scenario • The RFID technologyiswidelyused to trackmovingobjects (supplychain, people inside buildings, luggages in airports, etc.) • How RFID-basedtrackingworks: tagsand readers • Tags can emit radio signalsencodingidentifyinginformation; • Readers detect the presence of tagsthanks to theirantennas • LIMITATION:evenif inside the detectionrange of an antenna, a tagmaynot be detected (malfunctions, reflections, interferences) r2 The tagmay be detected by: • {r1, r2} • {r1} r1

  6. Scenario • The RFID technologyiswidelyused to trackmovingobjects (supplychain, people inside buildings, luggages in airports, etc.) • How RFID-basedtrackingworks: tagsand readers • Tags can emit radio signalsencodingidentifyinginformation; • Readers detect the presence of tagsthanks to theirantennas • LIMITATION:evenif inside the detectionrange of an antenna, a tagmaynot be detected (malfunctions, reflections, interferences) r2 The tagmay be detected by: • {r1, r2} • {r1} • {r2} r1

  7. Scenario • The RFID technologyiswidelyused to trackmovingobjects (supplychain, people inside buildings, luggages in airports, etc.) • How RFID-basedtrackingworks: tagsand readers • Tags can emit radio signalsencodingidentifyinginformation; • Readers detect the presence of tagsthanks to theirantennas • LIMITATION:evenif inside the detectionrange of an antenna, a tagmaynot be detected (malfunctions, reflections, interferences) r2 The tagmay be detected by: • {r1, r2} • {r1} • {r2} •  r1

  8. Interpreting the readings • For eachtag, the result of the tracking task is a sequence of readingsR1,…,RT • EachRiis the set of readersthatdetected the tagat time pointi

  9. Interpreting the readings • For eachtag, the result of the tracking task is a sequence of readingsR1,…,RT • EachRiis the set of readersthatdetected the tagat time pointi • The collected data must be translatedintosequences of positions (i.e., TRAJECTORIES) • Positions of interest can be room names, cells over a grid, etc.

  10. From sequences of readings to trajectories L3 Issues to deal with L2 r1 L1 r5 r0 L0 L4

  11. From sequences of readings to trajectories L3 Issues to deal with • No one-to-onecorrespondencebetweenreaders and locations • readers can cover portions of different locations; • Some zonesmay be covered by no reader L2 r1 L1 r5 r0 L0 L4

  12. From sequences of readings to trajectories L3 Issues to deal with • No one-to-onecorrespondencebetweenreaders and locations • readers can cover portions of different locations; • Some zonesmay be covered by no reader L2 r1 L1 r5 r0 L0 L4

  13. From sequences of readings to trajectories L3 Issues to deal with • No one-to-onecorrespondencebetweenreaders and locations • readers can cover portions of different locations; • Some zonesmaybecoveredby no reader L2 r1 L1 r5 r0 L0 L4

  14. From sequences of readings to trajectories L3 Issues to deal with • No one-to-onecorrespondencebetweenreaders and locations • readers can cover portions of different locations; • Some zonesmaybecoveredby no reader L2 r1 L1 r5 r0 L0 L4

  15. From sequences of readings to trajectories L3 Issues to deal with • No one-to-onecorrespondencebetweenreaders and locations • readers can cover portions of different locations; • Some zonesmaybecoveredby no reader L2 r1 L1 r5 r0 L0 L4

  16. From sequences of readings to trajectories L3 Issues to deal with • No one-to-onecorrespondencebetweenreaders and locations • readers can cover portions of different locations; • Some zonesmaybecoveredby no reader L2 r1 • False negatives • a tagmaynot be detectedevenif in the range of an antenna L1 r5 r0 L0 L4

  17. From sequences of readings to trajectories L3 Issues to deal with • No one-to-onecorrespondencebetweenreaders and locations • readers can cover portions of different locations; • Some zonesmaybecoveredby no reader L2 r1 • False negatives • a tagmaynot be detectedevenif in the range of an antenna L1 r5 r0 • An objectdetected by a set of readers can be in different locations • An undetectedobject can be anywhere! L0 L4

  18. From sequences of readings to trajectories L3 Issues to deal with • No one-to-onecorrespondencebetweenreaders and locations • readers can cover portions of different locations; • Some zonesmaybecoveredby no reader L2 r1 • False negatives • a tagmaynot be detectedevenif in the range of an antenna L1 r5 r0 A sequence of detections can be generated by differenttrajectories: whichis the actualone? L0 L4

  19. A naive probabilistic interpretation of the readings Table of detections L3 L2 • Consider the time pointsseparately (independenceassumption) • Model the correspondencebetweenlocations and set of readersas a PDF pa(l|R) • pa(l|R) is easy to obtain from the position of readers and theirphysical model r1 L1 r5 r0 L0 L4

  20. A naive probabilistic interpretation of the readings Table of detections L3 L2 r1 L1 r5 pa(L1|{r1,r5}) = 50% pa(L4|{r1,r5}) = 50% r0 L0 L4

  21. A naive probabilistic interpretation of the readings Table of detections L3 L2 r1 L1 r5 pa(L1|{r1,r5}) = 50% pa(L4|{r1,r5}) = 50% r0 L0 L4

  22. A naive probabilistic interpretation of the readings Table of detections L3 L2 r1 The sameas the previous time point: L1 r5 pa(L1|{r1,r5}) = 50% pa(L4|{r1,r5}) = 50% r0 L0 L4

  23. A naive probabilistic interpretation of the readings Table of detections L3 L2 r1 The sameas the previous time point: L1 r5 pa(L1|{r1,r5}) = 50% pa(L4|{r1,r5}) = 50% r0 L0 L4

  24. A naive probabilistic interpretation of the readings Table of detections L3 L2 r1 The detectionrange of r0isentirely inside L0: L1 r5 r0 pa(L0|{r0}) = 100% L0 L4

  25. A naive probabilistic interpretation of the readings Table of detections L3 L2 r1 The detectionrange of r0isentirely inside L0: L1 r5 r0 pa(L0|{r0}) = 100% L0 L4

  26. Probabilistic trajectories Table of detections L3 L2 r1 4 correspondingtrajectories: t1:L1–L1–L0 L1 r5 r0 L0 L4

  27. Probabilistic trajectories Table of detections L3 L2 r1 4 correspondingtrajectories: t1:L1–L1–L0 p=25% L1 r5 r0 p(t1)= pa(L1|{r1,r5}) × pa(L1|{r1,r5}) × pa(L0|{r0}) = 50% × 50% × 100 %= 25% L0 L4

  28. Probabilistic trajectories Table of detections L3 L2 r1 4 correspondingtrajectories: t1:L1–L1–L0 p=25% t2:L1–L4–L0 p=25% L1 r5 r0 L0 L4

  29. Probabilistic trajectories Table of detections L3 L2 r1 4 correspondingtrajectories: t1:L1–L1–L0 p=25% t2:L1–L4–L0 p=25% t3:L4–L1–L0 p=25% L1 r5 r0 L0 L4

  30. Probabilistic trajectories Table of detections L3 L2 r1 4 correspondingtrajectories: t1:L1–L1–L0 p=25% t2:L1–L4–L0 p=25% t3:L4–L1–L0 p=25% t4:L4–L4–L0 p=25% L1 r5 r0 L0 L4

  31. Probabilistic trajectories L3 … but some trajectories turn out to be impossiblewhenlookingat the map! L2 r1 4 correspondingtrajectories: t1:L1–L1–L0 p=25% t2:L1–L4–L0 p=25% t3:L4–L1–L0 p=25% t4:L4–L4–L0 p=25% L1 r5 r0 L0 L4

  32. Probabilistic trajectories L3 … but some trajectories turn out to be impossiblewhenlookingat the map! L2 r1 4 correspondingtrajectories: t1:L1–L1–L0 p=25% t2:L1–L4–L0 p=25% t3:L4–L1–L0 p=25% t4:L4–L4–L0 p=25% L1 r5 r0 L0 L4

  33. Probabilistic trajectories L3 … but some trajectories turn out to be impossiblewhenlookingat the map! L2 r1 4 correspondingtrajectories: t1:L1–L1–L0 p=25% t2:L1–L4–L0 p=25% t3:L4–L1–L0 p=25% t4:L4–L4–L0 p=25% L1 r5 r0 L0 L4

  34. Probabilistic trajectories L3 … but some trajectories turn out to be impossiblewhenlookingat the map! L2 r1 4 correspondingtrajectories: t1:L1–L1–L0 p=25% t2:L1–L4–L0 p=25% t3:L4–L1–L0 p=25% t4:L4–L4–L0 p=25% L1 r5 r0 L0 L4

  35. Probabilistic trajectories L3 Considering time pointsasindependent (thusdisregardingspatio-temporalcorrelations) yieldedinadmissibleinterpretations: 1) Three trajectories must be discarded; 2) The probabilities of the remainingones must be revised L2 r1 t1:L1–L1–L0 p=25% t2:L1–L4–L0 p=25% t3:L4–L1–L0 p=25% t4:L4–L4–L0 p=25% L1 r5 r0 L0 L4

  36. The trajectory cleaning problem • Start from the probabilistic trajectories resulting from interpreting the readings by considering them independently • Discard the impossible trajectories • Revise the probabilities of the possible trajectories Use integrityconstraints!

  37. Integrity constraints L3 • DU (directunreachability) • DU(L’, L’’) meansthereis no direct connection from L’ to L’’ L2 L1 Example: DU(L0, L4) L0 L4

  38. Integrity constraints L3 • DU (directunreachability) • DU(L’, L’’) meansthereis no direct connection from L’ to L’’ • TT (traveling time) • TT(L’,L’’, T) meansthat T is the minnumber of time pointsneeded to go from L’ to L’’ L2 L1 Example: TT(L0, L4, 4) L0 L4

  39. Integrity constraints L3 • DU (directunreachability) • DU(L’, L’’) meansthereis no direct connection from L’ to L’’ • TT (traveling time) • TT(L’,L’’, T) meansthat T is the minnumber of time pointsneeded to go from L’ to L’’ L2 L1 Example: TT(L0, L4, 4) L0 L4

  40. Integrity constraints L3 • DU (directunreachability) • DU(L’, L’’) meansthereis no direct connection from L’ to L’’ • TT (traveling time) • TT(L’,L’’, T) meansthat T is the minnumber of time pointsneeded to go from L’ to L’’ • LT (latency) • LT(L, T) meansthat T is the minnumber of time points for which an object, once entered L, must stay at L L2 L1 Example: LT(L0, 3) L0 L4

  41. Integrity constraints L3 • DU (directunreachability) • DU(L’, L’’) meansthereis no direct connection from L’ to L’’ • TT (traveling time) • TT(L’,L’’, T) meansthat T is the minnumber of time pointsneeded to go from L’ to L’’ • LT (latency) • LT(L, T) meansthat T is the minnumber of time points for which an object, once entered L, must stay at L L2 L1 Example: LT(L0, 3) L0 L4

  42. The trajectory cleaning problem • Start from the probabilistic trajectories resulting from interpreting the readings by considering them independently • Discard the impossible trajectories • Use integrity constraints • Revise the probabilities of the possible trajectories Probabilistic conditioning

  43. Conditioning probabilities • Given a PDF p(X) and an eventE, the conditioningproblemisthat of evaluatingp(X|E) • In probabilisticDBs, conditioningis a way for enforcingintegrityconstraints over a DB whereindependenceassumptionisused • In this case, Eis the eventthat the constraints are satisfied General framework for conditioningprobabilisticDBs: C. Koch, D. Olteanu: Conditioningprobabilisticdatabases. PVLDB 1(1). 2008. The general conditioning/confidencecomputationproblemis NP-hard on succintrepresentations

  44. Conditioning probabilities t1:L1–L1–L0 pa(t1)=25% t2:L1–L4–L0 pa(t2)=25% t3:L4–L1–L0 pa(t3)=25% t4:L4–L4–L0 pa(t4)=25% L3 Example L2 • LetIC be the set of DUconstraintsimplied by the map L1 L0 L4

  45. Conditioning probabilities t1:L1–L1–L0 pa(t1)=25% t2:L1–L4–L0 pa(t2)=25% t3:L4–L1–L0 pa(t3)=25% t4:L4–L4–L0 pa(t4)=25% L3 Example L2 • LetIC be the set of DUconstraintsimplied by the map • Three out of fourtrajectories are discarded L1 L0 L4

  46. Conditioning probabilities t1:L1–L1–L0 pa(t1)=25% t2:L1–L4–L0 pa(t2)=25% t3:L4–L1–L0 pa(t3)=25% t4:L4–L4–L0 pa(t4)=25% L3 Example L2 • LetIC be the set of DUconstraintsimplied by the map • Three out of fourtrajectories are discarded • The a-priori probability of t1isrevisedasp(t1)= pa(t1|IC)= 0.25/0.25=100% L1 L0 L4

  47. Conditioning probabilities t1:L0–L1–L1 pa(t1)=50% t2:L0–L1–L2 pa(t2)=25% t3:L0–L1–L4 pa(t3)=25% L3 Example 2 L2 • LetIC be the set of DU and TT constraints, containingTT(L1, L4, 4) L1 L0 L4

  48. Conditioning probabilities t1:L0–L1–L1 pa(t1)=50% t2:L0–L1–L2 pa(t2)=25% t3:L0–L1–L4 pa(t3)=25% L3 Example 2 L2 • LetIC be the set of DU and TT constraints, containingTT(L1, L4, 4) • Trajectoryt3violatesTT(L1, L4, 4) L1 L0 L4

  49. Conditioning probabilities t1:L0–L1–L1 pa(t1)=50% t2:L0–L1–L2 pa(t2)=25% t3:L0–L1–L4 pa(t3)=25% L3 Example 2 L2 • LetIC be the set of DU and TT constraints, containingTT(L1, L4, 4) • Trajectoryt3violatesTT(L1, L4, 4) • The a-priori probabilities of t1 and t2 are revisedas: p(t1)= 0.5/(0.5+0.25)= 66.6% p(t2)= 0.25/(0.5+0.25)=33.3% L1 L0 L4

  50. Conditioning probabilities t1:L0–L1–L1 pa(t1)=50% t2:L0–L1–L2 pa(t2)=25% t3:L0–L1–L4 pa(t3)=25% L3 Example 2 L2 • LetIC be the set of DU and TT constraints • Trajectoryt3violatesTT(L1, L4, 4) • The a-priori probabilities of t1 and t2 are revisedas: p(t1)= 66.6% p(t2)= 33.3% L1 t1istwiceasprobableast2, likebeforeconditioning L0 L4

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