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Target Tracking

Target Tracking. Target tracking problem. Problem statement A varying number of targets Arise at random in space and time Move with continuous motions Persist for a random time and possibly disappear Positions of targets are sampled at random intervals Measurements are noisy and

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Target Tracking

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  1. Target Tracking

  2. Target tracking problem • Problem statement • A varying number of targets • Arise at random in space and time • Move with continuous motions • Persist for a random time and possibly disappear • Positions of targets are sampled at random intervals • Measurements are noisy and • Detection probability < 1.0 • False alarms • Goal: detect, alert, and track for each target

  3. Frisbee model

  4. Issues in Frisbee model • Power savings with wake-up • Can be waked up by neighbors • Be able to form a “wakeup wavefront” that precedes the target • Localized algorithm for defining the Frisbee boundary • Each node autonomously decide if it is in the current Frisbee • Adaptive fidelity

  5. e e R Sensing model • Sensor detection model • Object always detected in rage R-e • Object never detected out of range R+e • Object possibly detected in range [R-e, R+e] • e≈ 0.1R • Comments: • Binary detection model is most simple and reliable. • Location resolution is the sensing range for one sensor, however, by combining multiple sensors, resolution is improved significantly. • The sensing range don’t have to be circular.

  6. Sensing model We express the general sensing model S at an arbitrary point p for a sensor s as: where d(s,p) is the Euclidean distance between the sensor s and the point p, and positive constants  and K are sensor technology dependent parameters

  7. A Cooperative tracking algorithm • When the object enters the region where multiple sensors can detect it, its position is within the intersection of the overlapping sensing ranges. • Algorithm: • Each node records the duration for which the object is in its range. • Neighboring nodes exchange these times and their locations. • For each point of time, the object’s estimated position is computed as the weighted average of the detecting nodes’ locations. • A line fitting algorithm is run on the resulting set of points.

  8. Weight assignments Sensors that are closer to the path of the target will stay in sensor range for a longer duration.

  9. Weight assignments • Equal weight • Proportional weight (r) • Logarithmic weight R: sensor radius v: estimated speed ti: detection duration f: sampling frequency

  10. Tracking methods • One sensor at a time • Each time, only the best sensor conducts tracking • Minimal sensor (binary) model • 1: target in range • 0: target out of range • Hierarchical method, clusters • Acoustic sensors (delay-based collaboration) • More than 3 sensors track a target jointly • Tree-based group collaboration

  11. IDSQ • Information-driven sensor query • Procedures • Each sensor performs detection by comparing measurement with a threshold (aka, likelihood ratio test) • Detecting nodes elect a leader • The leader suppresses the other nodes to prevent multiple tracks for the same target • The leader initializes the belief state and reports the sensory data to the sink

  12. IDSQ DETECTION message

  13. IDSQ Timestamp Likelihood ratio

  14. IDSQ SUPPRESSION message

  15. IDSQ HANDOFF message New leader reports sensory data to sink

  16. Acoustic target tracking Context • Delay based sound source locating algorithm, requires large number of redundant sensors for accuracy • Tiny wireless sensors to real-world acoustic tracking applications • Tracking only impulsive acoustic signals, such as foot steps, sniper shots, etc. No concept of tracking motion

  17. Acoustic target tracking • Two subsystems • Acoustic target tracking subsystem • Communication subsystem

  18. System Overview • Acoustic target tracking subsystem Sensor (mica motes) Sensors belong to clusters with singular cluster head. Cluster head knows the locations of its slave sensors. Raw data gathered from sensors are processed in cluster head to generate localization results Cluster Head (mono-board computer)

  19. Acoustic target tracking subsystem • Reference-broadcast synchronization (RBS) • Physical layer broadcast

  20. RBS • Reference broadcasts do not have an explicit timestamp • Receivers use reference broadcast’s arrival time as a point of reference for comparing nodes’ clocks • Receivers synchronize with one another using the message’s timestamp (which is different from one receiver to another)

  21. 1 2 A 3 4 RBS illustration • Transmitter A broadcasts a reference packet to two receivers (e.g., 1 and 2) • Each receiver records the time that the reference was received, according to its local clock • The receivers (1 and 2) exchange their observations

  22. Cross Correlation (to find out delays) Locate sound source location Detect interesting sound Broadcast sound signature ClusterHead Cross-correlation to detect local arrival time Report local arrival time SlaveSensor

  23. Final position fixed Sensor (mica motes) Sensors belong to clusters with singular cluster head. Cluster head knows the locations of its slave sensors. Raw data gathered from sensors are processed in cluster head to generate localization results Cluster Head (mono-board computer)

  24. Communication subsystem • Quality-driven redundancy suppression and contention resolution (QDR) • Overlapping of clusters’ monitoring areas (redundant areas) • CSMA MAC interval: time unit Q: 0 is the highest quality

  25. Scenario Sensor Router Cluster Head Sink/Pursuer Cluster Head Sink/ Pursuer

  26. Communication Subsystem: route back the reports generated by cluster heads to sink Multi-parent sink tree routing Sink cluster covered area cluster head router (mica motes)

  27. Dynamic convoy tree-based collaboration (DCTC) • Hierarchical (tree) • Refer to relevant slides for details

  28. references • K. Mechitov, S. Sundresh, Y. Kwon, G. Agha, “Cooperative Tracking with Binary-Detection Sensor Networks,” Technical Report UIUCDCS-R-2003-2379, Computer Science, UIUC, Sept. 2003 • Juan Liu, Jie Liu, James Reich, Patrick Cheung, Feng Zhao: Distributed Group Management for Track Initiation and Maintenance in Target Localization Applications. IPSN 2003: 113-128 • Qixin Wang, Wei-Peng Chen, Rong Zheng, Kihwal Lee, and Lui Sha, Acoustic Target TrackingUsing Wireless Sensor Devices, Proc. of the 2nd Workshop on Information Processing in SensorNetworks (IPSN03), April 2003 • Fine-Grained Network Time Synchronization using Reference Broadcasts, Jeremy Elson, Lewis Girod and Deborah Estrin, In Proceedings of the Fifth Symposium on Operating Systems Design and Implementation (OSDI 2002)

  29. Sensor coverage and sleeping

  30. Assumption • Sensing effectiveness diminishes as distance increases (monotonic) • E.g., • Homogeneous sensor nodes • Non-directional sensing technology • Centralized computation model

  31. Coverage Formulation How well can the field be observed ? • Worst Case Coverage:Maximal Breach Path • Best Case Coverage:Maximal Support Path The “paths” are generally not unique. They quantify the best and worst case observability (coverage) in the sensor field.

  32. Maximal Breach Path (PB) Given: Field A instrumented with sensors; areas I and F. Problem: Identify PB, the maximal breach path in S, starting in I and ending in F. PB is defined as a path with the property that for any point p on the path PB, the distance from p to the closest sensor is maximized.

  33. Voronoi diagram • The plane is partitioned by assigning every point in the plane to the nearest site

  34. Voronoi diagram • A Voronoi Line consists of points which are equidistant to two sites in the plane.

  35. Enabling Step: Voronoi Diagram By construction, each line-segment maximizes distance from the nearest point (sensor). Consequence: Path of Maximal Breach of Surveillance in the sensor field lies on the Voronoi diagram lines.

  36. Graph-Theoretic Formulation Given: Voronoi diagram D with vertex set V and line segment set L and sensors S Construct graph G(N,E): • Each vertex viV corresponds to a node ni N • Each line segment li Lcorresponds to an edge eiE • Each edge eiE, Weight(ei) = Distance of li from closest sensor skS Formulation: Is there a path from I to F which uses no edge of weight less than K?

  37. Finding Maximal Breach Path Algorithm • Generate Voronoi Diagram • Apply Graph-Theoretic Abstraction • Search for PB Check existence of path I --> F using binary search and BFS

  38. Delaunay triangulation • The Delaunay triangulation of a point set is a collection of edges satisfying an "empty circle" property • For each edge we can find a circle containing the edge's endpoints but not containing any other points

  39. Delaunay Triangulation The Delaunay triangulation is a triangulation which is equivalent to the nerve of the cells in a Voronoi diagram

  40. Maximal Support Path Given: Delaunay Triangulation of the sensor nodes Construct graph G(N,E): The graph is dual to the Voronoi graph previously described Formulation: what is the path from which the agent can best be observed while moving from I to F? (The path is embedded in the Delaunay graph of the sensors) Solution: Similar to the max breach algorithm, use BFS and Binary Search to find the shortest path on the Delaunay graph.

  41. PEAS: probing environment and adaptive sleeping

  42. Basic Approach and assumption • Exploit the redundancy • Keep a necessary subset of nodes working; turn off others into sleeping • Sleeping nodes replace failed ones as needed • Assume nodes can control the transmitting power to reach a given radius • Variable tx power available in Berkeley motes

  43. Probing Environment • Each node sleeps for a random time ts • ts follows an exponential distribution f(ts) = e- ts • The PROBE message is within a radius Rp (given by applications) • Rp < maximum tx range Rt • Working nodes send back REPLY when hearing the PROBE (also within radius Rp) working No REPLY is heard Broadcast a PROBE within Rp (probing range) sleeping probing Upon hearing a REPLY (, probing rate, is adjusted)

  44. Design rationale • Adjacent working nodes keep appropriate distances (at least Rp) • Redundancy in sensing and communicating function at appropriate levels • Probing avoid per-neighbor state about topology information maintenance • Randomized sleeping times • Spread over time to reduce “gap”, avoid prediction of a working node’s active time

  45. Adaptive Sleeping • Goal: keep the aggregate PROBE rate on a desired level _d (specified by the application) • independent from node densities at different locations, over time • Probing rate decides how quick a dead node can be replaced • Unnecessary overhead if too frequent • Long gaps if too slow • Basic idea • working node measures the aggregate PROBE rate • piggybacks the info in REPLY • probing nodes adjust their rates accordingly.

  46. How it works • A working node keeps • Counter C • Last measurement time t0 • Increase the counter each time a PROBE is heard • Calculate aggregate PROBE rate _a and includes it in REPLYs • Each probing neighbor adjusts its rate accordingly Ts Time … t t0 K wakeups Measure aggregate rate: _a = K / (t - t0) Each probing one adjusts: _new =  (_d / _a ) Example: An application wants _d = 6 times/min. Working node A has 5 sleeping neighbors, each probes at  =6. Node A measures aggregate _a = 30. Each sleeping one adjusts to _new = 6(6/30)=1.2, thus new _a = 6

  47. Maximum distance between working neighbors • Working node A puts nodes in cell 4, 5, 6 into sleep • To put node C in cell 2 into sleep, node B’s maximum distance to A is (1+5)Rp • Otherwise, C will be working • When there’s at least one node in each cell, distance between working neighbors is bounded • Theorem 3.1:when Rt > (1+5)Rp, and conditions in Blough’s Theorem 2 hold (mobicom ’02), working nodes are connected asymptotically. Rp 3 B C 4 5 A C 2 6 1

  48. references • Seapahn Meguerdichian, Farinaz Koushanfar, Miodrag Potkonjak, Mani Srivastava. "Coverage Problems in Wireless Ad-Hoc Sensor Networks." IEEE Infocom 2001, Vol. 3, pp. 1380-1387, April 2001. • Seapahn Meguerdichian, Farinaz Koushanfar, Gang Qu, Miodrag Potkonjak. "Exposure in Wireless Ad Hoc Sensor Networks." Procs. of 7th Annual International Conference on Mobile Computing and Networking, pp. 139-150, July 2001 • Fan Ye, Gary Zhong, Jesse Cheng, Songwu Lu, Lixia Zhang, "PEAS: A Robust Energy Conserving Protocol for Long-lived Sensor Networks", in ICDCS'03, 2003

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