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 Detection probability < 1.0 False alarms Goal: detect, alert, and track for each target

Frisbee model

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

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 e R 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.

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

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.

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

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

Tracking methods One sensor at a time Minimal sensor (binary) model 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

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

IDSQ DETECTION message

IDSQ Timestamp Likelihood ratio

IDSQ SUPPRESSION message

IDSQ HANDOFF message New leader reports sensory data to sink

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

Acoustic target tracking Two subsystems Acoustic target tracking subsystem Communication subsystem

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)

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

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)

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 A 1 3 2 4

Cross Correlation (to find out delays) Locate sound source location Detect interesting sound Broadcast sound signature Cluster Head Cross-correlation to detect local arrival time Report local arrival time Slave Sensor

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)

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

Scenario Sensor Router Cluster Head Sink/Pursuer Sink/ Pursuer

Multi-parent sink tree routing 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)

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

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 Tracking Using Wireless Sensor Devices, Proc. of the 2nd Workshop on Information Processing in Sensor Networks (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)

Sensor coverage and sleeping

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

How well can the field be observed ? 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.

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.

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

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

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.

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 L corresponds 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?

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

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

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

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.

PEAS: probing environment and adaptive sleeping

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

Probing Environment working No REPLY is heard 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)

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

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.

How it works … Time K wakeups Example: 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 t0 t 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

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

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