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
e e
R
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.
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
• Equal weight
• Proportional weight (r)
wi 
1
2
1
R  0.25(v  (ti 
))
f
2
• Logarithmic weight
wi  ln( 1  ti )
R: sensor radius
v: estimated speed
ti: detection duration
f: sampling frequency
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
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)
Cluster Head
(mono-board
computer)
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
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
1
2
A
3
4
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
Cross Correlation (to find out delays)
Cluster
Head
Slave
Sensor
Detect
interesting
sound
Locate
sound
source
location
Broadcast
sound
signature
Crosscorrelation to
detect local
arrival time
Report
local
arrival
time
Final position fixed
Sensor (mica motes)
Cluster Head
(mono-board
computer)
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
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
Cluster Head
Sink/
Pursuer
Communication Subsystem: route back the
reports generated by cluster heads to sink
Multi-parent sink tree routing
cluster covered area
cluster head
router (mica motes)
Sink
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
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
1. Generate Voronoi Diagram
2. Apply Graph-Theoretic
Abstraction
3. 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
I
F
PS
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
Broadcast a PROBE within Rp
(probing range)
sleeping
probing
Upon hearing a REPLY
(, probing rate, is adjusted)
• 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)
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
t0
• A working node keeps
Ts
…
K wakeups
Measure aggregate rate:
_a = K / (t - t0)
Each probing one adjusts:
_new =  (_d / _a )
t
Time
– 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
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
Rp
3
4
6
C
5
A
C
1
2
• 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
B
(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.
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