Tracking a Moving Object with a Binary Sensor Network

1
Tracking a Moving Object with a Binary Sensor
Network

• J. Aslam, Z. Butler, V. Crespi, G. Cybenko and D.
  Rus
• Presenter
• Qiang Jing

2
Outline

• Introduction
• Binary Sensor Network Model
• Tracking Algorithm
• Limitation of the Model
• Summary
• Open Issues

3
Introduction

• Sensors with a small number of bits save
  communications and energy
• Binary Sensor Network
• Each sensor can supply one bit of info only
• Plus Sensor Object is approaching!
• Minus Sensor Object is moving away!
• The sense bits are available to a centralized
  processor

4
Binary Sensor Network
v
X
a
ß
Sj

-
Si
O
(Sj X) v gt 0 ? Sj v gt X v
? Si v lt X v lt Sj v
(Si X) v lt 0 ? Si v lt X v
? maxSi v lt X v lt minSj v
5
Binary Sensor Network

• All plus sensors form a convex hull, so do all
  minus sensors
• The two convex hulls are disjoint
• And they are separated by the normal vector to
  the objects velocity

6
Binary Sensor Network

• Translate into linear programming equations (
  m0tan(?) )
• m0 lt 0
• yi y0 m0 (xi x0)
• yj y0 m0 (xj x0)
• m0 gt 0
• yi y0 m0 (xi x0)
• yj y0 m0 (xj x0)
• m0 0
• max( yj ) y0 max( yi )

7
Binary Sensor Network

• Incorporating history
• Future positions of the object have to lie inside
  all the circles whose center is located at a plus
  sensor and
• Outside all the circles whose center is located
  at a minus sensor
• Each sensor has a radius d(S,X) the distance
  between S and X

8
Tracking Algorithm

• Uses particle filtering
• Represent the location density function by a set
  of random points
• Compute the estimated object location based on
  these samples and their own weights
• A new set of particles is created for each sensor
  reading
• Previous position is chosen according to the old
  weights
• A possible successor position is chosen
• If the successor position meets acceptance
  criteria, add it to the set of new particles and
  compute a weight

9
Tracking Algorithm

• Constraints for particles x
• Outside the plus and minus convex hulls
• Inside the circle of center S and of radius
  D(S, x)
• S is any plus sensor at time k and k-1
• Outside the circle of center S- and of radius
  D(S-, x)
• S- is any minus sensor at time k and k-1
• Probability of particles is used to determine
  which position is the predicted one
• All particles with probability above a threshold
  are used

10
Limitation of the Model

• Only can detect the direction of motion not
  location
• Trajectories that have parallel velocities with a
  constant distance apart cannot be distinguished
  no matter where the sensors are

11
Tracking with a Proximity Bit

• In addition to the direction bit, sensors can
  have a proximity bit
• Proximity bit is set when the object is within
  some set range from the sensor
• Algorithm 1 is extended
• When a sensor detects an object the ancestors of
  every particle that has not been inside the range
  are shifted as far as the last time the object
  was spotted by proportional amounts

12
Summary

• Sensor nodes only can detect whether the object
  is approaching it or moving away
• Geometric properties can help to track the
  possible direction
• Additional proximity sensor bit can help to
  determine the likely location

13
Open Issues

• Use of only the frontier sensors those are
  visible from the convex hull
• When only part of sensors are known
• According to the partial knowledge, which is the
  best sensor to read next? Or, which are the best
  k sensor to read next?
• If all sensors have been read, where is the best
  location to put in a new sensor?
• If with the proximity bit, think of the above
  questions again
• How to decentralize the computation in the binary
  sensor network?

14
References

• J. Aslam, Z. Butler, V. Crespi, G. Cybenko, and
  D. Rus, Tracking a moving object with a binary
  sensor network, in ACM International Conference
  on Embedded Networked Sensor Systems, 2003.
• N. J. Gordon, D. J. Salmond, and A. F. M. Smith,
  Novel approach to nonlinear/non-Gaussian
  Bayesian state estimation, Proc. Inst. Elect.
  Eng. F, vol. 140, no. 2, pp. 107--113, Apr. 1993.