Tracking a Moving Object with a Binary Sensor Network

J. Aslam, Z. Butler, V. Crespi, G. Cybenko and D. Rus

Presenter:Qiang Jing

Outline

IntroductionBinary Sensor Network ModelTracking AlgorithmLimitation of the ModelSummaryOpen Issues

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

β

vα

Binary Sensor Network

+

-

X

Sj

Si

O

(Sj – X) · v > 0 Sj · v > X · v

(Si – X) · v < 0 Si · v < X · v Si · v < X · v < Sj · v

max{Si · v} < X · v < min{Sj ·

v}

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 object’s velocity

Binary Sensor Network

Translate into linear programming equations: ( m0=tan(θ) ) m0 < 0 :

yi – y0 ≥ m0 ∙ (xi – x0) yj – y0 ≤ m0 ∙ (xj – x0)

m0 > 0 : yi – y0 ≤ m0 ∙ (xi – x0) yj – y0 ≥ m0 ∙ (xj – x0)

m0 = 0 : max( yj ) ≤ y0 ≤ max( yi )

Binary Sensor Network

Incorporating history Future positions of the object h

ave 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

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

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

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

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

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

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?

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.