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 α β Sj + - Si O (Sj – X) · v > 0  Sj· v > X · v  Si· v < X · v < Sj· v (Si – X) · v < 0  Si· v < X · v  max{Si· v} < X · v < min{Sj· 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 object’s velocity

6. 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 )

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.