1 / 17

Corey Miller

Discussion of “Tracking a Moving Object with a Binary Sensor Network” Javed Aslam, Zack Butler, Florin Constantin, Valentino Crespi, George Cybenko, Daniela Rus. Corey Miller. One Bit Sensors. Sensors with a small number of bits save communications and energy Three assumptions

sarah-owens
Download Presentation

Corey Miller

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Discussion of“Tracking a Moving Object with a Binary Sensor Network”Javed Aslam, Zack Butler, Florin Constantin,Valentino Crespi, George Cybenko, Daniela Rus Corey Miller

  2. One Bit Sensors • Sensors with a small number of bits save communications and energy • Three assumptions • Sensors can identify a target approaching or moving away • The sense bits are available to a centralized processor • Can be done with a broadcast or other ways • For precise location, sensors have another sense bit that provides “proximity” information • Sensors indicate “plus” if object is approaching and “minus” if object is moving away

  3. The Basic Idea • A convex hull of a set of points is defined as: • Formally: It is the smallest convex set containing the points. • Informally: It is a rubber band wrapped around the "outside" points. • Plus and Minus sensors each have a convex hull • Current position of the object is between the convex hull of the plus sensors and the convex hull of the minus sensors • The object is moving towards the convex hull of the plus sensors

  4. Diagram of the Basic Idea • Sj is the minus sensor • Si is the plus sensor • X is the position of the object • V is direction of movement – X’(t) • dl is the increment of movement • From Lemma 1 Sj*V(t) < X(t) * V(t) < Si * V(t)  > /2 and  < /2

  5. Limits of the method • Coarse approximation • the object is outside the minus and plus convex hulls. (Theorem 2) • C(plus)  C(minus) =  • X(t)  C(plus)  C(minus) • The plus and minus hulls are separated by the normal to the object’s velocity (Theorem 2) • V points towards C(plus) • Can translate this into linear programming equations.

  6. Using 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

  7. Algorithm for a One Bit Sensor • Uses particle filtering • Translates continuous probability density function into a discrete probability vector • Allows non-Guassian errors • Predictive and update cycles • 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

  8. The Object Movement • Approximate inside area defined by • xkj (new particle) has to be outside plus and minus convex hulls • xkj is inside the circle of center S+ with radius the distance from S+ to xk-1j • S+ is any plus sensor at time k and k-1 • xkj is outside the circle of center S- and of radius S- to xk-1j • S- is any plus 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 • Low threshold increases estimation error • High threshold increases running time

  9. Experiments • Using MATLAB • Random and grid sensor alignment • Linear, random turns and mild turns (direction change of at most /6) • Used root mean square error • Particles with equal weight and • Particles with weight according to their probabilities • Not clear why trend of probability weighed answers changes for random, linear

  10. Limitations of the model • Can only distinguish direction of motion – not location • Trajectories that have parallel velocities with a constant distance apart cannot be separated. • The paper formally proves this

  11. Limitations of the model

  12. The Proximity Bit • In addition to the plus/minus bit, sensors can have a proximity bit • For example an IR sensor • Range can be different • Useful to set so proximity bits do not overlap • 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. • This is algorithm 1 when no proximity sensor is triggered

  13. Algorithm for Two Bit Sensors

  14. Experiments • Metric is relative position error after the object is detected by a proximity sensor • How many trajectories out of 10,000 are detected after k steps. • The distribution of the amount of time that passes until an object is first spotted is exponential

  15. Experiments

  16. Experiments • Algorithm 2 greatly improves the accuracy of location estimation. • Down to a RMSE of .02 for a 64 sensor network • Grid layout somewhat better than random • Sufficient for many tracking applications

  17. Summary • Basically the approach asks each sensor • Is the object moving toward or away from you? • Calculates velocity • Is the sensor in your proximity? • Determines likely position • Several open questions • How to handle noise • Report a 0 if signal is below a threshold? • Or declare the sensor untrustworthy through a central approximation • Use of only frontier sensors – those that are visible from the convex hull • Decentralize the computation

More Related