Upload
tanisha-patrick
View
32
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Discussion of “Tracking a Moving Object with a Binary Sensor Network” Javed Aslam, Zack Butler, Florin Constantin, Valentino Crespi, George Cybenko, Daniela Rus. Bill Kramer [email protected]. One Bit Sensors. Sensors with a small number of bits save communications and energy Three assumptions - PowerPoint PPT Presentation
Citation preview
04/19/23CS 294-1
Discussion of “Tracking a Moving Object
with a Binary Sensor Network”
Javed Aslam, Zack Butler, Florin Constantin, Valentino Crespi, George Cybenko, Daniela Rus
Bill [email protected]
04/19/23CS 294-1 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
04/19/23CS 294-1 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
04/19/23CS 294-1 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
04/19/23CS 294-1 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 huls are separated by the normal to the object’s velocity (Theorem 2) V points towards C(plus)
Can translate this into linear programming equations.
04/19/23CS 294-1 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
04/19/23CS 294-1 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
04/19/23CS 294-1 8
The Object Movement
Approximate inside area defined by xk
j has to be outside plus and minus convex hulls xk
j is inside the circle of center S+ and of radius S+ to xk-1
j 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
04/19/23CS 294-1 9
Experiments
Using MATLAB Random and grid
sensor alignment Linear, random turns
and mild turns (at most /6) directions
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
04/19/23CS 294-1 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
04/19/23CS 294-1 11
The Ultimate Goal
04/19/23CS 294-1 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
04/19/23CS 294-1 13
Algorithm for Two Bit Sensors
04/19/23CS 294-1 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
04/19/23CS 294-1 15
Experiments
04/19/23CS 294-1 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
04/19/23CS 294-1 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