ACE in the Hole - Adaptive Contour Estimation using Collaborating Mobile Sensors
Sumana Srinivasan, Krithi Ramamritham and Purushottam Kulkarni
Department of CSE, Indian Institute of Technology Bombay, Mumbai.
Contour Estimation
Estimation of the boundary formed by connecting a set of
points of equal value in a field e.g., temperature, pressure,
pollutant concentration
Applications: Estimating extent of oil spills - a prerequisite
for containment and corrective action (as in figure), tracking
pollutant flows, study of plankton assemblages
1.
2.
3.
Nest  #points on the estimated contour
Nact  #points on the actual contour
Uses image processing for Combine local samples to
estimation.
form a global estimate.
Exploit mobility
samples.
 Low accuracy due to
obstructions and inclement
weather affect accuracy
 High density and large
number of sensors for high
accuracy and coverage
+ Fewer sensors can yield high
accuracy and coverage
 Large coverage possible
+ Low sensor cost and
energy
 Higher sensor cost and
energy
 Cannot adapt to dynamic
contours, high cost of
redeployment
f
if f (x, y)  
) 2 else f (x, y)  
ACE Algorithm



 p3  e
 p 4 yi
  (x  x^ )2  (y  y^ )2
Size of contour, .

 = Area of envelope bounding estimated points on contour
Area of field
Spread of sensors, S
increase
+ Can adapt to dynamic
contours without redeployment
 p 2 xi
S = Area of convex hull of current positions
Parameter
Contour
Sensor
Communication
Energy
Movement
2. Spread Always SA
Assumptions
Choose direction that minimizes spread function
d 2
sf  ( )
2
Continuous
Error free,, self-localized
Single-hop
Mobility+Communication+Computation+ Sensing
Step-wise discrete
• ACE provides best-of-both-worlds solution
• Enables sensors to intelligently choose
between direct descent and spread
Target Angle '
• Adapts to type of deployment, size of
contour and distance from contour
• Distributed co-ordination for efficient
contour coverage
• Performs high precision, low latency and
low energy estimation
Evaluation Setup and Simulation Parameters
Pollutant Field
Light Field
WQMAP - a tool for simulating pollutant
dispersion, Three pollutant load sites, 120 time
steps for simulation
Measurements taken at every grid point on
15x15 grid with three light sources using
Crossbow Mote
Parameter
Description
Value
l
Length of grid
Maximum steps allowed per sensor
Number of simulation runs
Estimation frequency
Sensing radius
Transmission range
Large
Medium
Small
500, 140
2000
1000
Every 5 steps
√2
√l
nmax
nsim
nest
rsense
Rtrans
Contours
Large
Medium
Small
Large
Medium
Small
DD
Other Issues
• Handle limited transmission range
• Support discontinuous contours
Latency high when sensors are deployed far and
contour is small. Need to spread judiciously!!
Estimating centroid

Centroid of envelope bounding
• estimated points on contour if sensors converge or
• estimated convergence points if sensors not converged.
> 50% of field area
> 10% - 50% of field area
< 10% of field area
Precision Comparison (Bounded Energy)
Latency Comparison (Unbounded Energy)
ACE
Conclusions
Area of field

Contours
Use wall moving algorithm to trace
• Estimate (xˆ, yˆ) such that f((xˆ, yˆ) = 
• If (x,y) is the current position of the sensor, then


STEP 2: Coverage Phase
• Use Nonlinear regression to fit (xi, yi,zi) and compute
coefficients using Nelder Mead simplex optimization
zi  p0  p1  e
Pi  Path length of ith tracing sensor
Indicator of energy consumed
Mobile Sensors
to



)
2
Latency high when sensors are collocated and contour
is big. Need to spread!!
Nact
In-situ Sensing
Static Sensors
d f  (1
|
Latency
= argmaxi(Pi)


  tanh(  S) 0    1

Choose direction that minimizes the distance function
f
Distance from Contour, 
as f    d f  (1  )  s f
1. Direct Descent DD
d f  (1 
Precision = | Nact  Nest
Contour Estimation Techniques
 High deployment cost
STEP 1: Converge Phase
How do sensors approach and surround the contour efficiently?
How do sensors co-ordinate for distributed contour estimation?
How do sensors adapt to different deployments, sizes and shapes
of contours?
Given a scalar field with varying field value, the task is to
estimate a contour of a given value with maximum
precision and minimum latency
3. Adaptive Contour Estimation ACE
Choose direction that minimizes the adaptive spread function
System Model and Evaluation Metrics
Problem Definition
Remote Sensing
Movement Strategies
Challenges
Comparison of Sensors Movement Strategies
Feasibility and Energy Characterization on Robotic Test bed
SA
•11x8 grid with granularity 8 cm with single slit neon source.
• ATMEGA 128, 11MHz processor, 2.4GHz CDMA, 3 white line sensors, 2 shaft encoders, 2 ultra low power
DC motors, rotating arm with 2 servo motors
Deployment
Latency
CP
Latency
CP
Latency
CP
Non-clustered
139  2
498  11
248  8
100
100
100
142  2
681  15
268  7
100
71
63
229  4
780  16
319  7
100
78
29
Clustered
375  8
845  23
276  25
100
99
96
441  5
1006  17
319  7
100
31
11
483  5
1119  12
326  11
78
22
4
Convergence Percentage, CP = Number of runs at least one sensor converged on the contour
Total number of runs
Non-clustered: Large and Small contours: ACE  DD
Medium contour: ACE < DD by 22% and ACE < SA by 38%
Clustered: All contours, ACE < DD by 7-12% and ACE < SA by 4-20%
Acknowledgement: We thank Parmesh Ramanathan,
Sachitanand Malewar, Amey Apte and GRAM++ team
at IITB for their support.
Non-clustered deployment (Medium contour)
Clustered deployment (Medium contour)
Max. steps > 100:
• Non-clustered: ACE > DD by 20-25% and ACE > SA by 25-30%
• Clustered: ACE > DD and SA by 30-45%
Sensors directly approach the contour
DD Latency = 818
Max. steps ≤ 100: ACE  DD for all deployments
Sensors only spread around the centroid
SA Latency = 623
Contours
Sensitivity to Design Parameters
Deployment
Non-clustered
Medium
Convergence Percentage is uniformly higher than DD and SA
Clustered
Distribution of Latency Differences
Non-clustered
Small
Clustered
Algorithm
ACE
DD
ACE
DD
ACE
DD
ACE
DD
Total Energy
2030J
2700J
3342J
3890J
1249J
1335J
1417J
1587J
Summary of Results
Small Contour
Non-clustered deployment
(Medium contour)
Clustered deployment
(Medium contour)
Very high probability that ACE has lesser latency than DD
- Factor of 6 for non-clustered and 8 for clustered deployments
Medium Contour
ACE adapts best to distance from the contour, size of contour
and extent of spread of sensors
Sensors 7 and 8 overlap
ACE (without redirection) Latency = 451
Sensors 1,5,7,9 redirected without overlap
ACE (with redirection) Latency = 383
Adaptive Contour Estimation (ACE)
• Minimizes latency 7-22% over DD and 4-38% over SA
• Maximizes convergence percentage 8-45% over DD and 30-62% over SA
• Maximizes precision by 15-40% for bounded steps
• Consumes 7-24% less energy over DD
• Latency and prediction error are highly correlated