ace in the hole - adaptive contour estimation using collaborating mobile sensors
DESCRIPTION
Precision = N est #points on the estimated contour N act #points on the actual contour Latency = argmax i (P i ) P i Path length of i th tracing sensor Indicator of energy consumed. - PowerPoint PPT PresentationTRANSCRIPT
ACE in the Hole - Adaptive Contour Estimation using Collaborating Mobile SensorsSumana Srinivasan, Krithi Ramamritham and Purushottam KulkarniDepartment 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
Problem Definition
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
Problem Definition
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
Mobile SensorsStatic Sensors
In-situ SensingRemote Sensing
Exploit mobility to increase samples.
+ Fewer sensors can yield high accuracy and coverage
Higher sensor cost and energy
+ Can adapt to dynamic contours without redeployment
Combine local samples to form a global estimate.
High density and large number of sensors for high accuracy and coverage
+ Low sensor cost and energy
Cannot adapt to dynamic contours, high cost of redeployment
Uses image processing for estimation.
Low accuracy due to obstructions and inclement weather affect accuracy
Large coverage possible
High deployment cost
Contour Estimation Techniques
•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
Feasibility and Energy Characterization on Robotic Test bedFeasibility and Energy Characterization on Robotic Test bed
2700J
1587J
1417J
1335J
3890J
3342J
1249JACE
DD
ACE
DD
Non-clustered
Clustered
Small
2030JACE
DD
ACE
DD
Non-clustered
Clustered
Medium
Total EnergyAlgorithmDeploymentContours
Comparison of Sensors Movement StrategiesComparison of Sensors Movement Strategies
Summary of Results
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
Summary of Results
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
Sensors directly approach the contour DD Latency = 818
Sensors only spread around the centroid SA Latency = 623
Sensors 7 and 8 overlap ACE (without redirection) Latency = 451
Sensors 1,5,7,9 redirected without overlap ACE (with redirection) Latency = 383
AssumptionsParameterContinuous
Error free,, self-localized
Single-hop
Mobility+Communication+Computation+ Sensing
Step-wise discrete
Contour
Sensor
Communication
Energy
Movement
Challenges
1. How do sensors approach and surround the contour efficiently?2. How do sensors co-ordinate for distributed contour estimation?3. How do sensors adapt to different deployments, sizes and shapes
of contours?
Challenges
1. How do sensors approach and surround the contour efficiently?2. How do sensors co-ordinate for distributed contour estimation?3. How do sensors adapt to different deployments, sizes and shapes
of contours?
System Model and Evaluation MetricsSystem Model and Evaluation Metrics
|Nact Nest |Nact
Precision =
Nest #points on the estimated contourNact #points on the actual contour
Latency = argmaxi(Pi)
Pi Path length of ith tracing sensorIndicator of energy consumed
STEP 1: Converge PhaseSTEP 1: Converge Phase
STEP 2: Coverage PhaseUse wall moving algorithm to traceSTEP 2: Coverage PhaseUse wall moving algorithm to trace
1. Direct Descent DD
Choose direction that minimizes the distance function
Latency high when sensors are collocated and contour is big. Need to spread!!
2)1(f
d f
d f (1f)2
if f (x,y)
else f (x,y)
2. Spread Always SA Choose direction that minimizes spread function
Latency high when sensors are deployed far and contour is small. Need to spread judiciously!!
s f (d2)2
• ACE provides best-of-both-worlds solution• Enables sensors to intelligently choose between direct descent and spread
• 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
Other Issues• Handle limited transmission range• Support discontinuous contours
• ACE provides best-of-both-worlds solution• Enables sensors to intelligently choose between direct descent and spread
• 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
Other Issues• Handle limited transmission range• Support discontinuous contours
3. Adaptive Contour Estimation ACE Choose direction that minimizes the adaptive spread function
ACE Algorithm
as f d f (1 )s f
tanh(
S)
0 1
Movement StrategiesMovement Strategies
Evaluation Setup and Simulation ParametersEvaluation Setup and Simulation Parameters
ValueDescriptionParameter
500, 140
2000
1000
Every 5 steps
√2
√l> 50% of field area
> 10% - 50% of field area
< 10% of field area
Length of grid
Maximum steps allowed per sensor
Number of simulation runs
Estimation frequency
Sensing radius
Transmission range
Large
Medium
Small
lnmax
nsim
nest
rsense
Rtrans
Contours
Latency Comparison (Unbounded Energy)Latency Comparison (Unbounded Energy)
78
22
4
483 5
1119 12
326 11
100
31
11
441 5
1006 17
319 7
100
99
96
375 8
845 23
276 25
Clustered
Large
Medium
Small
100
78
29
229 4
780 16
319 7
100
71
63
142 2
681 15
268 7
100
100
100
139 2
498 11
248 8
Large
Medium
Small
CPCPCP LatencyLatencyLatency
SADD
Non-clustered
ACEDeploymentContours
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 deploymentsVery high probability that ACE has lesser latency than DD - Factor of 6 for non-clustered and 8 for clustered deployments
Sensitivity to Design ParametersSensitivity to Design Parameters
ACE adapts best to distance from the contour, size of contour and extent of spread of sensors ACE adapts best to distance from the contour, size of contour and extent of spread of sensors
Small Contour Medium Contour
Distribution of Latency DifferencesDistribution of Latency Differences
Precision Comparison (Bounded Energy)Precision Comparison (Bounded Energy)
Max. steps > 100: • Non-clustered: ACE > DD by 20-25% and ACE > SA by 25-30%• Clustered: ACE > DD and SA by 30-45%
Max. steps ≤ 100: ACE DD for all deployments
Max. steps > 100: • Non-clustered: ACE > DD by 20-25% and ACE > SA by 25-30%• Clustered: ACE > DD and SA by 30-45%
Max. steps ≤ 100: ACE DD for all deployments
Non-clustered deployment (Medium contour) Clustered deployment (Medium contour)
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%
Convergence Percentage is uniformly higher than DD and SA
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%
Convergence Percentage is uniformly higher than DD and SA
Pollutant Field WQMAP - a tool for simulating pollutant dispersion, Three pollutant load sites, 120 time steps for simulation
Light FieldMeasurements taken at every grid point on 15x15 grid with three light sources using Crossbow Mote
Distance from Contour, • Use Nonlinear regression to fit (xi, yi,zi) and compute coefficients using Nelder Mead simplex optimization
• Estimate (xˆ, yˆ) such that f((xˆ, yˆ) = • If (x,y) is the current position of the sensor, then
Size of contour, .
= Area of envelope bounding estimated points on contour Area of field
Spread of sensors, S
S = Area of convex hull of current positions
Area of field
Target Angle '
Estimating centroid
Centroid of envelope bounding • estimated points on contour if sensors converge or• estimated convergence points if sensors not converged.
zi p0 p1 e p2xi p3 e
p4 yi
(x x^ )2 (y y^ )2
ConclusionsConclusions
Convergence Percentage, CP = Number of runs at least one sensor converged on the contourTotal number of runs
Acknowledgement: We thank Parmesh Ramanathan, Sachitanand Malewar, Amey Apte and GRAM++ team at IITB for their support.