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.