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1Department of Computer ScienceCity University of Hong Kong

Department of Computer Science

City University of Hong Kong

A Statistics-Based Sensor Selection Scheme for Continuous Probabilistic

Queries in Sensor Networks

Song Han1, Edward Chan1, Reynold Cheng2, and Kam-Yiu Lam1

Department of Computer Science1, City University of Hong

Kong83 Tat Chee Avenue, Kowloon,

HONG KONG

Department of Computing2 Hong Kong Polytechnic UniversityPQ706, Mong Man Wai Building

Hung Hom, Kowloon, Hong Kong

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Statistics-Based Sensor Selection Scheme in Sensor Networks

Agenda

Introduction Objective System Model Methodology Performance Analysis Conclusion

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Introduction

Constantly-evolving Environment

Uncertainty of Sensor Data

Sensor Data are erroneous, unreliable and noisy Database may store inaccurate values Query results can be incorrect

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Introduction

Statistical Model of Sensor Uncertainty

A sensor value can be described more accurately as a Gaussian Distribution

Mean µ Variance σ2

Gaussian Distribution(,2)

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Introduction

Probabilistic Queries [SIGMOD03]

Represent the imprecision in the value of the data as a probability density function. e.g., Gaussian

Augment query answers with probabilities Give us a correct (possibly less precise) answer,

instead of a potentially incorrect answer

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Introduction

Query Quality and Variance

Query quality can be improved with lower variance To obtain a smaller σ2, a simple idea is to use more

sensors Get an average of these readings N(µ,σ2) becomes N(µ,σ2/ns), where ns is the number of

“redundant” sensors

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Introduction

Deploying Redundant Sensors Exploit the fact that sensors are cheap Example: 1000 sensors in the room to obtain average

temperature Variance decreased by a factor of 1000

Resource Limitation Problem Wireless network has limited bandwidth Sensors have limited battery power Can’t afford too many sensors!

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Introduction

The Sensor Selection Problem

How to decide sensors’ sampling period How many sensors to use for the guaranteed

level of query quality? Select which sensors?

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Objective

Adaptive Sampling Period Decision Scheme Find out the minimum variance of each entity

being monitored to meet the probabilistic query quality requirement

Select minimum number of “good” sensors to achieve the required variance

Decide which sensors should be selected

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System Model

User

Base Station

WirelessNetwork

region region

region

region

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System Model

User

Base Station

coordinator

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Methodology

Adaptive Sampling Period Decision

Sensor Selection Process1. obtain (, max 2) from sensors in region

2. Derive max 2 for each item to satisfy quality

3. Determine sensor nodes to be used

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Adaptive Sampling Period Decision

The region’s value is changing continuously Periodical Sample will consume excessive

system resource Adaptive Sample Scheme for MAX/MIN query

ESSENCE: To increase the sampling period for the regions whose values have little effect on the query result.

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Adaptive Sampling Period Decision Adaptive Sample Scheme for MAX/MIN query

Predicted Sampling Time (PST)

max max

max

(( 3 ( )),0)i ii

i

MaxPST

v v

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Sensor Selection Process

Types of Probabilistic Queries Factors Affecting Query Quality Probabilistic Query Quality An Example: MAX Query Reselection of Sensors for Continuous

Queries

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Types of Probabilistic Queries

MAX/MIN: Which region has max or min temperature? (A, 60%), (B, 30%), (C, 10%)

AVG/SUM: What is the average temperature of regions A, B and C?

Range Count: How many objects are within 50m from me?

COUNT 1 2 3 4 5

Probability 0.1 0.2 0.5 0.15 0.05

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Factors Affecting Query Quality

Error distribution of each sensor reading

Variance of Gaussian distribution

Each query has its own correctness requirement1. MAX / MIN

2. AVG / SUM

3. Range Count Query

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Probabilistic Query Quality

Probabilistic queries allow specification of answer quality

1. MIN/MAX: highest probability ≥ P

2. AVG/SUM: variance of answer ≤ T

3. Range count: Top K counts contribute total probability ≥ P

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Example: MAX Query

pi ( f i(s)

j1̂ ji

N

( f j (t)dt

s )ds)

Quality requirement: the maximum of pi must be larger than P

Let the probability of the i-th region be p i, where fi(s) is the pdf of N(µ,σ2)

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1. Set the variance of each region (σ1,σ2,…, σn) to their maximum possible

2. Find pimax, the maximum of pi’s

3. Find jmax, the index of the maximum of

i.e., the sensor with greatest impact to pimax

Finding variance for MAX

1 2( , ,..., )nk

P

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Finding variance for MAX (Cont.)

4. Adjust variance of the jmaxth sensor

σjmax=σjmax-∆σ

5. Keep reducing variances until

pimax(σ1,σ2,…, σn) P

6. Return σ1,σ2,…, σn as the variances for the n regions

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Deciding Set of Sensors

Distribution of ns samples follows normal distribution N(µ,σ2/ns)

Compute ns satisfying σ2/ns ≤ max variance

Compute expected value of E(s) Select ns sensors with the lowest difference of

readings from E(s) Only these sensors send their sampled values to

the coordinator for computing N(µ,σ2/ns)

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Reselection of Sensors for CQ

Sensor selection runs again when:

1. Probabilistic query quality cannot be met (e.g., due to change of mean)

2. Coordinator detects some sensor is faulty (e.g., its value deviates significantly from the majority) or gives no response after some timeout period

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Simulation Model

Continuous query length: 1000 sec Sensor sampling interval: 5 sec Number of regions: 4 Number of sensors per region: U [100,150] Sensor error variance range: 5-25% Difference in the values of different regions: 2-10% Quality requirement for MIN/MAX Query : 95% Variance Change Step (∆σ): 0.3

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Performance Analysis

% in Sensor Selected vs.Difference in Region’s Values

Accuracy vs.Difference in Region’s

Values

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Accuracy vs.Sensor Error Variance Percentage

Percentage of Sensors Selected vs.Sensor Error Variance

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Changes in Value of Regions over Time Percentage of Sensors Selected over Time for Continuous Changes in Values of Regions

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Conclusion

Accuracy improved through multiple sensors Adaptive Sample Period Decision Scheme Limited network bandwidth allows only limited

number of redundant sensors Sensor selection algorithm selects good sensors

for reliable readings

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Future Work

Region Selection Reducing the Computational Complex of the

sensor selection progress Differentiating bad sensors from “good ones”

that report true surprising events Hierarchical organization of coordinators How to assign coordinators?

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References

1. [VSSN04] K.Y. Lam, R. Cheng, B. Y. Liang and J. Chau. Sensor Node Selection for Execution of Continuous Probabilistic Queries in Wireless Sensor Networks. In Proc. of ACM 2nd Intl. Workshop on Video Surveillance and Sensor Networks, Oct, 2004.

2. [SIGMOD03] R. Cheng, D. Kalashnikov and S. Prabhakar. Evaluating Probabilistic Queries over Imprecise Data. In Proc. of ACM SIGMOD, June 2003.

3. [Mobihoc04] D. Niculescu and B. Nath. Error characteristics of adhoc positioning systems. In Proceedings of the ACM Mobihoc 2004, Tokyo, Japan, May 2004.

4. [WSNA03] E. Elnahrawy and B. Nath. Cleaning and Querying Noisy Sensors. In ACM WSNA’03, September 2003, San Diego, California.

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Thank you!

HAN Song

[email protected]

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