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 Kong
83 Tat Chee Avenue, Kowloon,
HONG KONG
Department of Computer Science
City University of Hong Kong
Department of Computing2
Hong Kong Polytechnic University
PQ706, Mong Man Wai Building
Hung Hom, Kowloon, Hong Kong
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Department of Computer Science
City University of Hong Kong
Agenda
 Introduction
 Objective
 System Model
 Methodology
 Performance Analysis
 Conclusion
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Department of Computer Science
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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
region
region
User
Wireless
Network
Base
Station
region
region
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System Model
User
coordinator
Base
Station
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Methodology
 Adaptive Sampling Period Decision
 Sensor Selection Process
1. 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)
PSTi 
Max(( max  i  3  ( max   i )), 0)
vi  vmax
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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 requirement
1.
2.
3.
MAX / MIN
AVG / SUM
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
 Let the probability of the i-th region be pi,
where fi(s) is the pdf of N(µ,σ2)
pi 
N
( 
j1^ ji


f i (s) (  f j (t)dt )ds)
s
 Quality requirement: the maximum of pi must

be larger than P
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Finding variance for MAX
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

 k
P ( 1 ,  2 ,...,  n )
i.e., the sensor with greatest impact to pimax
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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

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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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Performance Analysis
Accuracy vs.
Sensor Error Variance Percentage
Percentage of Sensors Selected vs.
Sensor Error Variance
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Performance Analysis
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
han_song@cs.cityu.edu.hk
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