Event Detection

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Event Detection

• From
• Mobile, Wireless, and Sensor Networks
  (Technology, Applications, and Future
  Directions), Chapter 6, Wiley and IEEE Press

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MODEL DESCRIPTION

• A typical wireless sensor network consists of a
  number of sensor nodes and a control center.
• To perform a detection function, each sensor node
  collects observation data from the surrounding
  environment, does some processing locally if
  needed, and then routes the processed data to the
  control center.
• The control center is responsible for making a
  final decision based on all the data it receives
  from the sensor nodes.

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Practical Wireless Sensor Network Model

• For a wireless sensor network to perform a
  detection function, routing usually is needed to
  transmit data from faraway nodes to the control
  center
• Spatial and temporal correlations exist among
  measurements across or at sensor nodes
• Noise interference must be considered as well.

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Simplified Wireless Sensor Network Model

• No cooperations among sensor nodes each sensor
  node independently observes, processes, and
  transmits data.
• No spatial or temporal correlation among
  measurements observations are independent
  across sensor nodes, and at each single node.
• No routing each sensor node sends data
  directly to the control center.
• No noise or any other interference data are
  transmitted over an error-free communication
  channel.

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Simplified Wireless Sensor Network Model
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Simplified Wireless Sensor Network Model

• Random variable H indicates whether an event
  occurs (H H1) or does not occur (H H0)
• Prior probabilities PHH1p and PH H01- p
  (0 lt p lt 1).
• We have K sensor nodes, S1, S2, . . .,SK
• Each node makes T binary observations
• Yi(j) is the jth observation at sensor Si,
  Yi(j)0 or 1, i 1, 2, . . ., K j 1, 2, . . . ,
  T.
• Observations are independently and identically
  distributed (i.i.d.)
• Observations have the identical conditional pmf
  of PYi(j)1H0p0 (false alarm) and PYi(j)1
  H1p1 (detection prob.), with 0 lt p0 lt p1lt1.
• ni the number of 1s out of T observations at
  sensor Si
• The processed data are transmitted to the control
  center, where a final decision H is made.
• Our objective is to minimize the overall
  probability of error (PH ? H ) at the control
  center.

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Three Operating Options

• Centralized Option
• Distributed Option
• Quantized Option

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Three Operating Options

• Centralized Option
• At each sensor node, the observation data are
  transmitted to the control center without any
  loss of information.
• The control center bases its final decision on
  the comprehensive collection of information.

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Three Operating Options
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Three Operating Options

• 3. Quantized Option
• Instead of sending all the information or sending
  a one-bit decision, each sensor node processes
  the observation data locally and sends a
  quantized M-bit quantity (qi for Si, qi ? 0, 1,
  . . . , 2M- 1, 1 ? M? T) to the control center
• The control center makes the final decision based
  on the basis of the k quantized quantities q1
  q2 . . . qk.

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Analysis Centralized Option
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Analysis Centralized Option
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Analysis Centralized Option
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Analysis Distributed Option

• For the distributed option we consider the local
  decision rule at the sensor nodes and the final
  decision rule at the control center,
  respectively.
• 1. Local Decision Rule. As we have specified
  before, each sensor node applies a local decision
  rule to make a binary decision based on the T
  observations.
• A question yields naturally whether we should
  have an identical local decision rule for all the
  sensor nodes.
• Generally, an identical local decision rule does
  not result in an optimum system from a global
  point of view. However, it is still a suboptimal
  scheme if not the optimal one, which has been
  observed by some previous work.
• Irving and Tsitsiklis 9 showed that for the
  binary hypothesis detection, no optimality is
  lost with identical local detectors in a
  two-sensor system
• Chen and Papamarcou 3 showed that identical
  local detectors are asymptotically optimum when
  the number of sensors tends to infinity.

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Analysis Distributed Option

• Identical local decision rule is assumed.
• Each sensor node does not have any information
  about other nodes, which means that the identical
  local decision rule would depend only on T, p,
  p0, p1
• The number of sensor nodes K is considered as
  global information and not available for decision
  making of sensor nodes.
• Eventually the problem is simplified to a similar
  case for the centralized option, where the only
  difference is the number of observations changes
  from KT to T.

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Analysis Distributed Option
18
Analysis Distributed Option
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Analysis Distributed Option
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Analysis Distributed Option
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Analysis Distributed Option
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Analysis Quantized Option

• For the quantized option, we develop the optimal
  quantization algorithm as well as the suboptimal
  quantization algorithm for different application
  scenarios.

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Analysis Quantized Option
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Analysis Quantized Option
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Analysis Quantized Option

• The optimal quantization algorithm can be
  obtained by exhaustive search.
• The one producing the minimal probability of
  error is the desired optimal quantization
  algorithm.

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Comparisons

• We evaluate the detection performance of the
  three operating options in terms of Pf, Pd, and
  Pe. Here we adopt the optimal quantization
  algorithm for the quantized option. We fix K4,
  M2, p 0.5, p00.2, and p10.7 and vary T from 3
  to 10. Figures 6.36.5 show Pf , Pd, and Pe
  versus T for three options.
• As we see in general, the centralized option has
  the best detection performance in the sense that
  it achieves the highest Pd and lowest Pf and Pe,
  while the distributed option has the worst
  performance.
• This is consistent with our expectation since the
  centralized option has a complete information of
  the observation data at the control center, while
  the distributed option has the least information
  at the control center.

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Comparisons
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Comparisons
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Comparisons
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Conclusion

• We have constructed a simplified wireless sensor
  network model that performs an event detection
  mission.
• We have implemented three operating options on
  the model, developed the optimal decision rules
  and evaluated the corresponding detection
  performance of each option.
• As we expected, the centralized option performs
  best while the distributed option is the worst
  regarding the accuracy of the detection.
• However, it is shown that the distributed option
  needs fewer than twice the sensor nodes for the
  centralized option to achieve the same detection
  performance.

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Conclusion

• We have modeled the energy consumption at the
  sensor nodes. The energy efficiency as a function
  of system parameters has been compared for the
  three options.
• The distributed option has the best performance
  for low values of Ec and high values of Et.(Ec
  represents the energy consumed for one comparison
  or one counting, and Et represents the energy
  consumed for transmitting one bit of data over a
  unit distance)
• For high Ec and low Et, the centralized option is
  the best for relatively short distances from
  sensor nodes to the control center, while the
  distributed option is the best for long distances.

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Conclusion

• Furthermore, we have examined the robustness of
  the wireless sensor network model by implementing
  two attacks.
• For both of them, the distributed option shows
  the least loss of performance in terms of ratio
  while the centralized option has the highest loss.

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