On the Energy Efficiency of Distributed Sensor Fusion

1
On the Energy Efficiency of Distributed Sensor
Fusion
CSNDSP 2006

• Jonathan R. Levesque Ioanis Nikolaidis
• Computing Science Department
• University of Alberta, Edmonton, Canada
• jrl2,yannis_at_cs.ualberta.ca

2
Outline

• Sensor Fusion (Definition)
• Distributed Sensor Fusion
• A Centralized Adversary (WR)
• Simulation Results
• Conclusion

3
Sensor Fusion Problem Statement

• (One of a large variety of similar
  definitions.)
• Sensors take measurements of parameters with
  unknown values which include the impact of
  Gaussian noise. ( )
• The data fusion algorithm/protocol dictates the
  message exchanges and processing to derive the
  parameter estimates and provide them to all
  sensors.

4
Distributed Sensor Fusion (DSF)
Xiao, Boyd Lall 2005

• A distributed algorithm based on distributed
  average consensus is used to compute the
  maximum-likelihood (ML) estimate of the
  parameters.
• The algorithm is fully distributed and requires
  at each sensor a fixed (constant) size space to
  maintain all relevant data structures.
• The algorithm is iterative (and in principle
  asynchronous) update of each sensor nodes local
  estimate based on a weighed average of its
  current estimate and that of its neighbours.

5
Strengths Features of DSF

• Fully distributed algorithm.
• Does not rely on routing.
• Communication only between neighboring peers.
• No reliable communication necessary (unreliable
  broadcast).
• No pre-set communication structure (e.g. tree).
• Purportedly suitable for changing (mobile?)
  topologies.
• Technicalities.
• Iterative, but unknown of iterations.
• Relies on underlying jointly connected graph.
• The main contribution is demonstrating
  convergence to global ML solution.

6
Jointly Connected Graphs

• Assume (the usual) adjacency binary matrix
  representation of network topology.
• A variable topology can be seen as a sequence of
  such binary matrices over time.
• Regular connectivity refers to the connectivity
  of the underlying graph represented by a single
  (snapshot) matrix.
• The jointly connected graphs are (finite) sets of
  graphs (matrices) whose union is connected.

7
DSF Iteration
8
DSF Weight Selection

Maximum Degree Weights

otherwise
Metropolis Weights
otherwise
Both converge as desired, but Metropolis version
converges faster.
9
Critique of Protocol Behind DSF

• There is no real description of a DSF protocol
  which raises concerns about
• The true message complexity ( and form).
• The control features (start, stop, etc.).
• The energy consumption.
• But first an example of a real protocol.

10
Weighed-Randomized (Tree-Based)
Zhou Krishnamachari 2003

• Construct a spanning tree by selecting one parent
  for each node based on weights
• Selection of parents attempts to balance energy
  spending amongst nodes.
• Sink node alone calculates solution and can
  (optionally) flood it through the network.

11
The Achilles Heel of Tree-Based Schemes

• The neighborhood around the sink node.
• The large fan-in of messages implies larger
  energy consumption to forward the messages.
• If the sink is always the same, depletion of
  near-the-sink nodes determines network lifetime.
• Some (obvious) alternatives exist, such as
  rotation of sinks (following an
  election-of-leader protocol).
• Caveat sometimes sinks are inevitable due to
  nature of how sensed data queries are formed.

Our task is DSF worth the trouble in terms of
energy consumed? It avoids near-the-sink energy
depletion but we deal with multiple Iterations
when we could have collected all data in one shot.
12
Simulations

• WR modified to broadcast to all nodes the result
  of the computation at the sink. Relevant energy
  cost to inform all nodes of the result is
  accounted for.
• Both DSF and WR subjected to the same link outage
  probability f but WR uses a reliable protocol to
  forward values.
• First-order energy model
• Heinzelman, Chandrakasan Balakrishnan 2000

13
Simulations (contd)

• 1000 nodes on a 260m x 120m area.
• Node range of 12.2m (40ft). Approximately
  7000 edges per graph.
• Message size was set to 10 bytes.
• Link outage probability f 0.5
• Measurement noise std. dev. 10.

14
Avg. Per-Node Energy Consumption
15
Max. Per-Node Energy Consumption
16
DSF Max. Energy Consumption vs. f
17
DSF Avg. Energy Consumption vs. f
18
WR Max. Energy Consumption vs. f
19
WR Avg. Energy Consumption vs. f
20
Simulation Observations

• Tree-based schemes use less energy on average
  than DSF.
• DSF has more variation in relation to link outage
  probability.
• DSF outperforms centralized schemes when
  approximating.
• Sink neighbors burdened in WR (sink rotation is
  essential).
• MAC coordination of DSF transmissions not
  studied.
• In-network aggregation potentially better than WR
  DSF.

21
Concluding Remarks

• DSF offers a novel distributed algorithm to have
  all sensors converge to an ML solution.
• DSF energy usage beyond the call of duty is the
  unfortunate drawback, compared to tree-based
  schemes like WR.
• Conceivably DSF would behave better at high(er)
  link error rates, but the energy cost and
  uncertainty of convergence defeat its purpose.
• In-network data aggregation stands in the gray
  area between WR (centralized processing) and DSF
  (completely distributed) and deserves our
  attention. (TODO)

22
CSNDSP 2006

• ?