5. Sensor Tasking and Control

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5. Sensor Tasking and Control

• Nodes must be carefully tasked to perform the
  given task while consuming few resources (e.g.,
  power, bandwidth)
• E.g., To detect and track a vehicle, a camera may
  be tasked to anticipate and follow it
• To achieve scalability and autonomy, sensor
  tasking and control must be done
• in a distributed way
• mostly with local info
• For a given task, as more sensors participate and
  more data is collected,
• the total utility of the data (e.g., info
  content) generally increases

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• But, as nodes are added, resource use (cost)
  increases and increment in benefit decreases
• Fig. 5.1 Diminishing marginal returns

• To address balance between utility and cost,
  introduce a utility-cost-based approach to SN
  management
• This chapter introduces topics in the context of
  localization and tracking tasks
• But info-based sensor tasking applies to more
  general sensing tasks

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• Chapter outline
• 5.1 General issues of task-driven sensing
• 5.2 Generic model of utility and cost
• 5.3 Main ideas of info-based sensor tasking and
• a specific realization in info-driven sensor
  querying (IDSQ)
• a cluster-leader based protocol where info about
  a phenomenon resides at a fixed leader for an
  extended period
• 5.4 Dynamic migration of info within a SN
  (e.g., tracking a moving object)
• Issues
• Info hand-off
• Greedy vs. multistep lookahead info routing
• Maintenance of collaborative processing sensor
  groups

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5.1 Task-Driven Sensing

• A naïve view of the purpose of a sensor system is
  to gather all we can and centrally aggregate and
  analyze it
• Too expensive
• Be selective in
• what sensor nodes to activate
• what info to communicate
• When the relevant manifest variables (defining
  the world state, e.g., target position and
  identity) are known,
• computing answers to queries about the world
  state is a standard algorithm design problem

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• But classical algorithm-complexity view must be
  changed in SN context
• Values of relevant manifest variables arent
  known but sensed
• Cost of sensing variables relations of the same
  type can vary greatly
• Variable values or relations may be impossible to
  determine with available resources
• But alternate variable values or relations may
  suffice
• Need a mathematical theory of algorithm design
  that includes cost of
• accessing the manifest variables of a problem or
• determining useful atomic relations among
  variable values
• In advance, costs can only be estimated
• Some values and relations may already be known by
  the SN and available at low cost
• Both push and pull info flow

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• Key questions for an overall strategy
• What are the important objects to sense?
• What object parameters are most relevant?
• What object relations are critical to the
  high-level info needed?
• Whats the best sensor for acquiring a given
  parameter?
• How many sensing and communication operations are
  needed to do the task?
• How coordinated must the sensors world models
  be?
• At what level (from signal to symbol) is info
  communicated ?
• Online nature of sensing requires sensor utility
  measures
• Sensor readings cant be known before theyre
  made

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5.2 Roles of Sensor Nodes and Utilities

• Sensors may take on different rolesFig. 5.2(a)
  chemical plant, sensors detecting toxic chemicals

• Data can be transmitted mulithop to the base
  station/gateway
• Toxicity detections may be aggregated at
  intermediate nodes
• A sensor takes on a role depending on the task
  requirement and resource availability

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• Fig. 5.2(b) Some nodes sense (S), route (R), do
  both (SR), or are idle (I)

• As conditions (e.g., energy reserve) change,
  roles change
• To study the role a sensor should play, introduce
  utility and cost models of sensors
• Develop techniques to (nearly) optimize
  assignments

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• A utility function assigns a (scalar) utility to
  each reading of a node
• U I ? T ? R
• where I 1, , K are sensor indices, T is the
  time domain
• Costs unit costs per datum/packet (assuming
  operation data thus encapsulated)
• Sensing operation cost Cs
• Aggregation cost Ca
• Reception cost Cr
• Assume, within a given period, transmissions
  receptions
• At time t,
• Vs (t ) sensing nodes
• Va (t ) aggregating nodes
• Vt (t ) transmitting nodes
• Vr (t ) receiving nodes

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• Recall the general constrained optimization
  problem (Chap. 2)
• ?G, T, W, Q, J, C ?
• G SN ?V, E, PV, PE ?
• V nodes
• E network edges, ? V ? V
• PV set of functions characterizing properties of
  each v ? V (location, energy reserve, etc.)
• PE set of functions characterizing properties of
  each e ? E (capacity, quality, etc.)
• T set of targets (specified by location, shape,
  signal source type)
• W model for how target signals propagate and
  attenuate
• Q set of user queries, specifying query
  instances and entry points
• J objective function, defined by task
  requirements
• C (C1, C2, specifies a set of constraints

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• Sensor tasking problem as an instance of
  constrained optimization problem
• Determine sets Vs, Vt, Vr, Va maximizing the
  utility over a period of time
• s.t.
• The utility of the network depends on the
  underlying routing structure
• Assume
• The aggregate utility is a monotonic function of
  the participating nodes
• The outcome of the aggregation operation is
  independent of the order in which sensor readings
  are combined
• Thus, the routing structure is determined a
  priori (static)
• Not always a good assumption

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5.3 Information-Based Sensor Tracking

• Main idea base sensor selection on
• info content and
• resource consumption, latency, other costs
• Using info utility measures, network sensors
• exploit info content of data already received
• to optimize utility of future sensing and
  communication actions
• E.g., IDSQ formulates the sensor tasking problem
  as distributed constrained optimization that
• maximizes info gain
• minimizes communication and resource usage

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5.3.1 Sensor Selection

• For a localization or tracking problem, a belief
  is knowledge about a target state
• In a probabilistic framework, a probability
  distribn over the state space
• Two scenarios
• In localizing a stationary source (this section)
• A leader node acts as a relay station to the user
  
• The belief resides at it for an extended time
• All info must travel to it
• In tracking a moving source (next section, 2.4)
  ,
• The belief travels through the network
• Nodes are dynamically assigned as leaders
• Consider here a fixed leader protocol

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• Given the current belief state, incrementally
  update it by incorporating measurements from
  nearby sensors
• But not all available sensors provide useful info
• Some is even redundant
• Task Select an optimal subset and an optimal
  order of incorporating these measurements into
  the belief update
• Cant have explicit knowledge of measurements in
  other sensorsprohibitive communication costs
• Decision based only on
• known characteristics of sensors (e.g., position,
  sensing modality)
• predictions of their contributions (given the
  current belief about the monitored phenomenon)

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• Fig. 5.3 Basic idea of sensor selection
• Assume estimation uncertainty effectively
  approximated by a Gaussian dsitribnsee
  uncertainty ellipsoids in the state space
• Ellipsoid at t residual uncertainty in current
  belief state

• Ellipsoid at t1 belief after incorporating
  additional sensora or b
• Both cases reduce area of high uncertainty by the
  same percentage
• But the residual uncertainty in case a retains
  the largest principal axis
• Might thus favor b over a (depends on task)

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• Principles developed here cover
• selection of a remote sensor by a cluster-head
• decision of an individual sensor to contribute
  its data and to respond to a query traveling the
  network
• Task Select the sensor providing best info among
  all available sensors whose readings havent yet
  been incorporated
• Compared with blind or nearest-neighbor sensor
  selection, this
• gives faster reduction in estimation uncertainty
• usually has lower communication cost in meeting a
  given estimation accuracy requirement

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Example Localizing a Stationary Source

• Fig. 5.4 14 sensors in a square region, 13 along
  diagonal
• Illustrate sensor selection among 1-hop
  neighbors
• assume all sensors can communicate with center
  node (leader)
• Assume each sensors measurement gives an
  estimate of distance to target as an annular
  likelihood function (Chap. 2)

• Localization based on sequential Bayesian
  estimation (Chap. 2)
• Assumes independence of likelihood functions when
  conditioned on target state
• Graphically Product of annuli

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• Selection based on nearest-neighbor (NN)
  criterion
• Leader node (at center) selects nearest node
  among those whose measurements havent been
  incorporated
• Fig. 5.5 Sequence of posterior distrns as more
  sensors included
• Bimodal until sensor at upper-left included

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• Mahalanobis selection
• Favors sensors along the longer axis of the
  covariance fit of residual uncertainty in
  localization
• For 1st 3 measurements, agrees with NN
• Covariance fit of residual uncertainty now
  elongated
• So upper-left sensor selects
• Fig. 5.6 Residual uncertainties after
  incorporating 4th and 5th sensors

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5.3.2 IDSQ Information-Driven Sensor Querying

• Balance info contribution of individual sensors
  against cost of communicating with them
• Consider task of selecting among K sensors with
  measures zi, i 1, , K
• U ? 1, , K is the subset of sensors already
  contributing
• Current belief p(x zi, i ? U)
• Determine which sensors among the unincorporated
  ones A 1, , K U to use
• This for stationary targets
• For moving targets (5.4.3), same sensor may
  provide informative and uninformative
  measurements at different times

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• Info utility function
• ? P (R d ) ? R
• P (R d ) is the class of probability distrns on
  d-dimensional state space Rd for the target state
  x
• ?s value for p ? P (R d ) shows how spread out
  (uncertain) distrn p is
• Smaller values more spread out larger less
• Cost of getting a measurement
• ? R h ? R
• Rh h-dimensional measurement space (of
  measurement vectors)

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• Sensor l holding the current belief is the leader
  node
• Reformulate constrained optimization problem of
  sensor tasking as an unconstrained optimization
  problem
• Objective function (mixture of info utility and
  cost)
• J(p (x) zi, i ? (U ? j )
• ? ?(p (x zi, i ? (U ? j )) (1 - ?)
  ?(zj )
• ? info utility of incorporating measurement
  zj(t ) from sensor j ? A
• ? cost of communication and other resources
• ? relative weighting of utility and cost