information-driven routingrakl/class5540/sensors/information-driven.pdf · sensor selection...
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Information-driven Routing
© Dr. Deepak Ganesan, edited by Dr. Robert Akl
Deepak Ganesan (UMass)
What is information-driven routing? Combine routing and sensing
Route towards a node that can provide the bestimprovement in sensing estimate.
Combine traditional routing metrics… power, packet-loss, neighborlist, geography
with sensing metrics Maximum information gain Best estimate of target location or target track
Powerful Paradigm that can be described indifferent ways Aggregate along better routing paths Route towards nodes that provide better
aggregation.
Deepak Ganesan (UMass)
IDSQ: Whats new?
The use of general form of informationutility that models the informationcontent as well as the spatialconfiguration of a network in adistributed way
Generalization of routing in the sensethat both information gain andcommunication cost are used to directthe next hop to route to.
Deepak Ganesan (UMass)
Sensor selection for localization andtracking
Liu, Reich, and Zhao, 2003
Deepak Ganesan (UMass)
Sensing Modelzi (t) = h(x(t), λi (t)), (1)
x(t) is parameter to be estimated, λi (t) andzi (t) are characteristics and measurementof sensor i respectively.
for sensors measuring sound amplitude zi = a / || xi - x ||α/2 + wi , (4)
a is target amplitude, α is attenuationcoefficient , wi is Gaussian noise
Deepak Ganesan (UMass)
Define Belief as ...
representation of the current aposteriori distribution of x givenmeasurement z1, …, zN: p(x | z1, …,zN)
expectation is considered estimate µx = ∫ xp(x | z1, …, zN)dxCovariance approximates residual
uncertainty Σ = ∫ (x - µx)(x - µx)p(x | z1, …, zN)dx
Deepak Ganesan (UMass)
Sensor Selection (omniscient case)
j0 = argj∈A max ψ(p(x|{zi}i∈ U ∪{zj})) A = {1, …, N} - U is set of sensors
whose measurements not incorporatedinto belief
ν ψ is information utility function definedon the class of all probabilitydistributions of x
ν intuitively, select sensor j for queryingsuch that information utility function ofupdated distribution by zj is maximum
Deepak Ganesan (UMass)
Sensor Selection (in practice)
zj is unknown before it’s sent back So, how can you select the next sensor? Use information about the type of sensor and
current error distribution
Deepak Ganesan (UMass)
Sensor selection illustration
Grid representation of prior targetlocation PDF pprior(x) and sensor-data-converted target location PDF pi(x)
Grid representation of posterior targetlocation PDF pposterior(x) = c * pprior(x)* pi(x)
Deepak Ganesan (UMass)
Optimization criteria
Average case j0 = argj∈A max Ezj
[ψ(p(x|{zi}i∈ U ∪{zj}))]
Worst case j0 = argj∈A max minzj
ψ(p(x|{zi}i∈ U ∪{zj}))
Best case j0 = argj∈A max maxzj
ψ(p(x|{zi}i∈ U ∪{zj}))
Deepak Ganesan (UMass)
Information Utility Measures
covariance-basedψ(pX) = - det(Σ), ψ(pX) = - trace(Σ)
Fisher information matrixψ(pX) = - det(F(x)), ψ(pX) = -
trace(F(x)) entropy of estimation uncertaintyψ(pX) = - H(P), ψ(pX) = - h(pX)
Deepak Ganesan (UMass)
Information Utility Measures
volume of high probability regionΓβ = {x∈S : p(x) ≥ β}, chose β so that Γβ = γ,γ is given
ψ(pX) = - vol(Γβ)sensor geometry based measuresin cases utility is function of sensor location
onlyψ(pX) = - (xi-x0)Σ-1(xi-x0), where x0 is
current estimate of target locationalso called Mahalanobis distance
Deepak Ganesan (UMass)
Composite Objective Function
Mc(λl, λj, p(x|{zi}i∈ U)= γMu(p(x|{zi}i∈ U, λj) – (1 - γ)Ma(λl, λj)
Mu is information utility measure Ma is communication cost measureν γ ∈ [0, 1] balances their contributionsν λl is characteristics of current sensor l
j0 = argj∈A max Mc(λl, λj, p(x|{zi}i∈ U)
Deepak Ganesan (UMass)
Incremental Update of Belief
p(x | z1, …, zN)= c p(x | z1, …, zN-1) p(zN | x)
zN is the new measurementp(x | z1, …, zN-1) is previous belifep(x | z1, …, zN) is updated beliefc is normalizing constant
for linear system with Gaussiandistribution, Kalman filter is used
Deepak Ganesan (UMass)
IDSQ Algorithm
Deepak Ganesan (UMass)
CADR Algorithm
with global knowledge of sensorpositions
optimal position to route query to isgiven by
xo = argx [∇Mc = 0] (10)
ο What if Mc has multiple localmax/min?
Deepak Ganesan (UMass)CADR Algorithm- no global knowledge of sensor position
1. j0 = argj max(Mc(xi)), ∀j ≠k 2. j0 = argj max((∇Mc)T(xi-xk) /
(|∇Mc||xi-xk|)), ∀j ≠k 3. instead of following ∇Mc only,
followd = β∇Mc + (1 - β)(xo - xk), ∀j ≠kfor large distance to xo, follow ∇Mc
for small distance to xo, follow (xo - xk)
Deepak Ganesan (UMass)
IDSQ Experiments- Sensor Selection Criteria
A. nearest neighbor data diffusionj0 = argj∈{1, …, N}-U min||xl-xj|| B. Mahalanobis distancej0 = argj∈{1, …, N}-U min(xi-x0)Σ-1(xi-x0)
C. maximum likelihoodj0 = argj∈{1, …, N}-U minp(xi|θ)
D. best feasible region, upper bound
Deepak Ganesan (UMass)CADR Experiments
Mc = γMu– (1 - γ)Ma
ν γ = 1
Figure12-1
Deepak Ganesan (UMass)
Belief Representation
Parametric, where each distribution isdescribed by a set of parameters,poor quality but light-weighted
Non-parametric, where eachdistribution is approximated by pointsamples, more accurate but morecostly
Deepak Ganesan (UMass)
Conclusion
composite objective function includesboth information utility andcommunication cost
two novel techniques: IDSQ, CADR tradeoff between information gain
anddetection latency/bandwidth
consumption