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