SCALABLE INFORMATION-DRIVEN SENSOR QUERYING AND ROUTING FOR AD HOC HETEROGENEOUS SENSOR NETWORKS

1. SCALABLE INFORMATION-DRIVENSENSOR QUERYING AND ROUTINGFOR AD HOC HETEROGENEOUSSENSOR NETWORKS Paper By: Maurice Chu , Horst Haussecker , Feng Zhao Presented By: D.M. Rasanjalee Himali

2. INTRODUCTION • Problem addressed: • How to dynamically query sensors and route data in a network so that information gain is maximized while latency and bandwidth consumption is minimized • Approach: • information driven sensor querying (IDSQ) • optimize sensor selection and • constrained anisotropic diffusion routing (CADR) • direct data routing and • incrementally combine sensor measurements so as to minimize an overall cost function.

3. INTRODUCTION • Use information utility measures to optimize sensor selection • Use incremental belief update • Each node can : • evaluate an information/cost objective, • make a decision, • update its belief state, and • route data based on the local information/cost gradient and end-user requirement.

4. SENSING MODEL AND MEASURE OF UNCERTAINTY • uses standard estimation theory. • zi(t): The time-dependent measurement of sensor i • λi(t):sensor i characteristics, • x(t): unknown target position • h: possibly non-linear function depending on x(t) and parameterized by λi(t). • Characteristics of λi(t) about sensor i: • Sensing modality (type of sensor i ) • Sensor position xi, • Noise model of sensor i • Node power reserve of sensor i

5. SENSING MODEL AND MEASURE OF UNCERTAINTY • BELIEF: • Is a representation of the current a posteriori distribution of x given measurements z1, ..., zN • Typically, the expected value of this distribution is considered to be the estimate: • Residual uncertainty is approximated by the covariance:

6. SENSING MODEL AND MEASURE OF UNCERTAINTY • knowledge of the measurement value zi and sensor characteristics λi normally resides only in sensor i. • To compute the belief based on measurements from several sensors, we must pay a cost for communicating that information.

7. SENSING MODEL AND MEASURE OF UNCERTAINTY • Incorporating measurements into the belief are now assigned costs • Therefore, should intelligently choose a subset of sensor measurements which: • provide “good” information for constructing a belief state and • minimize the communication cost of sensor measurements • Information Content of sensor i: • a measure of the information a sensor measurement can provide to a belief state.

8. SENSOR SELECTION • Given the current belief state, need to incrementally update the belief by incorporating measurements of previously not considered sensors. • However, among all available sensors in the network, not all provide useful information that improves the estimate. • Furthermore, some information might be useful, but redundant. • The task is to select an optimal subset and to decide on an optimal order of how to incorporate these measurements into our belief update. This provides a faster reduction in estimation uncertainty

9. SENSOR SELECTION • Assume there are N sensors labeled from 1 to N and the corresponding measured values of the sensors are {zi}. 1<=i<=N • Let U ⊂ {1, ...,N} be the set of sensors whose measurements have been incorporated into the belief. • The current belief is:

10. SENSOR SELECTION • Information utility function • The sensor selection task is to choose a sensor which has not been incorporated into the belief yet which provides the most information • Def (Information Utility): •  acts on the class P(Rd) of all probability distributions on Rd and returns a real number with d being the dimension of x.

11. SENSOR SELECTION •  assign a value to each element p ∈ P(Rd) which indicates how spread out or uncertain the distribution p is. • Smaller values represent a more spread out distribution while larger values represent a tighter distribution.

12. SENSOR SELECTION • Incorporating a measurement zj, where j∉U, into the current belief state p (x|{zi} i∈U) is accomplished by further conditioning the belief with the new measurement. • Hence, the new belief state is

13. SENSOR SELECTION • Incorporating a measurement zjhas the effect of mapping an element of P(Rd) to another element of P(Rd). • Since ψ gives a measure of how “tight” a distribution in P(Rd) is, it is clear that the best sensor j∈A={1, ...,N}−U to choose is

14. SENSOR SELECTION • However, in practice, we only have knowledge of h and λi to determine which sensor to choose. • We don't know the measurement value zjbefore it is being sent. • Nevertheless, we wish to select the “most likely” best sensor. • Hence, it is necessary to marginalize out the particular value of zj.

15. SENSOR SELECTION • For any given value of zjfor sensor j, we get a particular value for ψ acting on the new belief state p(x|{Zi} i∈U {Zj}) • For each sensor j, consider the set of all values of ψ( ) for choices of zj: • Best average case • Maximizing worst case • Maximizing best case

16. INFORMATION UTILITY MEASURES • To quantify the information gain provided by a sensor measurement, it is necessary to define a measure of information utility. • The intuition: • information content is inversely related to the “size” of the high probability uncertainty region of the estimate of x. • Ex: • Covariance-Based • Fisher Information Matrix • Entropy of Estimation Uncertainty • Volume of High Probability Region

17. INFORMATION UTILITY MEASURES • Covariance-Based • Used in the simplest case of a uni-modal posterior distribution that can be approximated by a Gaussian • Derive utility measures based on the covariance Σ of the distribution px(X). • The determinant det(Σ) is proportional to the volume of the rectangular region enclosing the covariance ellipsoid. • Hence, the information utility function for this approximation can be chosen as:

18. INFORMATION UTILITY MEASURES • Entropy of Estimation Uncertainty • If the distribution of the estimate is highly non-Gaussian, then the covariance Σ is a poor statistic of the uncertainty. • One possible utility measure is the information-theoretic notion of information: • the entropy of a random variable. • the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable

19. INFORMATION UTILITY MEASURES • For a discrete random variable X taking values in a finite set S, the Shannon entropy H(X) is defined to be: • Entropy is a measure of uncertainty which is inversely proportional to our notion of information utility. • Thus we can define the information utility as:

20. COMPOSITE OBJECTIVE FUNCTION • Up till now, we have ignored : • the communication cost of transmitting information across the network, and • which sensor actually holds the current belief. • Leader Node: • sensor, l, which holds the current belief

21. COMPOSITE OBJECTIVE FUNCTION • Leader node might act as a relay station to the user, • the belief resides at this node for an extended time interval • all information has to travel to this leader. • Another scenario: • the belief itself travels through the network, and • nodes are dynamically assigned as leaders. • Depending on the network architecture and the measurement task, both or a mixture of both cases can be implemented.

22. COMPOSITE OBJECTIVE FUNCTION • Assume that : • The leader node temporarily holds the belief state and • Information has to travel a certain distance through the network to be incorporated into the belief state.

23. COMPOSITE OBJECTIVE FUNCTION • The objective function for sensor querying and routing is a function of both: • information utility and • cost of bandwidth and latency.

24. COMPOSITE OBJECTIVE FUNCTION • This can be expressed by a composite objective function, Mc, of the form: • where • ψ = Mu(p(X|{zi},i∈U), λj) • Ma = the cost of the bandwidth, and latency of communicating information between sensor j and sensor l • :The tradeoff parameter ∈[0,1] balances the contribution from the two terms

25. COMPOSITE OBJECTIVE FUNCTION • The objective is to maximize Mc by selecting a sensor j from the remaining sensors A={1, ...,N}−U by:

26. INFORMATION-DRIVEN SENSORQUERY • A sensor selection algorithm based on the cluster leader type of distributed processing protocol • Assume we have a cluster of N sensors each labelled by a unique integer in {1, ..., N}. A priori, each sensor i only has knowledge of its own position xi ∈R2

27. Select cluster leader Activate if a target is present in sensor cluster

28. Test Results • Apply the sensor selection algorithm to the problem of spatial localization of a stationary target based on amplitude measurements from a network of sensors. • Sensor Selection • Nearest Neighbor Data Diffusion • Mahalanobis distance • Maximum likelihood • Best Feasible Region

30. Test Results