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A Brief Review of Theory for Information Fusion in Sensor Networks

A Brief Review of Theory for Information Fusion in Sensor Networks. Xiaoling Wang February 19, 2004. What is Information Fusion.

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A Brief Review of Theory for Information Fusion in Sensor Networks

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  1. A Brief Review of Theory for Information Fusion in Sensor Networks Xiaoling Wang February 19, 2004

  2. What is Information Fusion • “Information Fusion, encompasses the theory, techniques and tools conceived and employed for exploiting the synergy in the information acquired from multiple sources (sensors, databases, information gathered by human, etc.) such that the resulting decision or action is in some sense better than (qualitatively or quantitatively, in terms of accuracy, robustness and etc.) than would be possible if any of these sources were used individually without such synergy exploitation.” - Belur V. Dasarathy, Ph.D.

  3. Methods and Applications • Generally, information fusion methods includes: • Data fusion • Decision fusion • Topics of interest: • Sensor fusion • Classifier fusion

  4. Representation of information from different sources • Point estimates • Corresponding to the definition of concrete sensor • Interval estimates – to achieve fault tolerance • Corresponding to the definition of abstract sensor Physical value

  5. Information Fusion Hierarchy for Target Classification in Sensor Networks Balance redundancy & efficiency Multi-sensor Fusion Mobile Agent Framework Mobile Agent Framework …… Multi-modality Fusion Multi-modality Fusion Temporal Fusion Temporal Fusion Temporal Fusion Temporal Fusion … … Local Processing Local Processing Local Processing Local Processing sensor sensor sensor sensor node x node y

  6. Enabling Algorithms • Temporal fusion • Majority voting • Multi-modality fusion (acoustic + seismic) • Behavior-knowledge space (BKS) method • Multi-sensor fusion • Multi-resolution integration (MRI) method

  7. Temporal Fusion – Majority Voting • Objective: to reduce noise and to deal with signal non-stationarity • Majority voting – weighted average function • Consider each classifier has a function where j – classifier i - class - true class discriminant function - noise function, zero mean

  8. Multi-modality Fusion • Objective: to employ complementary aspects in the feature space • Treat results from multiple modalities as classifiers – classifier fusion • Majority voting won’t work • BKS method

  9. Assumption: - 2 classifiers - 3 kinds of targets - 100 samples in the training set Then: - 9 possible classification combinations c1, c2 samples from each class fused result 1,1 10/3/3 1 1,2 3/0/6 3 1,3 5/4/5 1,3 … 3,3 0/0/6 3 BKS Method

  10. Multi-sensor Fusion • Objective: to combine the results from spatially distributed sensors • Two main points: • reliability • robustness - fault tolerance • Given signal inaccuracy, uncertainty, and sensor fault, interval integration methods are used in sensor fusion • Marzullo, 1990 • Multi-resolution integration (MRI) algorithm

  11. Fault Tolerant Sensor Fusion • Fault tolerance concerns: • how many component failures a sensor network can tolerate and still be reliable • how to separate the output of correct functioning component from that of defective component • To solve the first question • Byzantine generals problem • N >= 3f+1 • To solve the second question • Definition: abstract sensor, interval integration

  12. Byzantine Generals Problem • Problem description • Commander-in-chief <-> messengers <-> generals • This problem is directly applicable to distributed sensor fusion • This problem can be solved only if the number of traitors is less than one third of the total number of processing elements • Every processing element must be connected directly to at least 2f+1 other processing elements

  13. BGP Example 1 attack attack Node 2 faulty 3 2 retreat Node 1 faulty 1 attack retreat 3 2 retreat

  14. Mathematical Formulation for Marzullo’s Method Interval output of sensor j Characteristic function Overlap function Characteristic function of the set of all points lying in (n-f) or more intersections of the intervals Fused result interval

  15. MRI Interval Fusion Method – An Example 4th node 1st node [0.08 0.16] [0.08 0.16] [0.51 0.60] [0.10 0.29] [0.46 0.65] [0.10 0.21] 2nd node [0.05 0.14] [0.05 0.41] [0.22 0.58] 3rd node [0.05 0.15] [0.05 0.15] [0.49 0.59]

  16. Integration Results 1st node 2nd node 3rd node 4th node

  17. Class 1 Class 2 … Class n k=5 3/5 2/5 … 0 k=6 2/6 3/6 … 1/6 … … … … … k=15 10/15 4/15 … 1/15 {2/6, 10/15} {4/15, 3/6} … {0, 1/6} confidence level confidence range largest in this column smallest Interval Generation • Generation of local confidence ranges (At each node i, use kNN for each k{5,…,15})

  18. Reference • K. Marzullo, “Tolerating failures of continuous-valued sensors”, ACM Transactions on Computer Systems, 8(4), 1990 • L. Prasad, S. S. Iyengar, R. L. Kashyap, R. N. Madan, “Functional characterization of fault tolerant integration in distributed sensor networks”, IEEE Transactions on Systems, Man, and Cybernetics, 21(5), 1991 • L. Prasad, S. S. Iyengar, R. L. Rao, “Fault-tolerant sensor integration using multiresolution decomposition”, Physical Review E, 49(4), 1994 • R. R. Brooks, S. S. Iyengar, “Robust distributed computing and sensing algorithm”, IEEE Computer, June, 1996

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