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

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.

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

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

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

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

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 wherej – classifier i - class - true class discriminant function - noise function, zero mean

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

BKS Method Assumption: - 2 classifiers - 3 kinds of targets samples in the training set Then: - 9 possible classification combinations c 1, c 2 samples from each classfused result 1,110/3/31 1,23/0/63 1,35/4/51,3 … 3,30/0/63

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

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

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

BGP Example 1 23 attack Node 2 faulty retreat 1 23 attackretreat Node 1 faulty retreat

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

MRI Interval Fusion Method – An Example [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] 1 st node 2 nd node 3 rd node 4 th node

Integration Results 1 st node 2 nd node 3 rd node4 th node

Interval Generation Generation of local confidence ranges (At each node i, use kNN for each k  {5,…,15}) confidence range confidence level smallest largest in this column 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}

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