This chapter investigates distributed detection of a phenomenon of interest (POI) via decision fusion in wireless sensor networks (WSNs). The decisions are collected by a fusion center (FC), which is in charge of performing a more accurate global decision. So as to account for a realistic scenario, it is assumed that the POI presents a signature with limited spatial extent, and its exact location and emitted amplitude (or energy) are not known. More specifically, when the POI is present, the sensors observe a signal with an attenuation depending on the distance between the sensor and the (unknown) target position, embedded in Gaussian noise. The unavailability of a completely specified model defeats the applicability of the well-known (optimal) likelihood-ratio (LR) test (LRT). As a consequence, in the general case, the FC is usually in charge of solving a composite hypothesis test and the generalized LRT (GLRT) is commonly employed. Unfortunately, in these scenarios, its complexity is typically high. Accordingly, the present chapter discusses the development of generalized score tests as alternatives with reduced computational complexity. After a brief recall of the GLRT for the considered problems, fusion rules corresponding to generalized versions of well-known score tests are introduced, based on Davies'framework, since the resulting problems include nuisance parameters only under the POI-present hypothesis. The focus is on two relevant signal models, i.e., the cases of random and deterministic unknown signals, leading to one-sided and two-sided testing, respectively. Finally, a convincing (semi-theoretical) rationale for threshold-optimization is presented and analyzed.

Chapter Contents:

• 1.1 Uncertainty in decision fusion sensing model
• 1.2 Problem statement
• 1.2.1 Sensing model
• 1.2.2 Local processing and reporting
• 1.2.3 Resulting hypothesis testing
• 1.2.4 Background on clairvoyant LLR
• 1.3 Design of generalized score tests
• 1.3.1 Counting rule (CR) and GLRT
• 1.3.2 Generalized score tests
• 1.3.3 Computational complexity
• 1.4 Quantizer design
• 1.5 Conclusions and further reading
• A.1 Appendix: Sketch of generalized score tests derivation
• References

Inspec keywords: wireless sensor networks; maximum likelihood estimation; signal detection; Gaussian noise; statistical testing; sensor fusion; computational complexity

Other keywords: likelihood-ratio test; Gaussian noise; threshold-optimization; fusion center; Davies framework; GLRT; relevant signal models; composite hypothesis test; wireless sensor networks; semitheoretical rationale; two-sided testing; accurate global decision; deterministic unknown signals; fusion rules; POI-present hypothesis; generalized score tests; computational complexity; decision fusion; sensing model uncertainty; generalized LRT; nuisance parameters; one-sided testing

Subjects: Other topics in statistics; Wireless sensor networks; Signal detection