Generalized score-tests for decision fusion with sensing model uncertainty

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