Localization leads to improved distributed detection under non-smooth distributions

We consider a detection network of sensors that measure intensity levels due to a source amidst background inside a two-dimensional monitoring area. The source intensity decays away from it possibly in discrete jumps, and the corresponding sensor measurements could be random due to the nature of source and background, or due to sensor errors, or both. The detection problem is to infer the presence of a source based on sensor measurements. In the conventional decision/detection fusion approach, detection decisions are made at the individual sensors using Sequential Probability Ratio Test (SPRT), and are combined at the fusion center using a Boolean fusion rule. We show that better detection can be achieved by utilizing sensor measurements at the fusion center, by first localizing the source and then utilizing a more effective SPRT. This approach leads to the detection performance superior to any Boolean detection fuser, under fairly general conditions: (i) smooth and non-smooth source intensity functions and probability ratios, and (ii) a minimum packing number of the state-space. We apply this method to improve the detection of (a) low-level point radiation sources amidst background radiation under strong shielding conditions, and (b) the well-studied Gaussian source amidst Gaussian background.