Classifier design for decentralised sensing with digital communication

We consider the problem of classifying the operating mode of a plant, using distributed sensors and a digital channel. The abstract problem is formulated using simplifications, where the plant only has two modes, the sensors have independent and identically distributed (but possibly mode-dependent) measurement noise, and a noise-less digital communication channel. The objective is to design a combined distributed digitisation (quantisation) and centralised classification strategy that maximises accuracy while observing n messages, each of which can take k unique values. Even in this simplistic scenario, our analysis shows that (i) the optimal decision boundaries even in the fully observable (analog) case depend strongly on the assumptions about measurement noise, (ii) as a result, the classification strategy selection is non-trivial, and (iii) the distributed quantisation algorithm design also has a strong influence on the final classification accuracy. We support the analytical arguments by empirical simulation experiments.