A new approach of decentralized detection

The problem of decentralized detection appears when various sensors are used simultaneously. In the centralized vision all the information arriving at each sensor is sent to the fusion center, while in the decentralized a local processing is realized and the global procedure needs a fusion of the signals coming from the sensors. The authors study the problem by imposing two constraints: the first is that the local procedure reduces the information to a scalar quantity and the second is that the fusion rule is only an addition of the signals coming from each sensor. With these constraints, the problem can be stated in a geometrical context. Using the projection theorem, the authors state the general equation giving the local optimum procedure. This equation is very difficult to solve. The results in some particular cases, for example when the noise at each of the sensors are independent, are presented