Unified nonparametric data fusion

In several recent papers we demonstrated that classical single-sensor, single-source statistics can be directly extended to the multisensor, multisource case. The basis for this generalization is the finite random set, together with a set of direct parallels between random-set and random- vector theories which allow familiar statistical techniques to be directly transferred to data fusion problems. We previously showed that parametric point estimation theory can be thus generalized, resulting in fully integrated data fusion algorithms. However, parametric estimation is not appropriate when sensor noise distributions are poorly known. Also, since most data fusion algorithms are partially ad hoc constructions it is difficult to determine the overall statistical behavior of such algorithms even if the statistics of the sensors are well understood. This paper shows how a standard nonparametric estimation technique, the projection kernel approach to estimating unknown probability distributions, can be extended directly to the data fusion realm.