Nonlinear fusion of multi-dimensional densities in joint state space

Nonlinear fusion of multi-dimensional random variables is an important application of Bayesian estimation. In the approach proposed here, a joint density over all considered densities is approximated by means of a Dirac mixture density by partitioning the joint state space into regions that are represented by single Dirac components. This approximation procedure depends on the nonlinear fusion model and only areas relevant to this model are considered. The processing in joint state space has advantages, especially when fusing Dirac mixture densities. Within this approach, degeneration can be avoided and even densities without mutual support can be combined. Thus, this approach gives an alternative to multiplication of Dirac mixtures with a likelihood, as used in the particle filter. Furthermore, a nonlinear Bayesian estimator with filter and prediction step can be formulated, which is able to cope with both discrete and continuous densities.