On fusion of probability density functions using tensor train decomposition

Abstract

Non-linear filters consider probability density functions in various non-parametric representations. They often suffer from the curse of dimensionality. Computation of weights over a grid of points becomes infeasible even for low dimensions. Filters processing data produced in different sensor nodes provide their own probability densities. Combination of such densities is desired. A favourite paradigm is to construct a fused density as a weighted arithmetic or geometric mean of the individual densities. This paper prospects the fusion for tensor train representation of densities produced by point-mass filters. In this representation, the weights are neither evaluated for a whole grid nor fully stored in the memory of the filters. Aspects of tensor-train-based fusion are discussed, such as computation of auxiliary characteristics and experience with numerical examples.