On Statistics based Prediction of Decomposed 1–6 Tensor Probability Density Functions

In this paper a novel prediction for tensor decomposition based probability density functions is presented. Tensor representations for target tracking have various advantages such as that arbitrary (non-Gaussian) densities and non-linear models can be used, resulting in densities, which represent the knowlege on a state conditioned on sensor data with high accuracy. By using tensor decompositions such as the Canonical Polyadic Decomposition, the curse of dimensionality can be circumvented by some degree. The prediction of such decomposed tensors is obtained by solving the Fokker-Planck Equation, which is a partial differential equation parametrized by the used state evolution model. Since this can be computationally very demanding, an approximate solution is presented based on the statistics of the velocity components. The presented approach can well be extended for higer order models. A numerical evaluation shows that the method is robust and precise.