On a CPD Decomposition of a Multi-Variate Gaussian

Tensor decomposition based sensor data fusion is a novel field of numerical solutions to the Bayesian filtering problem. Due to the exponential growth of high dimensional tensors, this approach has not got much attention in the past. This has changed with the rise of efficient decomposition algorithms such as the 'Canonical Polyadic Decomposition' (CPD), which allow a compact representation of the precise, discretized information in the state space. As solutions of the prediction-filtering cycle were developed, it usually is assumed that a decomposition of the likelihood or the initial prior is available. In this paper, we propose a numerical method to compute the CPD form of a multivariate Gaussian, either a likelihood or a prior, in terms of an analytical solution in combination with the Taylor approximation of the pointwise tensor exponential.