An Introduction to Non-linear State Estimation and Target Tracking Based on Tensor Decompositions

The increasing trend towards connected sensors (“internet of things” and “ubiquitous computing”) derives a demand for powerful non-linear estimation methodologies. Conventionally, algorithmic solutions in the field of Bayesian data fusion and target tracking are based on either a Gaussian (mixture) or a particle representation of the prior and posterior density functions (pdf). The discrete filters reduce the state space to a fixed grid and represents the pdf in terms of an array of function values in high to extraordinary high dimensions. Due to the “curse of dimensionality”, data compression techniques such as tensor decompositions have to be applied. Though those methods are computationally burdensome, their advantage is the precise information processing and the ability to model all kinds of stochastic behaviour. In this tutorial, the basic methods for a Bayes formalism in discrete state spaces is explained. Possible solutions to the tensor decomposition (and composition) process are presented. Algorithms will be provided for each solution. The list of topics includes: Short introduction to target tracking and non-linear state estimation, discrete pdfs, Bayes recursion on those, PARAFAC/CANDECOMP Decomposition (CPD), Tucker and Hierarchical Tucker decomposition.