Tensor Train Discrete Grid-Based Filters: Breaking the Curse of Dimensionality

TL;DR

This paper introduces tensor-train decompositions to enhance grid-based filtering for stochastic systems, significantly reducing computational and storage costs while maintaining accuracy, supported by algorithms and numerical tests.

Contribution

It demonstrates that tensor-train decompositions can effectively break the curse of dimensionality in grid-based filters, offering a scalable solution.

Findings

Significant reduction in computational complexity

Lower storage requirements for high-dimensional filters

Maintained accuracy in state estimation

Abstract

This paper deals with the state estimation of stochastic systems and examines the possible employment of tensor decompositions in grid-based filtering routines, in particular, the tensor-train decomposition. The aim is to show that these techniques can lead to a massive reduction in both the computational and storage complexity of grid-based filtering algorithms without considerable tradeoffs in accuracy. This claim is supported by an algorithm descriptions and numerical illustrations.