Exploiting Linear Substructure In LRKFs (Extended)

TL;DR

This paper leverages linear substructure in LRKFs to simplify moment matching, achieving significant computational speedups without sacrificing estimation accuracy in partially linear models.

Contribution

It introduces a method to exploit linear substructure in LRKFs, reducing computational complexity while maintaining accuracy, applicable to any symmetrical LRKF.

Findings

Significant computational speedups demonstrated

Applicable to any symmetrical LRKF

Reductions depend on cubature rule and state linearity

Abstract

We exploit knowledge of linear substructure in the linear-regression Kalman filters (LRKFs) to simplify the problem of moment matching. The theoretical results yield quantifiable and significant computational speedups at no cost of estimation accuracy, assuming partially linear estimation models. The results apply to any symmetrical LRKF, and reductions in computational complexity are stated as a function of the cubature rule, the number of linear and nonlinear states in the estimation model respectively. The implications for the filtering problem are illustrated by numerical examples.