Design of Unitless Normalized Measure of Nonlinearity for State Estimation

TL;DR

This paper introduces a new, unitless, and normalized measure of nonlinearity for state estimation, addressing limitations of existing measures and demonstrated through numerical tracking experiments.

Contribution

It proposes a novel nonlinearity measure that is both unitless and normalized, improving assessment accuracy in state estimation.

Findings

The new measure is demonstrated to be effective in numerical tracking experiments.

It overcomes the unit selection issues of previous measures.

The measure provides a reliable indicator of nonlinearity effects.

Abstract

The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or parameters, or iii) to indicate the possible effect of strong nonlinearity that leads to estimate credibility loss. This paper summarizes the state of the art of nonlinearity measures, focusing on the mean-square-error-based measure of nonlinearity. Its weak point related to unit selection is illustrated, and based on this, requirements for a new measure of nonlinearity are formulated. A new nonlinearity measure that is both unitless and normalized is designed. Its properties are demonstrated using numerical tracking experiments.